# Deep Learning-Based Speech and Vision Synthesis to Improve Phishing Attack
Detection through a Multi-layer Adaptive Framework
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1st Tosin Ige  Dept. of Computer Science
The University of Texas at El Paso
Texas, USA
<EMAIL_ADDRESS>2nd Christopher Kiekintveld  Dept. of Computer Science
The University of Texas at El Paso
Texas, USA
<EMAIL_ADDRESS>3rd Aritran Piplai  Dept. of Computer Science
The University of Texas at El Paso
Texas, USA
<EMAIL_ADDRESS>
###### Abstract

The ever-evolving ways attacker continues to improve their phishing techniques
to bypass existing state-of-the-art phishing detection methods pose a mountain
of challenges to researchers in both industry and academia research due to the
inability of current approaches to detect complex phishing attack. Thus,
current anti-phishing methods remain vulnerable to complex phishing because of
the increasingly sophistication tactics adopted by attacker coupled with the
rate at which new tactics are being developed to evade detection. In this
research, we proposed an adaptable framework that combines Deep learning and
Randon Forest to read images, synthesize speech from deep-fake videos, and
natural language processing at various predictions layered to significantly
increase the performance of machine learning models for phishing attack
detection. To validate both the effectiveness and adaptability of our proposed
framework in overcoming limitations in current approaches and its ability to
detect complex phishing site, we created 4 categories of phishing sites and
uploaded them to a secure server with a compromised DNS on a friendly URL; the
first was a text-only phishing site, image-only phishing site, video-only
phishing site, and a phishing site combining all the features. We use SEO
friendly URLs, and hacked legitimate DNS on the text-only phishing site, so
that they can evade detection at 1st layer until the 4th layer of the
framework where they were detected, we also created phishing sites where text
are in image only format, text-only, and video only format using deep-fake
video to test the adaptability of our proposed framework to different
scenarios of a sophisticated or complex phishing site, our proposed framework
successfully overcome limitations in existing approaches, significantly
improve phishing attack detection, and successfully detect complex phishing
webpages with multi-dimensional deep-fake videos, images, and texts.

###### Index Terms:

Phishing, Random Forest, Deep Learning, Recurrent Neural Network, Long Short-
Term Memory, Speech Synthesis, Vision Synthesis, Phishing Detection Framework,
Adaptive Framework

##  I Introduction

The insufficiency of traditional phishing detection methods such as user
education [27] and rule-based methods [13] against sophisticated phishing
attack techniques has led researchers to exploration of possible AI-based
solutions. While several machine learning-based models have been proposed, the
fact that attackers use advanced innovative methods that are continuously
changing to carry out phishing attacks renders previously proposed machine
learning models ineffective against sophisticated attacks [11]. Although tools
like PhishTank, and OpenPhish were created for the effective detection of
malicious Uniform Resource Locator (URL) the rate at which malicious websites
are created coupled with the sophistication of the deception method easily
overwhelm the system as phishing sites are being created every 11 seconds
according to dataprot 2023 phishing statistic report.

One of the common problems with the current ML model is the quality of the
dataset used for the training model which has a significant impact on both the
accuracy and overall performance of the model [30]. These data do not reflect
the ever-changing strategies through which attackers continue to fool existing
machine learning-based models to evade detection. In addition, the balancing
problem between human factors and model accuracy causes illegal flagging of
newly registered legitimate websites due to weak domain authority. Phishing
websites have a short life span as they are quickly taken down before
detection and another one is created, It is the rate at which an existing
phishing website is taken down after launching a campaign and the immediate
creation of a new phishing website [6] to begin another campaign coupled with
the ever-changing but sophisticated techniques that makes the problem very
potent and significant.

While several models and machine learning-based frameworks have been proposed,
the ever-evolving ways attacker increases the sophistication of phishing
attack to bypass existing state-of-the-art anti-phishing detection and
prevention systems pose a mountain of challenges leading to the relative
ineffectiveness of previously proposed models against a more complex phishing
attack. Thus, the constant evolvement and innovation in phishing techniques
adopted by attackers are the reason why current detection method remains
vulnerable to complex or more sophisticated forms of phishing due to their
reliability on [1, 5, 8], blacklists/whitelists [9], natural language
processing [15], visual similarity [15], rules [14],[24], remains vulnerable
to attack due to the following reasons;

  * •

Having understood how the machine learning-based model works, attackers are
now increasingly relying on asymmetrical methods by uploading images and
videos to evade detection under various pretexts, and none of the proposed
models can single-handedly be effective against such.

  * •

Very small or minute changes to the uniform Resource Locator (URL) of a
blacklisted URL will make the blacklist/ whitelist phishing detection method
fail. Also, the fact that there is no worldwide centralized database for
whitelisted or blacklisted URLs makes this method even more vulnerable, and so
if company X blacklisted my phishing URL on their internal server, I can try
it with company Y and be successful.

  * •

In machine learning phishing detection method that relies on relevant features
like URL, webpage content, website traffic, search engine, WHOIS record, and
Page Rank have their vulnerabilities because firstly, such classifier will
misclassify a phishing URL that is hosted on a hacked or compromised server as
benign leading to false negative, secondly using domain age as a feature to
train a model will always lead to higher false positive simply because the URL
of a newly registered legitimate company website will be misclassified. After
all, the domain name was recently registered, the page rank is zero, and with
low traffic, and thirdly the fact that parameters for those features are
gotten from a third-party website is another concern. What will happen if the
third-party website is having a downtime?

  * •

The issue with the visual similarity-based heuristic method which compares
both the pre-stored signature such as images, font styles, page layout,
screenshot, and so on of the new website with the old website will have
general difficulty in detecting anomalies in a newly hosted phishing site.

  * •

The fact that the majority of the existing machine learning models are trained
based on textual features such as “#”,”.”, Internet Protocol address, URL
Length, domain levels, and so on from the Uniform Resource Locator (URL) does
not help as any phisher or attacker with little web technologies can develop
what we called ”friendly URL” depending on the programming language adopted
whether JAVA, C#, Python, PHP or framework to avoid all those features. With a
friendly URL, such models are bound to misclassify leading to an increment in
false negative rate.

For any Machine learning-based phishing detection method to be effective in
real-time combat against phishing attacks, it must address each of the stated
reasons above for which existing state-of-the-art anti-phishing methods
continue to be vulnerable due to the increasingly sophisticated techniques by
which phishing attacks are being carried out. It is worth noting that past
research work on phishing attack detection had been largely based on
approaches, classification, etc. RASHA ZIENI et al.. [35] focus their review
on list-based, similarity-based, and machine learning-based categories of
approaches for phishing detection to identify pending research gap, Angad et
al.. [21] focus theirs on the advantages and limitations of existing
approaches to phishing detection, while also using discussion of related
application scenarios as guidance to propose a new method of anti-phishing
detection, Yifei Wang [32] categorizes widely used phishing detection methods
into seven categories and summarizes them. All previously proposed models,
approaches, and frameworks have common limitation, there limitation was that
they are either text-based or URL-based which makes it difficult for them to
detect complex phishing attack where the attacker uses deep-fake videos, deep-
fake images, textual-based images, or combination of any with traditional
textual content.

In this research, we first reviewed some of the most recent works on phishing
detection, and state-of-the-art algorithms from the past 5 years to
investigate the performance of state-of-the-art machine learning and deep
learning classifiers for phishing detection tasks, before proposing a multi-
layered adaptive framework that uses computer vision to read images on a
phishing webpage, and condense videos from a webpage to audio before
synthesizing the speech into a condensed text to increase detection of a
phishing attack. We use a combination of random forest algorithm and Long-
Short Term Memory (LSTM) at different layers of the framework for effective
coordination. The contributions of our research include the proposal of an
adaptive multi-layered framework that uses computer vision to read graphic
images, synthesize speech from uploaded videos, and natural language
processing at various predictions layered to significantly increase the
performance of machine learning-based models for phishing detection. Our
artifacts which consist of source code, dataset, images, videos, and audio
files for this research had been uploaded to a public GitHub repository for
reproducibility of our research. Artifact can be found on GitHub at;
Deep Learning-Based Speech and Vision Synthesis to Improve Phishing Attack
Detection through a Multi-layer Adaptive Framework and also at Code Ocean
computational research platform, with the exception of the internally
generated deep-fake video and audio data files for privacy.

##  II Related Work

###  II-A Natural Language Processing (NLP)

NLP-based models use existing relationships between sentences, words, or
letter parts of a language in a given text dataset. This made us explore the
possibility of synthesizing an uploaded video from a phishing webpage to feed
our neural network model. NLP architectures use modeling, preprocessing, and
feature extraction:

Data preprocessing: It is imperative for text in a given dataset to be
preprocessed into a pattern that the model can easily understand because
preprocessing effectively turns every character and word in the dataset into a
format that the machine learning classifier can understand to extract useful
patterns or learn from them. The fact that algorithms learn from data and the
quality of the dataset used in training an ML model directly impacts the
performance of that model making AI to be data-centric, and hence, priority is
given to data preprocessing during NLP.

NLP stemming and Lemmatization

$\begin{split}a&<b\\\ ab&<bc\\\ abc&>bcd\qquad\qquad\hbox
to0.0pt{\text{Lemma\leavevmode\nobreak\ \ref{lem:mylemma}}\hss}\\\
abcd&>bcde\end{split}$ (1)

Stemming and lemmatization are the two major data preprocessing tasks for
natural language processing. During stemming, there is an end-to-end iteration
of each word in the dataset to convert them to their base forms such as the
mapping of ”university” to ”univers”, and ”calamity” to ”calam” while
lemmatization uses the word’s morphology from vocabulary dictionary to find
their corresponding roots.

$[T_{i}=\begin{cases}1,&T\leq 1\\\ 1+\beta T,&T>1\end{cases},\text{ in which
}T=\begin{cases}T_{\mathrm{now}}-T_{\mathrm{last}},&T_{\mathrm{last}}\neq\mathrm{NULL}\\\
T_{\mathrm{now}}-T_{\mathrm{update}},&T_{\mathrm{last}}=\mathrm{NULL}\end{cases}]$
(2)

The final preprocessing stage of NLP is sentence segmentation, this process
breaks large text into linguistically meaningful sentences where trivial words
such as “an,” “the,” “a,” etc that don’t add much meaning or information to
the text are removed during stop word removal, next we use tokenization to
split every text into words and fragments, the result is a combination of word
index and tokenized text which could be represented by a numerical token
before feeding them to any of the deep learning or machine learning models for
prediction.

###  II-B Long Short-Term Memory (LSTM)

For this research, We opted for Long Short-Term Memory a variant of recurrent
neural network (RNN) because of its effective solution to vanishing and
exploding gradients which are Long-term dependency problems in Recurrent
Neural Networks. The most important functioning part of an LSTM network is the
cell state which serves as a memory to the network thereby enabling it to
remember the past. Hence their suitability for capturing long-term
dependencies and sequence prediction problems [3]. LSTM network has an input
gate, a forget gate, and an output gate which are sigmoid activation functions
with an output value of 0 or 1.

$-10$$-5$$5$$10$$0.2$$0.4$$0.6$$0.8$$1$$x$$y$

It was easy to use the sigmoid function as a gate because we are only given
out positive values that could give a straight answer on whether a particular
feature should be kept or discarded.

$\sigma$$\sigma$Tanh$\sigma$$\times$+$\times$$\times$Tanh$c^{\langle
t-1\rangle}$Cell$h^{\langle t-1\rangle}$Hidden Layer 1$x^{\langle
t\rangle}$Input$c^{\langle t\rangle}$Cell$h^{\langle t\rangle}$Hidden Layer
3$h^{\langle t\rangle}$Hidden Layer 2

In an LSTM network, the Input Gate tells what new information is to be stored
in the cell state, the forget gate gives clear instructions by telling what
information is to be thrown away from the cell state, while the output gate
gives activation to the output for more accurate prediction. It is during this
activation which occurs after filtering the cell state that the output goes
through the activation function where the output portion to be predicted is
determined, and this occurs when the current LSTM block goes through softmax
layer to predict value for the current block.

To mitigate the effect of phishing attack, several methods, frameworks had
been proposed for phishing attack detection but with varying results, these
methods are classified based on their different approaches which we classified
as Non-Machine Learning, machine learning (Bayesian-based, non-Bayesian-based)
and deep learning-based. As attackers continue to navigate potential
vulnerabilities to existing phishing detection solution, they are begining to
rely on several images and uploaded videos rather than traditional text to
enable them to evade detection, the inability of existing machine learning-
based model to detect such phishing site is a peculiar limitation to existing
AI-based solution. Palla Yaswanth and V. Nagaraju [33] used Huang and
Premaratne data from Kaggle repository with an equal number of phishing and
legitimate datasets for novel network of phishing predictions with an accuracy
of 95% for naive Bayes and 94.67% for random forest based on parameter
turning. During the comparison of the performances of naive Bayes [10] and
random forest for detection of phishing sites in a network, there was no
testing of the model against sophisticated form of phishing attack and causes
of the 5% failure rate of naive bayes in the research.

Abdul Karim et al.. [19] proposed a hybrid model which combines logistic
regression, support vector machine, and decision tree in conjunction with soft
and hard voting, the proposed hybrid model used Grid Search Hyper-parameter
Optimization, cross fold validation, and canopy feature selection method to
select relevant features from the dataset. The proposed hybrid model resulted
in an accuracy of 98.2% by using the only attribute properties of the uniform
resource locator. The sole reliance on the attribute of the URL makes this
approach extremely vulnerable to URL manipulations as any attacker with little
experience in web technology can use a malicious webpage with a friendly URL
to fool the model.

Ishwarya et al. [12] proposed a phishing detection method comprising of Naive
Bayes algorithm, SVM, KNN, and random forest including evaluation of the
performances of each of the four (4) classifiers in detection of phishing
email. The implementation of each classifiers resulted in the highest accuracy
of 98.2% for naive Bayes, albeit the use an imbalance dataset comprising 87%
ham and 13% spam for the research surely indicate biased in the proposed
model, and the problem of Bayesian poisoning was not addressed in the proposed
model.

Kamal Omari [26] used the UCI phishing domains dataset to proposed machine
learning-based model for the purpose of investigating Logistic Regression
(LR), k-Nearest Neighbors (KNN), Support Vector Machine (SVM), Naive Bayes
(NB), Decision Tree (DT), Random Forest (RF), and Gradient Boosting for
phishing detection task. Hence, we believed that the 98.1% accuracy for
phishing detection task obtained from the Naive Bayes classifier by Ishwarya
et al. (2023) [12] was due to a massive imbalance in the dataset having 87%
ham and 13% spam which was not addressed, also the proposed model doesn’t
address detection evasion through uploaded video and images on a phishing
webpage.

Ann Zeky et al. [20] proposed an extraction-based Naive Bayes model for
phishing detection with emphasis on the extraction of relevant features like
unusual characters, spelling mistakes, domain names, and URL analysis from
unseen web pages for effective classification of a website into malicious and
benign. By training the proposed model with a relatively balanced dataset of
7000 records in which 54% are malicious and 46% are benign leading to an
accuracy of 99.1%. By using a combination of content extraction and URL
analysis, we believed the proposed model would not be vulnerable to malicious
URLs in the sense that even if the attacker tried to use a friendly URL to
deceive the model, that the model does not rely on the properties of URL alone
but also uses background webpage extraction means the proposed model will
still be able to classify webpages correctly, albeit an attacker will still be
able to use Bayesian poisoning.

Nishitha et al. [23] compared performances of machine learning algorithms and
deep learning for phishing detection classification by implementing KNN,
Decision tree, Random Forest, Logistic Regression as machine learning
algorithm, convolusional neural network and recurrent neural network as deep
learning in which logistic regression and CNN had the best performances with
an accuracy of 95% and 96% respectively, albeit the proposed model only uses
the URL properties and so couldn’t be used for a sophisticated phishing attack
that relies on images and video content.

Twana and Murat [22] while assuming the absence of a single solution to detect
most phishing attacks and to investigate the impact of feature selection on
Naive Bayes model. They [22] developed 6 Naive Bayes-based models in which
each model involves a single feature selection technique chosen from
individual FS, forward FS, Backward FS, Plus-I takeaway-r FS, AR1, and All.
The experiment resulted in the Naive Bayes model with Plus-I takeaway-r
feature selection having the best performance with an accuracy of 93.39% while
the Naive Bayes classifier with individual feature selection technique has the
least performance with an accuracy of 92.05% thereby leading to the conclusion
that feature selection has a direct impact on the accuracy of phishing
detection.

Jaya T et al. [16] explored the prospect of using unsupervised learning to
cluster spam and ham messages in mail using frequency weight-age of words in
the message content in more of a natural language processing task and
comparing the performances of each of Random Forest, Logistic, Random Tree,
Bayes Net, and Naive Bayes algorithms with LTSM Algorithms for phishing
detection. The experiment resulted in LSTM which is deep learning based having
an encouraging performance, followed by random forest.

One limitation that is peculiar to each and every previously proposed models,
frameworks, and approaches is that they can only detect text-based and URL-
based phishing webpages and URLs as they are only trained based on text and
properties of the Uniform Resource Locator. Current machine learning and deep
learning models are not trained to detect more complex and increasingly
sophisticated phishing attack which relies heavily on SEO friendly URL,
putting text-on images, and Deep-fake AI generated video to evade detection.
Hence, there vulnerabilities to complex form of phishing attack.

##  III Experimental Setup

###  III-A Dataset

The complexity of the research means we cannot rely on a single data. So, we
use two publicly available datasets. There is no publicly available dataset
for video-based, audio-based, and image-based phishing dataset, so we use
simulation to internally generate them.

We use the ”B” version of Mendeley phishing dataset which was designed as a
benchmark dataset for training a machine learning models for phishing
detection. It includes 11430 URLs and 87 extracted features from which models
could be trained. Features in the dataset are classified further into three
(3) different categories in which 56 extracted features are from the structure
and syntax URL, 24 features were extracted from the content of the URL
correspondent pages, and the remaining 7 features which are features with the
greatest impact on prediction outcome are extracted from external services.
50% of the dataset used are ”phishing” while the remaining 50% are from
”legitimate” URLs. This balance of the dataset ensures that the prediction
result is not unfairly tilted toward or against a particular category.

The second public dataset that we used was the Spam Message Classification
dataset from KAGGLE containing 5157 unique records. The remaining datasets in
the form of deep-fake videos and images were simulated and internally
generated due to unavailability of such datasets in the public repository.

###  III-B Settings

The proposed framework has 4 predictive layers, with each layer suitable for a
specialized category of dataset to ensure adaptability. We show the results in
several settings.

• Layer 1 (URL-Based Training): We did traditional machine learning training
on the first layer using the Mendeley phishing dataset. Out of possible 87
features, we use chi2 from sklearn feature selection library to select the
best 19 features, having set the hyper-parameter k-value to 7 for optimal
result which gave us a combination of the best 19 features. The dataset was
split into two such that 80% was used for training, while the remaining 20%
was used for validation tests. We choose random forest because of its
suitability for URL-based phishing detection relative to other classifiers
[4],[29],[31],[25],[28],[18].During iteration, we set both the depth and
random variable to several values for optimal result but only observed a small
but negligible change in the variation of the accuracy until 39. with depth ¿
39, the accuracy remains constant, at least till when we increase the
randomness of the tree to 1 before observing little change. We finally settled
on setting the randomness state to 0 so that each tree remains the same each
time it is generated.

Table I: Negligible impact of max_depth and random_state on accuracy.
max_depth | random_state | accuracy
---|---|---
30 | 0 | 90.1
20 | 0 | 90.0
10 | 0 | 88.1
40 | 1 | 88.2
50 | 1 | 89.8
60 | 1 | 88.1

• Layer 2 (Image Processing): This is the layer where the Hypertext Markup
Language (HTML) of the actual phishing webpage is secretly web-scrapped behind
the scenes without any actual navigation for security purposes. The behind-
the-scenes mode of web scrapping the HTML content protects the server and the
network from potential drive-by attacks that might originate from the phishing
site. All the syntax of HTML mark-up language was removed From the extracted
HTML by REGEX as we needed only the content within the opening and closing of
the body tag which is the section being served by web server to potential
victims while on a phishing website, this step securely brings whatever
content (textual, videos, or images) that will be served to potential victim
into the framework for series of processing, and this effectively ensure that
they cannot evade detection.

Next, we wrote an algorithm to iterate through every filtered word in the
sentence, returning only the list of words with any image extension. The fact
that the webpage was webs crapped means our program automatically returns a
list of the full path of those images from the web server where they are
hosted. The returned list is further iterated and passed through an Optical
Character Recognition (OCR) library which uses computer vision to read content
of each images into a raw text message and forward it to the next layer for
further processing.

Algorithm 1 LSTM Model Training for Natural Language Processing (NLP) task

$\mathrm{train\\_LSTM}(f_{i},w_{i},o_{j})$

for epochs = $1$ to $N$ do

while $(j\leq m)$ do

Randomly initialize $w_{i}=\\{w_{1},w_{2},\dots,w_{n}\\}$

input $o_{j}=\\{o_{1},o_{2},\dots,o_{m}\\}$ in the input layer

forward propagate $(f_{i}\cdot w_{i})$ through layers until getting the
predicted result $y$

compute $e=y-y^{2}$

back propagate $e$ from right to left through layers

update $w_{i}$

end while

end for

• Layer 3 (Speech Synthesis): Having successfully web-scrapped the hypertext
mark-up language of the potential phishing site behind the scenes, and without
any actual navigation for security purposes at the previous layer. Returned
content from the previous layer 2 is further iterated through with ”for” loop.
”for” loop iterates through every filtered word in the sentence, returning
only the list of words with any video extension, the return list is
automatically the full path of those videos from the server where they are
hosted.

Figure 1: Step-wise speech synthesis of each audio file during execution of
”for” loop in layer 3 to produce text which was later passed on to layer 4.
Texts from the phishing sites were processed at Layer 1, images were processed
at Layer 2, while Layer 3 processed videos. All text was finally outputted to
layer 4 for final prediction using a variant of Recurrent Neural Network in
Long Short-Term Memory.

Next, we did further iteration through each of the returned video files, and
on each iteration step, we used a combination of gtts, pydud, and moviepy for
conversion from video file to audio file ”.wav” format, after which the actual
synthesis of each speech across the ”loop” began with natural language
processing speech recognition. The final operation output at this layer is a
raw text file obtained from synthesizing the speech. At this stage, we have
the images read to text from the previous layer 2 and speeches in the video
synthesized to text, next, we combined each of the text from layer 1, layer 2,
to layer 3 forwarding them to layer 4 for final prediction.

• Layer 4 (Speech Synthesis): We choose LSTM network because of the effective
solution it offers to vanishing and exploding gradient which are Long term
dependency problem in Recurrent Neural Network, the cell state in LSTM network
serves as a memory to the network thereby given it the ability to remember the
past. At layer 4, we have all outputted and processed text contents from each
of the previous layers, and there is need to capture every long-term
dependencies, short term dependencies, and sequences which could be provided
by the cell state in LSTM network to ensure a more accurate prediction.

We built an LSTM deep learning-based model, in which 80% of 5572 samples were
used as training samples while the remaining 20% was used for validation. The
dataset has a maximum of 10,000 features from the word sample, out of which we
have 9004 unique words from the dataset. During training and validation, we
had wide validation loss leading to low prediction ability but continued to
adjust the number of layer, features, epoch, batch size, and activation. We
obtained the best result at the following parameter;
dense layer = 1
activation layer= sigmoid
epochs = 10
batch size=60
feature size = 32

Figure 2: LSTM network resulting in 0.98 accuracy at optimal parameter

Figure 3: LSTM network resulting in 0.08 loss at optimal parameter.

The built LSTM network model is at the 4th layer of the framework where all
processed output from each of the previous layers are merged and passed to the
newly built LSTM model to make the final prediction.

##  IV Framework Adaptability and Performance Evaluation

To stretch and validate our multilayered adaptive framework for its
effectiveness in the detection of phishing sites containing any of (Text,
videos, and images), or a combination of any, or all of the 3. It is worth
remembering that all existing AI or machine learning-based phishing detection
techniques and frameworks can only detect text-based [7], [17],[13],[31] or
URL-based [29], [7],[34],[2] phishing sites leading to their vulnerabilities
to;
-phishing sites with friendly URL
-phishing site on hacked legitimate domain name server (DNS)
-Image-only phishing site
-video-only phishing site
or, combination of any of them in any order. To validate both the
effectiveness and adaptability of our proposed framework in overcoming such
limitations, we created 4 categories of phishing sites and uploaded them to a
secure server with a compromised DNS on a friendly URL; the first was a text-
only phishing site, image-only phishing site, video-only phishing site, and a
phishing site combining all the features. We use friendly URLs, and hacked
legitimate DNS on the text-only phishing site, so that they can evade
detection at layer 1 until the 4th layer where it will be detected, while we
created phishing sites containing each image-only, text-only, and a
combination of both to test the adaptability of the framework to different
scenarios of a phishing site.

In each scenario, we have 100% accuracy as the framework successfully adapts
to each scenario and detects accordingly, thereby overcoming limitations
associated with current approaches to phishing detection methods.

##  V Conclusion

In this research, we proposed a multi-layer adaptive framework that uses the
computer vision capability of Optical Character Recognition (OCR) to read
images on live phishing sites to text, and synthesize speech from uploaded
deep-fake videos, while using Random Forest, and LSTM network, along with web
scrapped text at various predictions layered of the framework to significantly
improve the detection rate and performance of AI-based models for phishing
detection. Considering the fact that existing AI-based phishing detection
techniques, frameworks, and approaches can only detect text-based [7],
[17],[13],[31] or URL-based phishing [29], [7],[34],[2] sites which leads to
their vulnerability and inability to detect image-based, or video-based
phishing sites, the proposed framework is able to overcome limitations in
existing approaches, significantly improve phishing attack detection, and
successfully detect complex phishing webpages with multi-dimentional deep-fake
videos, images, and texts.

##  VI Limitation and Future Research direction

We used Mendeley and Kaggle phishing datasets which are URL-based and Text-
based respectively. image-based and video-based phishing datasets are not
publicly available because they are newly adopted forms of phishing websites
to evade detection, we simulated them to get the data internally generated for
this research especially with regard to deep-fake videos, hence getting
publicly available image-based or Video-based phishing datasets will
significantly help the research community in this.

The other research direction we will point at is the computational aspect
during training. The proposed framework uses Random Forest and LSTM network at
Layer 1 and Layer 4 respectively. The fact that Random Forest algorithm
creates multiple trees each time to combine individual tree decisions for more
accurate prediction leads to an increment in computation time, we have to set
the random state to zero while changing the maximum depth for optimal hyper-
parameter. Apart from the training computation time, there is also the server
response time as the framework web scrapped the content behind the scenes
thereby protecting the server against potential drive-by attacks. Hence,
reducing the server response and computational to fraction of a second is an
area open to future research in this domain.

It is also worth noting that our artifacts which consist of source code,
dataset, images, videos, and audio files for this research had been uploaded
to a public GitHub repository for reproducibility of our research. Artifact
can be found on GitHub at;
Deep Learning-Based Speech and Vision Synthesis to Improve Phishing Attack
Detection through a Multi-layer Adaptive Framework and also at Code Ocean
computational research platform, with the exception of the internally
generated deep-fake video and audio data files for privacy.

## References

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# Hydrodynamic interactions change the buckling threshold of parallel flexible
sheets in shear flow

Hugo Perrin, Heng Li, and Lorenzo Botto  Process & Energy Department, Faculty
of Mechanical, Maritime and Materials Engineering, Delft Univ. of Technology,
Delft, The Netherlands

###### Abstract

Buckling induced by viscous flow changes the shape of sheet-like nanomaterial
particles suspended in liquids. This instability at the particle scale affects
collective behavior of suspension flows and has many technological and
biological implications. Here, we investigated the effect of viscous
hydrodynamic interactions on the morphology of flexible sheets. By analyzing a
model experiment using thin sheets suspended in a shear cell, we found that a
pair of sheets can bend for a shear rate ten times lower than the buckling
threshold defined for a single sheet. This effect is caused by a lateral
hydrodynamic force that arises from the disturbance flow field induced by the
neighboring sheet. The lateral hydrodynamic force removes the buckling
instability but massively enhances the bending deformation. For small
separations between sheets, lubrication forces prevail and prevent
deformation. Those two opposing effects result in a non-monotonic relation
between distances and shear rate for bending. Our study suggests that the
morphology of sheet-like particles in suspensions is not purely a material
property, but also depends on particle concentration and microstructure.

††preprint: APS/123-QED

##  I Introduction

Soft biological or synthetic objects, such as cells, lipid bilayers,
macromolecules, and nanoparticles, can deform when suspended in sufficiently
strong shear or extensional flows PhysRevLett123048002 ; PhysRevLett98188302 ;
D0SM02184A ; Marlow2002ve . Predicting flow-induced morphological changes is
crucial in many fields, ranging from biophysics, where swimming of micro-
organisms relies on fluid-structure interactions ANFBacteria , to soft matter
physics, where the rheological response of a particulate suspension is
affected by the instantaneous particle shape oldroy53 . Model studies in
canonical flows have provided profound physical insights of general
applicability. For example, the theoretical prediction of the coil-stretch
transition of polymers in simple shear flow pgdg74 ; PhysRevLett108038103  was
instrumental in the development of rheological models for dilute polymer
solutions RheoLarson .

The recent need to develop liquid-based methods to process two-dimensional
(2D) nanomaterials Nicolosi1226419 ; C3MH00144J ; Paton2014ty  has triggered
new interest on the effect of flow on the morphology of sheet-like materials
D0SM01630F ; D0SM02184A ; Nicolosi1226419 ; C3MH00144J ; D0SM02081H ;
JCP14Green ; YuPRF22 ; Giulapof . Two-dimensional materials have low bending
modulii and therefore can undergo transient or permanent buckling in flow
D0SM02184A . Recent numerical studies D0SM02184A ; D1SM01510A  demonstrate
that purely mechanical models based on the competition between hydrodynamic
compressive force and elastic-bending forces can capture the change of
morphology of isolated graphene sheet and 2D polymers suspended in a simple
shear flow. This agreement demonstrates that the morphology of a single sheet
is determined by a buckling instability whose threshold depends, for a given
fluid shear rate and viscosity, only on the bending modulus and length of the
sheet. However, the extension of this result to suspensions of many particles
is an open question. Because of their relatively large contact area, sheet-
like particles are prone to stacking at small inter-particle separations
WANG2020230 ; C3MH00144J . Hydrodynamic interactions between nearly parallel
sheets are thus expected to alter the buckling dynamics predicted for single
sheets.

In this study we investigate parallel pairs of flexible sheets in a shear flow
as a function of their separation distance, and study how the buckling
instability threshold depends on hydrodynamic interactions. By performing
model experiments, and interpreting the results with the help of boundary-
integral simulations and theoretical modeling, we demonstrate that
hydrodynamic interactions can trigger bending far below the buckling threshold
of a single sheet. Hydrodynamic interactions cannot therefore be considered
second-order effects when predicting the morphology of flexible sheets in
flow. More specifically, our simulations and theoretical modeling show that
the dipolar disturbance flow field induced by each sheet gives rise to a
lateral hydrodynamic force. This lateral force modifies the mechanical
response of the sheet pair to the compressive axial hydrodynamic force
experienced when the pair is oriented in the compressional quadrant of the
shear flow. On the other hand, for small separations, the lubrication forces
overcome this dipolar contribution and prevent bending. These two competing
effects result in a non-monotonic relation between interparticle distance and
critical shear rate for buckling. More generally, our results suggest that the
deformation of close sheets in a suspension may not only depend on the
mechanical and geometric properties of each sheet but also strongly on the
pair-particle separation and thus on the concentration.

##  II  Experiments

Figure 1: (a) Schematic of the shear cell. (b) Schematic of a buckled sheet
viewed along the vorticity direction of the shear flow and definition of the
mid-point orientation angle $\theta$ and mid-point curvature $\bar{\kappa}$.
The compressional quadrant and the extensional quadrant are shown. In this
schematic, the sheet is oriented in the compressional quadrant
($-\pi/2<\theta<0$).

Mylar sheets (Young’s modulus $E\simeq 4\;\rm{GPa})$ of different thicknesses
($h=23,\ 50\ \rm{and}\ 125\;\rm{\mu m}$), width $w=1\;\rm{cm}$ and length $L$
ranging from $1$ to $4\;\rm{cm}$ were used. Corresponding sheet bending
modulii are $B\simeq 5.0\times 10^{-6},\ 5.0\times 10^{-5},\ \rm{and}\
8.1\times 10^{-4}\;\rm{J}$ ($B=Eh^{3}/12(1-\nu^{2})$ where $\nu\simeq 0.5$ is
the Poisson’s ratio). The shear cell is composed of a belt driven by two co-
rotating cylinders of diameter $6\;\rm{cm}$ – see fig.1(a). A motor, connected
to one of the cylinders, imposes a controlled shear rate in the range
$\dot{\gamma}=0.4-10\;\rm{s^{-1}}$. We considered single sheets, and pairs of
parallel sheets with separation distance $d$ varying in the range
$d/L=0.03-1$. The sheets were placed in glycerol (the viscosity is $\eta\simeq
1\;\rm{Pa.s}$ and the density is $\rho\simeq 1.2\times
10^{3}\;\rm{kg.m^{-3}}$). The maximum Reynolds number
$Re=\rho\dot{\gamma}L^{2}/\eta$ is of order 1 at the maximum shear rate. With
the use of tweezers, the sheets were set with their normal vector in the flow-
gradient plane. The cylinders were set in motion after the sheets were placed.
During the dynamics, the normal vector remains in the flow-gradient plane and
thus the dynamics is two-dimensional. Optical measurements with a camera were
carried out from the top, i.e. along the vorticity direction of the
undisturbed shear flow. We extracted from the images the midpoint orientation
angle $\theta(t)$ by fitting a line to each sheet’s profile – see fig.1(b).
The mid-point curvature $\bar{\kappa}(t)$ was obtained by fitting a parabola
to each sheet’s profile. Measurements were performed with a time resolution of
$0.1\;\rm{s}$ and with a spatial resolution of $25\;\rm{\mu m/pixel}$. Even
though the maximum $Re$ is of order $1$, in analyzing the results we will
consider a low Reynolds approximation (Stokes flow). As it will appear later,
this approximation gives a reasonable agreement between the simulations and
the experimental data.

##  III Simulation Method

We simulated the fluid-structure interaction of thin sheets in Stokes flow by
a regularized Stokeslet approach smith2009boundary ; olson2015hydrodynamic ;
montenegro2017microscale ; Giulapof . The regularized Stokeslet method has
been used to study a variety of fluid-structure interaction problems at low
Reynolds number, including cilia-driven transport smith2009boundary , flagella
synchronization olson2015hydrodynamic , and flow around double helices
montenegro2017microscale . As in the experiment the flow and the sheet
dynamics are two-dimensional, we simplified the simulation choosing a two-
dimensional description. For a two-dimensional slender body, the approach
consists in placing regularized force singularities along the body’s
centerline. The integral of the regularized force density over each
discretization line segment represents the force exerted by that segment of
the slender body on the fluid. Owing to the linearity of the Stokes equation,
the velocity field $\mathbf{u}(\mathbf{x},t)$ at position $\mathbf{x}$ and
time $t$ obeys the following boundary integral equation pozrikidis1992boundary
:

$\displaystyle\mathbf{u}(\mathbf{x},t)=\mathbf{u}^{\infty}(\mathbf{x})+\frac{1}{4\pi\eta}\int_{C}\mathbf{G}_{\epsilon}(\mathbf{x},\mathbf{x}_{0})\cdot\mathbf{f}(\mathbf{x}_{0},t)\mathrm{d}l,$
(1)

where $\mathbf{u}^{\infty}$ is the undisturbed background flow, $\eta$ is the
dynamic viscosity, $\mathbf{f}(\mathbf{x}_{0},t)$ is the force density exerted
on the fluid by the sheet element $\mathrm{d}l$ centered at $\mathbf{x}_{0}$
and $\mathbf{G}_{\epsilon}$ is a 2D regularized Stokeslet for an unbounded
flow cortez2001method . Here, we neglected the double-layer potential because
of the inextensibility approximation for the sheets montenegro2017microscale ;
Giulapof . Since the sheets are inertia-less, the hydrodynamic force
$(-\mathbf{f})$ is balanced by the local internal elastic force. Numerically,
we compute the elastic force from the derivative of the bending energy, as
done in fauci1988computational ; olson2015hydrodynamic ; Giulapof . The
kinematics of each sheet is governed by the no-slip boundary condition on the
surface of the sheet. In the slender body approximation, this condition is
approximated by a no-slip condition at the centerline of the sheet:

$\displaystyle\frac{\partial\mathbf{X}(s,t)}{\partial
t}=\mathbf{u}(\mathbf{X}(s,t)),$ (2)

where $\mathbf{X}(s,t)$ is the position vector along the centerline of the
sheet at the curvilinear coordinate $s$ and time $t$. In this numerical method
the sheet has zero thickness, therefore in order to observe tumbling and
bending, the sheet needs to be initialized at an orientation angle different
from $\pm\pi/2$ and the initial shape set to a perturbation from a straight
line PRLShelley01 . Based on our previous work Giulapof  we chose for the
initial orientation $\theta_{0}=-\pi/2+\pi/10$ and for the initial shape
perturbation the first buckling mode $\kappa(s)=\kappa_{0}\sin(s\pi/L)$ with a
small amplitude $\kappa_{0}=8\times 10^{-3}/L$, where $\kappa(s)$ is the local
curvature at $s$. At each time step, the velocity field is calculated first by
eq.(1), then eq.(2) is advanced in time by a first-order explicit Euler scheme
to obtain the sheet’s configuration at the new time step. In the simulations,
each sheet is discretized by 51 nodes and the time step is
$10^{-5}\dot{\gamma}^{-1}$. Validations of the code on two cases for which
asymptotic solutions are known can be found in our previous article Giulapof .
Those two cases are the relaxation of an initially deformed sheet in a
quiescent flow and the tumbling dynamics of a single sheet in a shear flow.
During the simulation, at each time step the mid-point curvature
$\bar{\kappa}(t)=\kappa(s=L/2,t)$ of a sheet is calculated by fitting a
parabola to its center.

##  IV  Dynamics of a single sheet

For an inextensible flexible sheet of length $L$, width $w$ and bending
modulus $B$, the Euler buckling force for axial compression scales
proportionally to $wB/L^{2}$ ARFMbico18 ; Audoly2000ElasticityAG . The viscous
compressive force in a shear flow in the Stokes limit scales as
$\eta\dot{\gamma}Lw$. Its dependence on the orientation angle is
$-2\sin\theta\cos\theta$ ARFLindner ; D0SM02184A , which is maximum when the
sheet is oriented along the compressional axis $\theta=-\pi/4$ of the shear
flow (see fig.1(b)). The buckling dynamics of a single flexible sheet depends
therefore on the elasto-viscous number D0SM02184A

$\displaystyle E_{v}=\frac{\eta\dot{\gamma}L^{3}}{B}.$ (3)

This non-dimensional number can be also interpreted as the ratio of two time
scales: $1/\dot{\gamma}$, the characteristic time scale of the shear flow, and
$\eta L^{3}/B$, the characteristic time scale of curvature relaxation in a
quiescent viscous liquid.

Figure 2: (a) Normalized mid-point curvature $\bar{\kappa}L$ (crosses) and
mid-point orientation angle $\theta$ (triangular markers) versus rescaled time
$\dot{\gamma}t$ for $E_{v}\simeq 21$. Time has been shifted so that
$\dot{\gamma}t=0$ corresponds to the orientation $\theta=0$. The black line is
Jeffery’s prediction $\theta(t)=\arctan(\dot{\gamma}t)$ Jeffery . (b) Maximum
normalized curvature versus elasto-viscous number for a single sheet. The dark
and light grey regions delimit the rigid limit and the buckling region,
respectively. The measured critical elasto-viscous number from this diagram is
$E_{v}^{c}\simeq 11$. (c) Normalized curvature versus normalized time from
dynamic simulations of a single sheet for different elasto-viscous numbers.

We determined the single-sheet buckling threshold by measuring experimentally
the sheet curvature $\bar{\kappa}$ corresponding to different elasto-viscous
numbers, placing only one sheet in the shear cell. For small elasto-viscous
numbers, the sheet tumbles in the flow and remains straight. For relatively
large elasto-viscous numbers, for example $E_{v}\simeq 21$ (fig.2(a)), the
sheet deforms during tumbling. The time dependence of the angle $\theta(t)$ in
fig.2(a) is well described by Jeffery’s solution for rigid oblate ellipsoids
Jeffery ; kamalJFM21 ; D0SM02184A . This agreement validates the Stokes flow
assumption we made for the simulations. This agreement also shows that the
tumbling dynamics is not significantly affected by the sheets deformations for
curvatures smaller than $1/L$. The time-dependent curvature is seen to grow
when the sheet is oriented in the compressional quadrant
($-\pi/2\\!<\\!\theta\\!<\\!0$), which is the signature of the buckling
instability. Then the curvature decays to zero, over a time scale
$1/\dot{\gamma}$, as $\theta(t)$ spans the extensional quadrant
($0\\!<\\!\theta\\!<\\!\pi/2$) – see fig.2(a). To identify the single-sheet
buckling threshold, we measured the maximum curvature $\bar{\kappa}_{max}$
attained during a tumbling cycle for different elasto-viscous numbers (see
fig.2(b)). The results lie in two regions sharply separated by a critical
elasto-viscous number $E_{v}^{c}\simeq 11$ above which the sheet deforms with
a curvature larger than the experimental resolution. Below this number the
sheets curvature is negligible. To corroborate this observation, we performed
numerical simulations of single sheets for different elasto-viscous numbers,
see fig.2(c). For elasto-viscous numbers larger than $E_{v}=8$, the curvature
increases in time, signature of the growth of the buckling instability. For
elasto-viscous numbers smaller than $E_{v}=8$, the curvature decays. The
agreement between the numerical prediction ($\simeq 8$) and the experimental
value ($\simeq 11$) is acceptable considering the finite experimental
resolution, which makes a very precise determination of the buckling threshold
difficult ARFLindner . In literature, a mathematical model based on applying
Jeffery’s solution for the hydrodynamic stress on an oblate ellipsoids to a
flexible disk predicted a threshold values $\simeq 10^{2}$ LINGARD1974119 .
Recent simulations of an hexagonal flexible sheet modeled as a collection of
beads interacting via long-range hydrodynamic interactions - represented at
the Rotne-Prager-Yamakawa level - suggested a critical buckling threshold of
about $50$ D0SM02184A . Since the hydrodynamic compressive force depends on
the shape, it is expected that the buckling threshold for rectangular sheets
is different than the ones for ellipsoids and hexagonal sheets, so differences
with published work are expected. The experimental determination of the
buckling threshold for single rectangular sheets, confirmed by our numerical
simulation, is an important step that provides a reference case for the study
of pairs of parallel sheets.

##  V  Dynamics of a pair of parallel sheets

Figure 3: Comparison between single sheet dynamics and dynamics of a pair of
parallel sheets below the single-sheet buckling threshold. (a) Experimental
normalized curvature $\bar{\kappa}L$ versus normalized time $\dot{\gamma}t$
for a single sheet (in black) and a sheet pair separated by $d/L\simeq 0.2$
(in red) for $E_{v}\simeq 3.6$. (b) Images of a pair of parallel sheets at two
selected times. (c) Normalized curvature $\bar{\kappa}L$ versus normalized
time $\dot{\gamma}t$ for simulation of a single sheet (in black) and a pair of
sheets separated by $d/L=0.1$ (in red) for $E_{v}=7$. (d) Simulated shapes of
a pair of parallel sheets corresponding to the two selected times of fig.3(b).

A body formed by two sheets bonded together by adhesion or friction has a
larger bending rigidity than a single sheet Poincloux21 ; MultiPRL19 ;
Audoly2000ElasticityAG . Therefore one may intuitively assume that two sheets
separated by a layer of viscous liquid would have a larger buckling threshold
than a single sheet. In contrast, we found that a pair of parallel sheets can
deform for values of $E_{v}$ below the single-sheet threshold. For example,
for $E_{v}\simeq 3.6$ the single-sheet curvature is negligible (see fig.2(b)
and fig.3(a)) while for the same parameter two sheets separated by $d/L\simeq
0.2$ display a finite curvature. The curvature of the two sheets increases
with time, then decreases, changes sign and finally decays to zero at the end
of the tumbling motion (see fig.3(a)). In the single-sheet case, for
$E_{v}>E_{v}^{c}$ the curvature relaxes while the sheet is oriented in the
extensional quadrant (see fig.2(a)). In contrast, pair of sheets deform while
oriented in the extensional quadrant (fig.3(b) right panel). These two changes
of behavior for a pair of sheets, bending below the buckling threshold and
bending in the extensional quadrant, are consequences of hydrodynamic
interactions between the sheets, as it will be demonstrated below.

To rationalize the experimental observations, we simulated the dynamics of two
parallel flexible sheets. For $E_{v}=7$, the simulations indicate that the
single sheet dynamics is stable: a small initial curvature decreases in time –
see the black line in fig.3(c). For a pair of parallel sheets separated by a
distance $d=0.1L$ and the same value $E_{v}=7$, the computed curvature follows
qualitatively the experimental dynamics, see the red line in fig.3(c): each
sheet of the pair deforms, adopts a concave shape in the compressional
quadrant (fig.3(d), left panel), then the curvature changes sign, the sheets
adopt a convex shape in the extensional quadrant (fig.3(d), right panel) and
finally the deformation relaxes to zero. Because in the simulation only
hydrodynamic interactions are accounted for, the simulation results support
the hydrodynamic origin of the two changes of behavior discussed above in
relation to experiments.

Figure 4: Hydrodynamic interactions from simulation. (a) Lateral force induced
by the first sheet on the second sheet in the case of two parallel sheets in a
shear flow, oriented in the compressional quadrant (at
$\theta_{0}=-\pi/2+\pi/10$), for $d/L=1,\ 0.7\ \rm{and}\ 0.5$. (b) Magnitude
of the lateral force at the center of the sheet versus the separation distance
when the sheets are oriented in the compressional quadrant (at
$\theta_{0}=-\pi/2+\pi/10$). The line is the best fit $y=Ax^{\alpha}$ with
$A\simeq 0.02$ and $\alpha\simeq-1.1$. (c) Vector plot of the 2D disturbance
flow. The rectangle represents the sheet. (d) Magnitude of the disturbance
flow velocity $u_{dist}$ induced by a sheet in a 2D compressional flow, versus
the distance $r$ measured orthogonally to the sheet.

From the numerical simulations of two sheets we computed the lateral force on
one of the two sheets, when oriented in the compressional quadrant and for
varying distance $d/L$, see fig.4(a). The lateral force is non-uniform along
the sheet, with a maximum value in the center of the sheet and minima located
at the two edges. The force distribution can be described, to a first
approximation, as a parabola. As $d/L$ increases it is seen from fig.4(b) that
the amplitude of the parabolic profile decreases, following a power law with
an exponent close to $-1$. To explain and model this lateral force, we
quantified the disturbance flow field set up by a sheet. Because the sheet is
inertia-less and the flow 2D, the disturbance flow field in the far field is
that of a 2D force dipole whose amplitude decreases as $1/r$ BookMorris ,
where $r$ is the distance from the geometric center of the sheet. The flow
disturbance induced by a body oriented along the compressional or extensional
axis of a shear flow can be approximated by placing an elongated particle in a
two-dimensional purely straining flow batchelor1971stress , with the long axis
of the particle along the extensional direction. We performed simulations with
this simplified flow configuration. The computed vector plots in fig.4(c)
illustrate the dipolar characteristics of the flow, where it is seen that the
spatial variation of the flow corresponds to the parabolic distribution of the
lateral force. The amplitude of the disturbance flow field is reasonably well
captured by a $1/r$ dependence for $r$ as small as $0.5L$ (see fig.4(d)). The
sign of the background straining flow governs the sign of the dipole: with our
convention the sign is positive for compressional background flow and negative
for extensional background flow. Hence, the simulations show that the presence
of one sheet generates a parabolic lateral force on the other sheet; this
lateral force originates from the disturbance dipole flow field, its amplitude
scales as $L/d$ and its sign is governed by the background flow field, being
positive when the sheets are in the compressional quadrant and negative in the
extensional quadrant.

The information above enables to construct a minimalistic model of flow-
induced shape changes that takes into account the dependence on sheet-to-sheet
distance. From a balance of forces and moments on an inextensible sheet, in
the linear approximation the curvature $\kappa$ obeys the Euler-Bernoulli
equation

$\displaystyle Bw\frac{d^{2}\kappa}{ds^{2}}-T_{t}(s)\kappa(s)-f_{n}(s)=0,$ (4)

where $s$ is the curvilinear coordinate, $f_{n}$ is the lateral hydrodynamic
force per unit length and $T_{t}$ is the axial tension Audoly2000ElasticityAG
; Wexler2013aa . The axial tension satisfies

$\displaystyle\frac{dT_{t}}{ds}+f_{t}(s)=0,$ (5)

where $f_{t}$ is the axial hydrodynamic force per unit length
Audoly2000ElasticityAG ; Wexler2013aa . To model $f_{n}$ and $f_{t}$ we used a
quasi-static approximation that consists of two main assumptions. First, we
neglected the effect of the lateral hydrodynamic drag force caused by the time
variation of the curvature. Second, we assume that the curvature is only
coupled to the orientation $\theta$ through the amplitude of $f_{t}$, which we
assume to be $-2\sin\theta\cos\theta$. Considering the two extreme cases
$\theta=-\pi/4$ (orientation at maximum compression) and $\theta=\pi/4$
(orientation at maximum extension) and modeling the axial force per unit
length as an edge force arising from the straining component of the imposed
shear rate, we obtain $T_{t}=-\eta\dot{\gamma}Lw$ for $\theta=-\pi/4$ and
$T_{t}=\eta\dot{\gamma}Lw$ for $\theta=\pi/4$. Fitting the results of our
numerical simulations, we modeled the lateral force per unit length arising
from the dipolar flow field as

$\displaystyle f_{n}(s)=\pm\,w\,\frac{L}{d}\,\eta\dot{\gamma}\,Kg(s)\ $ (6)

where the sign depends on whether the sheet is oriented along the
compressional or the extensional axis. The function
$g(s)=\frac{1}{12}-\left(\frac{s}{L}-\frac{1}{2}\right)^{2}$ is a symmetric
parabola of zero mean that reproduces the spatial variation of the lateral
force seen in fig.4(a) and $K$ is a numerical pre-factor. We estimated
$K\simeq 0.4$ from the force amplitude computed at the orientation
$\theta_{0}$, see fig.4(b) (by definition $K=A\
g(1/2)/2\sin\theta_{0}\cos\theta_{0}$, where $A$ is a fitting parameter). The
moment balance then reads

$\displaystyle\frac{d^{2}\tilde{\kappa}}{d\tilde{s}^{2}}\pm
E_{v}\left(\tilde{\kappa}(\tilde{s})-\frac{K}{\tilde{d}}g(\tilde{s})\right)$
$\displaystyle=$ $\displaystyle 0,$ (7)

where $\tilde{\kappa}=\kappa L$, $\tilde{s}=s/L$ and $\tilde{d}=d/L$. The
”$+$” sign corresponds to the maximum compression ($\theta=-\pi/4$). The ”$-$”
sign corresponds to the maximum extension ($\theta=+\pi/4$). At maximum
compression, for the single sheet case ($1/\tilde{d}\to 0$) this differential
equation reduces to the classical Euler-buckling equation for an edge axial
load. If $E_{v}=\pi^{2}$, the Euler-buckling equation admits two solutions
verifying the free end boundary conditions
$\tilde{\kappa}(0)=\tilde{\kappa}(1)=0$. One solution is the trivial solution
$\tilde{\kappa}(\tilde{s})=0$ and the other is the first buckling mode
$\tilde{\kappa}(\tilde{s})=\tilde{\kappa}_{0}\sin\left(\pi\tilde{s}\right)$
for a purely axial load. The value of the buckling threshold, here $\pi^{2}$,
corresponds to a uniform axial tension. However, it can be shown that for a
more realistic model of the axial hydrodynamic force $f_{t}(s)$, i.e. a linear
variation along the sheet ARFLindner , the axial tension is a parabola and the
threshold is reduced by only $15\%$ with respect to $\pi^{2}$. Therefore the
model of uniform axial tension captures the essential behavior of buckling.
The value $E_{v}^{c}\simeq 11$ we measured experimentally is comparable with
the prediction $\pi^{2}$ of this minimal model. On the other hand, at the
maximum compression, for finite $\tilde{d}$ eq.(7) admits only one solution
satisfying the boundary conditions for any given value of $E_{v}$:

$\displaystyle\tilde{\kappa}(\tilde{s})=\frac{K}{6\tilde{d}E_{v}}\left(\left[E_{v}(-6(\tilde{s}-1)\tilde{s}-1)+12\right]+\left(E_{v}-12\right)\cos\left(\sqrt{E_{v}}\tilde{s}\right)+(E_{v}-12)\tan(\sqrt{E_{v}}/2)\sin\left(\sqrt{E_{v}}\tilde{s}\right)\right).$
(8)

The existence of a unique non-zero solution means that there is no buckling
instability in the strict sense. Hydrodynamic interactions remove the buckling
instability and the curvature has a finite bending amplitude for all values of
$E_{v}$. To summarize, for a single sheet in pure compression there is a
buckling instability while for a pair of sheets, there is no buckling
instability but bending deformations do occur. Taking the limits $E_{v}\to 0$
and $E_{v}-E_{v}^{c}\to 0$ with $E_{v}<E_{v}^{c}$, one can derive from eq.(8)
the following approximation for the maximum curvature (at $\theta=-\pi/4$) of
the mid-point of the sheet:

$\displaystyle\bar{\kappa}\sim+\,K\frac{L}{d}\frac{E_{v}}{E_{v}^{c}-E_{v}}.$
(9)

Here we have indicated explicitly the sign of the lateral force, the $"+"$
sign corresponding to the compressional quadrant. In the extensional quadrant,
by solving eq.(7), one can show that the curvature scales as
$\bar{\kappa}\sim-KE_{v}\,L/d$. As illustrated in the sketch on the left panel
of fig.5, the change of sign of the dipole force as the sheet tumbles explains
the change from concave to convex morphologies seen in fig.3(b). Equation (7)
is linear, so the scaling in $L/d$ for the dipole amplitude determines the
dependence of the bending curvature with respect to $d$.

Figure 5: Left panel: sketch of the hydrodynamic forces distribution in the
single and two sheet cases. The black line segments represent the sheets. The
green arrows represent the compressional or extensional tangential forces. The
red arrows represent the dipolar lateral forces. For $E_{v}<E_{v}^{c}$ the
single sheet remains straight while the pair of sheets adopts concave and
convex shapes. Right panel: morphology diagram. Maximum normalized curvature
for different normalized separation distances $d/L$ and elasto-viscous numbers
$E_{v}=\eta\dot{\gamma}L^{3}/B$. The black squares correspond to deformation
below the experimental resolution $\kappa_{r}=0.01/L$, the color circles to a
finite curvature. The shadow regions are guides for the eye. The experimental
data for single sheets of fig.2(b) are reported in correspondence to
$d/L=\infty$. The equation of the dashed line is
$d/L=KE_{v}/\left(\kappa_{r}L(E_{v}^{c}-E_{v})\right)$, with $E_{v}^{c}=11$,
$\kappa_{r}L=0.01$ and $K=0.01$. The dashed line is plotted for $d/L>0.05$

To evaluate the ability of the model above to capture essential features of
the experimental data, for each value of the parameters $(E_{v},d/L)$, we
measured the maximum rescaled curvature $\bar{\kappa}_{max}L$ during tumbling.
For pair of sheets, the results indicate two regions of behavior (see right
panel fig.5). A first region where each sheet’s curvature is lower than the
experimental resolution. The label ”Straight” in the figure indicates this
first region. And a second region where the sheets deform significantly
(indicated by the label ’Bent’ in the figure). Significant deformations are
seen to occur for $E_{v}$ as small as $0.8-1$, i.e. approximately ten times
smaller than in the single-sheet case. Sheet proximity has thus a strong
effect on the morphology. Our simple model provides a criterion for which the
curvature becomes larger than the experimental resolution $\kappa_{r}=0.01/L$.
This criterion defines two regions in the morphology diagram delimited by the
dashed line of equation $d/L=KE_{v}/\left(\kappa_{r}L(E_{v}^{c}-E_{v})\right)$
in fig.5. The model predicts a much larger amplitude of deformation than
observed in the experiments, but a similar trend with respect to $E_{v}$.
Indeed, the value of $K$ used in fig.5, $K=0.01$, is smaller than the one
obtained from fitting the lateral force profiles of fig.4(b), $K\simeq 0.4$.
The overestimation of the amplitude of deformation in the model likely
originates from two aspects of the quasi-static approximation we used: first,
we neglected the hydrodynamic drag force in the normal direction to the
sheets, which delays the curvature response time; second, we assumed that the
compressive force $f_{t}$ is constant while in the experiments the sheets
tumbles and thus are not submitted to a constant force. But it can be seen
accounting for the difference in the value of $K$ that the model is in
reasonably good agreements with experimental data for $d/L\gtrsim 0.05$, as
the dashed line in this interval separates the circles from the squares
symbols with the correct scaling law in $L/d$. For $d/L\lesssim 0.05$, the
sheets are observed to remain straight during the tumbling motion for all
$E_{v}$ tested and the $L/d$ prediction fails. The experimental data of fig.5
reveal thus that the relation between the separation distance and the critical
elasto-viscous number to observe significant bending is non-monotonic.
Lubrication forces between two plates separated by a distance $d$ scale as
$1/d^{3}$ for a normal displacement SRIDHAR20022547  and so are dominant at
small distances over the dipolar forces. The time scale for the growth of the
deformation in the case of a steady compressive force and lubrication scales
as $(L/d)^{3}\tau$ SRIDHAR20022547  where $\tau=\eta L^{3}/B$ is the elasto-
viscous time scale. This time scale is much longer than the tumbling time
scale $1/\dot{\gamma}$ for moderate $E_{v}=\dot{\gamma}\tau$ and small $d/L$.
Thus, lubrication forces constrain dynamically the deformation for very small
distances and moderate $E_{v}$.

##  VI Conclusion

In this study we measured for the first time the effective buckling threshold,
which we define as the threshold to observe significant bending, for a pair of
flexible sheets suspended in a viscous simple shear flow as function of the
sheet-sheet distance. In experiments, we obtain a value of the critical
elasto-viscous number for buckling of a single rectangular sheet of
$E_{v}^{c}\simeq 11$. This number is quite close to the one we obtain form 2D
simulations, $E_{v}^{c}\simeq 8$. Our main result is the demonstration of a
large reduction, by about a factor of ten, of the elasto-viscous number for
which a close pair of parallel sheets bend significantly. This reduction is
caused by the dipolar flow disturbance induced by one sheet. This disturbance
induces a lateral force on the second sheet. With a minimal model we showed
that this lateral force enhances the effect of the compressional force
experienced by the pair when oriented along the compressional axis of the
shear flow. Furthermore, we showed that the dipolar flow disturbance induces
bending also when the pair is oriented in the extensional quadrant.
Experiments and simulations suggest that the amplitude of bending is inversely
proportional to the distance between the sheets. For small separations, the
lubrication force prevails and limits the dynamical deformation of the sheets.
The competition between the dipolar enhancement and lubrication leads to a
non-monotonic relation between distance and effective buckling threshold.

In the applied context of designing macroscopic materials, for instance
nanocomposites, from sheet-like nanoparticles by liquid-based methods (as ink
printing, coating, polymer nano-composite processing and liquid-phase
exfoliation Nicolosi1226419 ; C3MH00144J ), our results suggest that at finite
volume fraction hydrodynamic interactions could amplify deformations induced
by the shear flow. The effect could alter thermal, optical or electrical
properties that are dependent on the nanoparticle shape. In the context of
rheology, by focusing on hydrodynamic pair-interactions our results provide a
first step to understand the dynamics of flexible sheets in suspension. In
particular, it has been evidenced for suspensions of fibers that buckling
produces normal stress differences PRLShelley01 . Hence, our results suggest
that the microstructure of a suspension of sheet-like particles, including the
statistics of pair-particle orientation and inter-particle distance, could
have a profound influence on the rheology by affecting the instantaneous
particle shape. Therefore, the microstructure of suspensions of sheet-like
particles should be well-characterized in future rheological studies.

###  Acknowledgment

We thank D. Tam and B. Metzger for discussions. This project has received
funding from the European Research Council (ERC) under the European Union’s
Horizon 2020 research and innovation program (Grant agreement No. 715475)

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