# Ostwald ripening of aqueous microbubble solutions

Sota Inoue  Yasuyuki Kimura  Department of Physics, Kyushu University, Fukuoka
819-0395, Japan  Yuki Uematsu<EMAIL_ADDRESS>Department of
Physics and Information Technology, Kyushu Institute of Technology, Iizuka
820-8502, Japan  PRESTO, Japan Science and Technology Agency, 4-1-8 Honcho,
Kawaguchi, Saitama 332-0012, Japan

###### Abstract

Bubble solutions are of growing interest because of various technological
applications in surface cleaning, water treatment, and agriculture. However,
their physicochemical properties such as the stability and interfacial charge
of bubbles are not fully understood yet. In this study, the kinetics of radii
in aqueous microbubble solutions are experimentally investigated, and the
results are discussed in the context of Ostwald ripening. The obtained
distributions of bubble radii scaled by mean radius and total number were
found to be time-independent during the observation period. Image analysis of
radii kinetics revealed that the average growth and shrinkage speed of each
bubble is governed by diffusion-limited Ostwald ripening, and the kinetic
coefficient calculated using the available physicochemical constants in
literature quantitatively agrees with the experimental data. Furthermore, the
cube of mean radius and mean volume exhibit a linear time evolution in
agreement with the Lifshitz-Slezov-Wagner (LSW) theory. The coefficients are
slightly larger than those predicted using the LSW theory, which can be
qualitatively explained by the effect of finite volume fraction. Finally, the
slow down and pinning of radius in the shrinkage dynamics of small
microbubbles are discussed in detail.

##  I Introduction

Aqueous bubble solutions are of growing interest [1, 2, 3] because they have
potential technological applications in surface cleaning, water treatment,
oyster cultures, and cultivation of vegetables despite their physicochemical
and hydrodynamic simplicity. The stability of a single isolated bubble in
water has been studied theoretically [4, 5, 6, 7]. For example, the lifetime
of a 100nm-radius bubble is calculated to be less than $1\,\mu$s due to the
dissolution of gas molecules to the surrounding water driven by a strong
Laplace pressure of approximately $1\,$MPa [4, 5, 6, 7, 8, 9]. In contrast, a
stable bulk nanobubble solution without any surfactants has been repeatedly
reported using ultrasonic irradiation [10], decompression of pressurized
gas/water mixture [11], alcohol/water exchange [12], and shrinkage of
microbubbles [13]. These nanobubbles have radii of less than $1\,\mu$m and
negative zeta potential [10, 11], and are sufficiently stable through various
experimental characterizations. Most theoretical studies have explained this
anomalous stability by introducing the impurity film at the interface [14] or
considering the electrostatic stress effect [15, 16] focused on a single
isolated bubble. However, in practice, micro- and nanobubbles are usually used
as aqueous solutions, not as isolated bubbles, and the stability of
dispersions may differ from that of a single isolated bubble.

In this context, Ostwald ripening of surface bubbles was studied by an
analytic theory [17] and numerical simulations [18, 19]. Ostwald ripening is a
characteristic coarsening process of multiple particles, in which small
particles dissolve rapidly, whereas large particles grow slowly because of the
Gibbs-Thomson effect [20]. This process is a kind of phase transition dynamics
in quenched systems [21, 22], and it is ubiquitous in nature, for example, in
supersaturated solutions of crystals [20], metal particles in an alloy [23,
24, 25, 26], mineral particles in its vapor [27], and oil-in-water emulsions
[28, 29, 30, 31, 32, 33]. Half a century after Ostwald’s work [20], the
quantitative theory on the asymptotic behavior of coarsening was established
using the mean-field kinetic theory [34, 35, 36] called Lifshitz-Slezov-Wagner
(LSW) theory. This theory demonstrated that the scaled distribution of
particle radii has a universal shape in the limit of infinite time. Moreover,
the cube of the mean radius and the inverse of number density obeys a power
law as $t^{\alpha}$ in this limit [34, 36]. The exponent is $\alpha=1$ for
diffusion-limited Ostwald ripening, and another exponent is predicted for
different mass-transfer mechanisms of particle coarsening [37]. It is known
that experimental scaled distributions are broader than the universal scaled
distribution derived by the LSW theory [38, 39, 40, 41]. Several theories have
been proposed to explain this discrepancy between the LSW theory and
experiments, including the finite-volume fraction effect of coarsening phase
[42, 43, 44, 45, 38, 39, 46, 40, 47, 48, 41]. A major explanation for this
discrepancy is the omission of long-range interaction of diffusion fields in
the LSW theory. However, a quantitative description is still under debate.

Although the Ostwald ripening of gas bubbles have been well studied by theory
[49, 50, 17] and simulations [51, 52, 18, 19] so far, few studies
experimentally investigated the Ostwald ripening of bubbles [53, 54]. In Refs.
53 and 54, they studied the Ostwald ripening of bubbles in glycerin/water
mixture and compared the results with the LSW theory. However, they could not
discuss quantitative aspects of coarsening dynamics because the
physicochemical constants of the glycerin/water mixture were unavailable.
Moreover, they did not deduce the shrinkage and growth rate of individual
bubbles from image analysis. Thus, an experimental study on quantitative
examination of the theories of Ostwald ripening in aqueous microbubble
solutions is still lacking. In this paper, we performed experiments on the
kinetics of microbubble radii and examined the theory of Ostwald ripening in
aqueous microbubble solutions. Using microscope observations and image
analysis, we experimentally deduced the kinetic equations and obtained the
time evolution of distribution function and mean radius. Finally, we present a
quantitative analysis by comparing our experimental data with the reported
theories of Ostwald ripening using literature values for physicochemical
constants. Our results clearly demonstrate that aqueous microbubble solutions
confined in a narrow rectangular glass capillary exhibit diffusion-limited
Ostwald ripening. Furthermore, the average growth rate of each bubble radius
is equal to the LSW theory without any fitting parameters. We believe that
these findings reveal new insights into the stability of bubbles and the
general theory of Ostwald ripening.

##  II Experimental

A commercial pressurized-dissolution microbubble generator (Aura Tec,
OM4-MDG-045) was used to produce microbubble solutions. This generator
comprised inlet filters for water and gas, a pump, a pressurized tank, and an
outlet nozzle. Water was pumped into the tank, and air dissolved into the
water under a gauge pressure of $0.25\,$MPa. Next, the air-saturated water was
sent to the outlet nozzle and released under atmospheric pressure to generate
microbubbles. Approximately $3\,$L of an aqueous $10\,$mM potassium chloride
solution was used to produce microbubble solutions. Deionized water and
potassium chloride (FUJIFILM Wako, $\geq 99.9\%$) were used without further
purification. Few minutes after circulating the microbubble solution, the
solution was injected into a rectangular glass capillary (VitroCom, 3536-050
and 4806-050, length: $50\,$mm, width: $6\,$mm, and inner thickness:
$d=0.3\,$mm and $0.6\,$mm). The reference time was set to $t=0$ at the
injection of the solution. Then, the capillary was quickly set on the
microscope (Olympus, BX50), and observed by a bright-field microscope with an
objective lens of $\times 4$ and a relay lens of $\times 0.5$. The images were
captured by a camera (Motic, Moticam 2000) for a total duration of $90\,$min
at $1\,$min intervals until ($t=1$, $2,\cdots 90\,$min) and after that
$30\,$min intervals from $t=120\,$min until $600\,$min. The $10\,$fps images
were captured by another camera (The Imaging Source, DMK33UX174) with an
objective lens of $\times 20$. During the experiments, the capillary was open
to the external atmosphere. Fig. 1a shows a schematic of the experimental
setup.

Fig. 1b is a typical snapshot of observed bubbles at $t=1\,$min. The optical
imaging revealed that the bubbles were on both the top and bottom capillary
surface. However, the number of bubbles is typically much less on the bottom
compared to the top surface. We focused on the bubbles attached to the top
surface.

The captured images were first processed by an ImageJ macro to obtain the
bubble lateral positions and their radius $R_{i}$. The macro is composed of
the following functions: subtract background, threshold, convert to mask, fill
holes, watershed, and analyze particles. Then, we used a homemade python
script to track the bubbles using maximum speed of the center of bubbles
$30\,\mu$m/frame. When no bubbles was detected in the next frame in the circle
of radius $30\,\mu$m, we interpreted that the bubble disappeared. Although few
bubbles on the bottom surface were detected in the image analysis, most of the
detected bubbles were on the top surface.

After injection of microbubbles solutions to the capillary, bulk microbubbles
approach to the top surface by buoyancy. Because the glass surface and bubble
interface are negatively charged [55], the electrostatic repulsion forms a
water film at the contact point of the bubble. When microbubble solutions was
produced from deionized water without salts, the film lubricated the bubbles
to easily move by a small tilt or flow during the experiments. In contrast,
using $10\,$mM potassium chloride solutions made the bubbles remain fixed in
their position during observation periods. This can be explained that the
addition of salts screens the electrostatic repulsion and makes the film
thinner to prevent bubbles from moving. As a result, Brownian motion was not
observed, and flocculation and coalescence did not occur. We also assume that
the bubbles are not deformed from the spherical shape. This can be justified
that the capillary length of the air/water interface is few millimeters [56],
and it is much larger than the microbubble radius in the experiment. Taking
the spherical shape and thin water film at the contact point of bubbles into
account, the contact angle of the bubbles can be considered as 180∘. The
addition of potassium chloride at $10\,$mM affects the surface tension, Henry
constant, and viscosity less than 0.1%. [57, 58] Therefore, we decided to use
$10\,$mM potassium chloride solutions in the following experiments.

Figure 1:  (a) Schematic of the experimental setup. (b) Typical snapshot of
microscope observation at $t=1\,$min.

##  III Results and Discussion

###  III.1 Short summary of the Lifshitz-Slezov-Wagner theory

Ostwald ripening is a characteristic coarsening process observed in various
systems where particles of different sizes are dispersed. Because the chemical
potentials of molecules in particles depend on their curvatures due to the
Gibbs-Thomson effect, the molecules diffuse from small to large particles
resulting in the small particles shrinking and the large particles growing.
The critical radius, which determines the shrinkage or growth, increases with
time while the total number of particles decreases. This characteristic
coarsening was investigated theoretically by Lifshitz and Slezov [34, 35], and
later by Wagner [36]. In this section, we summarize the LSW theory and then
discuss our experimental results.

A multi-particle system is considered where the particle radius is
characterized by the radius distribution $F(R,t)$. The total number of
particles is defined as $N=\int^{\infty}_{0}F(R,t)dR$. The continuity equation
for $F(R,t)$ is given by

$\frac{\partial F}{\partial t}=-\frac{\partial}{\partial
R}\left(F\frac{dR}{dt}\right).$ (1)

In the LSW theory, the particle radii $R$ are assumed to obey a kinetic
equation [34, 35, 36] expressed by

$\frac{dR}{dt}=\frac{K}{{R}^{n}}\left(\frac{1}{R_{\mathrm{c}}}-\frac{1}{R}\right),$
(2)

where $K$ is the kinetic coefficient, $R_{\mathrm{c}}$ is the critical radius.
The index $n$ denotes the types of mass-transfer mechanisms, for example,
$n=1$ is volume diffusion, and other $n$ correspond to other mass transfer
mechanisms [37] The critical radius $R_{\mathrm{c}}$ is determined by the
conservation of the volume fraction of particles, $\phi$, given by

$\phi=\frac{1}{V}\int^{\infty}_{0}\frac{4\pi R^{3}}{3}F(R,t)dR,$ (3)

where $V$ is the volume of the system. For any $n(\geq-1)$, a universal scaled
distribution exists [59, 37], and almost any initial distribution of radii
approaches it in the limit of $t\to\infty$ [59, 60]. The scaling relations for
asymptotic regime are $R_{\mathrm{c}}\sim t^{1/(n+2)}$ and $N\sim
t^{-3/(n+2)}$ where $N$ is the total number of particles.

When the volume diffusion is the mechanism of mass transfer ($n=1$), the
critical radius is equal to the mean radius,

$R_{\mathrm{c}}=\langle
R\rangle=\frac{\int^{\infty}_{0}RF(R,t)dR}{\int^{\infty}_{0}F(R,t)dR},$ (4)

and the universal scaled distribution is

$P(u)=\frac{324u^{2}\mathrm{e}^{-u/(3/2-u)}}{(u+3)^{7/3}(3-2u)^{11/3}}\quad\textrm{for
}0<u<\frac{3}{2},$ (5)

otherwise $P(u)=0$ for $u\geq 3/2$. The scaled distribution is defined by
$P(u)=\langle R\rangle F(R)/N$ where $u=R/\langle R\rangle$. When the scaled
distribution is described by Eq. (5), the mean radius cubed and mean volume
obey the following equations, [34, 35, 36, 21]

$\displaystyle\langle R\rangle^{3}$ $\displaystyle=$
$\displaystyle\frac{4K}{9}t,$ (6) $\displaystyle\langle R^{3}\rangle$
$\displaystyle=$ $\displaystyle\frac{4AK}{9}t,$ (7)

where $A=\int^{3/2}_{0}u^{3}P(u)du=1.13$. Eq. (7) is usually written as
$N=27V\phi/16\pi AKt$, but here we use this description to remove the
dependence on $\phi$ [34, 35].

After the seminal works of LSW theory, many experimentalists tested the
validity of the theory. The experimental scaled radii distribution was
generally broader than Eq. (5). An explanation was given that Eq. (2) was
valid for only infinitesimal particle volume fraction, whereas experiments
were usually performed at finite volume fractions. To include the effect of
finite volume fraction into LSW theory, many theories were suggested [42, 43,
44, 45, 38, 39, 46, 40, 47, 48, 41]. These theories reveal that the finite-
volume effect broadens the scaled distribution more than the LSW theory and
increases the linear coefficients in Eqs. (6) and (7). However, these
enhancements of coarsening speed quantitatively differ from each theory [38,
41] because they were based on different approximations.

###  III.2 Time evolution of radius distribution

Figure 2:  Normalized distributions $F(R,t)/N$ of microbubble radii in the
rectangular capillary at $t=1\,$min. The discrete histogram $F(R,t)$ is
calculated using the bin width $3\,\mu$m. Average and standard deviation of
four independent measurements for each thickness. The dashed line is the
normalized distribution derived by Eq. (5), and the dashed-dotted and solid
lines are extracted from Ref. 47 including the effect of finite volume
fraction at $\phi=0.01$ and $0.06$. $\langle R\rangle=21.5\,\mu$m is plugged
in to calculate both theoretical predictions. The inset shows the total bubble
number in the observed area $S=8.3\,$mm2 with varied thickness.

In Fig. 2, the normalized distributions $F(R,t)/N$ of bubble radii at
$t=1\,$min are plotted. The points are the discrete histograms $F(R,t)$
calculated using bin width of $3\,\mu$m, and $N$ is the total number of
bubbles in the observation area. The inset shows the total number of observed
bubbles, which is not proportional to the capillary thickness $d$ because they
are not homogeneously distributed due to buoyancy. The time $t=1\,$min is the
first frame of the observations by microscope after the injection of solution.
The data points are the average of four independent measurements. Fig. 2
suggests that the normalized distributions at $t=1\,$min are reproducible and
independent of the capillary thickness, $d$. The mean radius $\langle
R\rangle$ is defined by

$\langle R\rangle=\frac{1}{N}\sum_{i=1}^{N}R_{i},$ (8)

where $R_{i}$ is the radius of the $i$th bubble. The averages, $\langle
R\rangle$, of four independent measurements are $\langle R\rangle=21.5\,\mu$m
for $d=0.3\,$mm and $\langle R\rangle=21.4\,\mu$m for $d=0.6\,$mm, almost
identical. The dashed line is the universal distribution function for the time
$t\to\infty$ derived by LSW theory, Eq. (5). The experimental radii
distribution is broader than the prediction by LSW theory. This deviation is
not surprising because it has been known that experimental radii distributions
of Ostwald ripening are generally broader than that of LSW theory [38, 39, 40,
41]. Many theories considering the effect of finite volume fraction were
formulated [42, 43, 44, 45, 38, 39, 46, 40, 47, 48, 41]. In this work we
compare our results to the theory developed by Yao et al. [47]. The dashed-
dotted and solid lines are the distribution extracted from the numerical
solution in Ref. 47. These distributions are parameterized by the volume
fraction, and $\phi=0.01$ (dashed-dotted line) and $0.06$ (solid line) [47].
$\phi=0.06$ is the upper limit of the volume fraction applicable to their
theory. [47]

The volume fraction of our system is defined by

$\phi=\frac{N}{Sd}\frac{4\pi\langle R^{3}\rangle}{3},$ (9)

where $S$ is the observed area $S=8.3\,$mm2. It was almost constant with time
in agreement with Eq. (3) and the order of $10^{-2}$ as shown in Fig. 3f.
Therefore, if the distribution at $t=1\,$min was already in an asymptotic
state, and Yao’s theory [47] was applicable, the distribution should be close
to the dashed-dotted line ($\phi=0.01$) in Fig. 2. Instead, however, the
observed distribution was close to the solid line ($\phi=0.06$). This
quantitative disagreement can be explained by the inhomogeneous position
distribution of bubbles caused by buoyancy. The bubbles were on the glass
surfaces and their positions were laterally distributed. In the middle of the
capillary, no bubble exists. All the theories, including the effect of finite
volume fraction, assume that the particles are randomly distributed in a
three-dimensional space [42, 43, 44, 45, 38, 39, 46, 40, 47, 48, 41].
Therefore, we introduce the effective volume fraction by subtracting the empty
region of the capillary, as

$\phi_{\mathrm{eff}}=\frac{N}{2S\langle R\rangle}\frac{4\pi\langle
R^{3}\rangle}{3}.$ (10)

The effective volume fraction $\phi_{\mathrm{eff}}$ is plotted as a function
of time in Fig. 3g. As seen, it is no longer constant and the order of
$10^{-1}$ in the beginning, is closer to $\phi=0.06$. Because the theory does
not take the particular lateral distribution of bubbles into account, it is
not conclusive. However, the effect of finite volume fraction, in our opinion,
explains the broadness of bubble radii distributions in this work.

Figure 3:  (a, b, c, d, e) Time evolution of scaled distribution of radii
$\langle R\rangle F/N$ is plotted where $0.15$ was used for the bin width. The
average and the standard deviation of four independent measurements are
plotted for the time series $t=3\,$min, $9\,$min, $27\,$min, $81\,$min, and
$240\,$min. The solid lines are $P(u)$ derived and extracted from Ref. 47 for
$\phi=0.06$. (f, g) The volume fraction $\phi$ and the effective volume
fraction $\phi_{\mathrm{eff}}$ are plotted as a function of $t$.

In Fig. 3a, b, c, d, and e, scaled distributions $\langle R\rangle F/N$ at
$t=3\,$min, $9\,$min, $27\,$min, $81\,$min, and $240\,$min are plotted
together with the distribution considering the finite volume fraction
($\phi=0.06$, solid line) [47]. Figs. 2 and 3 demonstrated that the scaled
distribution was not significantly different from the first observation at
$t=1\,$min. This suggests that the distribution of radii already achieved a
time-independent scaled distribution $1\,$min after the injection.

###  III.3 Examination of the radii kinetic equation

Figure 4:  Examination of the kinetic equation of bubble radii. The left panel
(a) denotes the capillary thickness $d=0.3\,$mm whereas the right panel (b)
denotes $0.6\,$mm. $dR_{i}/dt$ is plotted as a function of $R_{i}$ at
different times: $t=3\,$min (red circle), $9\,$min (blue square), $27\,$min
(green up-pointing triangle), and $81\,$min (purple down-pointing triangle).
Colored dashed lines denote Eq. (11). The data for $R_{i}(t+\Delta t)=0$ was
omitted. All the data points were sorted in $R_{i}$ and categorized into 20
data groups, and the average and standard deviation were calculated and
plotted for each data group. The data were obtained by a single experimental
measurement.

The late stage of diffusion-limited coarsening dynamics of the supersaturated
gas solution is driven by the diffusion of gas molecules between bubbles. The
kinetics of the bubble radii in the mean-field level is given by Eq. (2) with
$n=1$ [50],

$\frac{dR_{i}}{dt}=\frac{K}{R_{i}}\left(\frac{1}{\langle
R\rangle}-\frac{1}{R_{i}}\right),$ (11)

where $K$ is the kinetic coefficient defined by

$K=\frac{(2\ln 2)\gamma HD}{p_{0}}.$ (12)

Here, $\gamma$ is the surface tension of the bubble interface, $H$ is the
dimensionless Henry constant for air, $D$ is the diffusion constant of air in
water, and $p_{0}=0.10\,$MPa is the atmospheric pressure. The derivation of
Eq. (11) in the bubble solutions were described in literature [50], assuming
that the Laplace pressure of bubbles is much smaller than the atmospheric
pressure, $2\gamma/R_{i}\ll p_{0}$. The critical radius $R_{\mathrm{c}}$ in
Eq. (11) is replaced by $\langle R\rangle$ to simplify the comparison with
experimental data. The factor $\ln 2$ in Eq. (12) becomes 1 when the bubble is
isolated in the three-dimensional infinite media [50]. We assumed that the
contact angle of bubbles on the glass surface is $180^{\circ}$ and bubbles are
not deformed. In that case, the factor, $\ln 2$, can be obtained by the method
of image charges in electrostatics [61, 9]. Table 1 lists the literature
values of $\gamma$, $H$, and $D$.

Table 1: Surface tension of the air/water interface, and Henry and diffusion constant of air used in this paper. Name | Quantity | Value | Ref.
---|---|---|---
Surface tension | $\gamma$ |  $72\,$mN/m | [62]
Henry constant | $H$ | $1.9\times 10^{-2}$ |  [62, 63]111Calculated by $H=1353.96(0.2H^{xp}_{\mathrm{O_{2}}}+0.8H^{xp}_{\mathrm{N_{2}}})$ where $H^{xp}_{\mathrm{O_{2}}}=2.293\times 10^{-5}\,$/atm and $H^{xp}_{\mathrm{N_{2}}}=1.183\times 10^{-5}\,$/atm are the Henry constants of oxygen and nitrogen gas at $298.15\,$K defined by the molar fraction divided by the pressure [62], and $1353.96\,$atm is the conversion constant for non-dimensional Henry constants [63].
Diffusion constant | $D$ |  $2.1\times 10^{-9}\,$m2/s |  [62]222Calculated by $D=0.2D_{\mathrm{O_{2}}}+0.8D_{\mathrm{N_{2}}}$ where $D_{\mathrm{O_{2}}}=2.42\times 10^{-9}\,$m2/s and $D_{\mathrm{N_{2}}}=2.0\times 10^{-9}\,$m2/s are the diffusion constants of oxygen and nitrogen gas in water at $298.15\,$K [62].

First, we examined the kinetic equation of the diffusion-controlled Ostwald
ripening, Eq. (11). In Fig. 4, experimentally obtained $dR_{i}/dt$ were
plotted as a function of $R_{i}$ at different times $t=3\,$min (red circle),
$9\,$min (blue square), and $27\,$min (green up-pointing triangle), and
$81\,$min (purple down-pointing triangle). For the discretization,

$\frac{dR_{i}}{dt}=\frac{R_{i}(t+\Delta t)-R_{i}(t-\Delta t)}{2\Delta t},$
(13)

was used where $\Delta t=1\,$min. Because the number of data points is as
large as $10^{2}$ to $10^{3}$, all the data points were sorted in $R_{i}$ and
categorized into 20 data groups, and the average and standard deviation were
calculated and plotted for each data group. The colored dashed lines denotes
Eq. (11), which agree well with the experimental data. Surprisingly, this
comparison needs no fitting parameters, demonstrating that Eq. (11) well works
as the mean field description of the bubble radius kinetics. Furthermore, this
quantitative agreement was not obtained without the factor $\ln 2$ in Eq.
(12). This result implies that the inhomogeneous distribution of the bubble
positions is not relevant for the mean field description because Eq. (11)
assumes infinite separation between any bubble pairs.

For small bubbles about $R<10\,\mu$m, Fig. 4 shows no data. The reason is that
for small bubbles, the shrinkage speed is fast, and they often disappear
during the period $2\Delta t$. In the calculation of shrinkage speed in Fig.
4, we rejected the data corresponding to bubbles disappearing at $t+\Delta t$.

Figure 5:  $\langle R\rangle^{3}$ and $\langle R^{3}\rangle$ as a function of
$t$ in double logarithmic and linear plots. (a) $\langle R\rangle^{3}$ in
double logarithmic scale. (b) $\langle R\rangle^{3}$ in linear scale. (c)
$\langle R^{3}\rangle$ in double logarithmic scale. (d) $\langle R^{3}\rangle$
in linear scale. The points and error bars are the averages and standard
deviations of four independent measurements. In (a) and (c), the entire range
of data was used for the fit (colored solid lines), whereas in (b) and (d),
the data of $t\leq 10\,$min was used for the fit (colored dashed lines). The
numbers in (a) and (c) denote the exponents of fitted power law functions. The
inset in (b) shows the theoretical and simulated normalized coarsening speed
$9a/4K$ as a function of the volume fraction $\phi$ extracted digitally from
Ref. 47. Line represent theoretical calculation, while the points are their
simulation results [47].

###  III.4 Examination of coarsening speed

Although our scaled distributions shown in Figs. 2 and 3 have a different
shape compared to that predicted by the LSW theory, it is worth discussing the
experimental data using Eqs. (6) and (7). In Fig. 5a and c, the mean radius
cubed, $\langle R\rangle^{3}$, and the mean volume $\langle R^{3}\rangle$ are
plotted as a function of $t$ in a double logarithmic scale. Both $\langle
R\rangle^{3}$ and $\langle R^{3}\rangle$ were monotonically increasing and
well fitted to the power law $t^{\alpha}$ (colored solid line), and the
exponents of $\langle R\rangle^{3}$ and $\langle R^{3}\rangle$ are similar and
almost independent of $d$. When the general version of kinetic equation, Eq.
(2), is taken into account, these exponents about $\alpha=0.7$ correspond to
the intermediate index between $n=3$ and $4$. However, these higher-order
kinetic equations are derived for other mass transfer mechanisms in
supersaturated solid solutions [37]. Thus, it is unsuitable for bubble/water
systems where volume diffusion is the primary mechanism for mass transfer. In
our opinion, the apparent power-law behavior and dependence of power-law
amplitude on $d$ are caused by the effect of finite volume fraction.

Table 2: Fitted and theoretical values for Eqs. (6) and (7). $d$ |  $0.3\,$mm |  $0.6\,$mm | LSW
---|---|---|---
$a$ ($10^{3}\,\mu\mathrm{m}^{3}/$min) | 3.0 | 3.7 | 1.1
$c_{1}$ ($\mu$m) | 20 | 20 | –
$b$ ($10^{3}\,\mu\mathrm{m}^{3}/$min) | 3.6 | 4.6 | 1.2
$c_{2}$ ($\mu$m) | 23 | 23 | –

In Figs. 5b and d, $\langle R\rangle^{3}$ and $\langle R^{3}\rangle$ were
plotted using a linear scale up to $t=20\,$min. These plots revealed that both
$\langle R\rangle^{3}$ and $\langle R^{3}\rangle$ grow linearly in the first
ten minutes, and their slopes decrease with time. The colored dashed lines are
the linear fits, $\langle R\rangle^{3}=at+{c_{1}}^{3}$ and $\langle
R^{3}\rangle=bt+{c_{2}}^{3}$, using the data of $t\leq 10\,$min. Because Eqs.
(6) and (7) are asymptotic equations for $t\to\infty$, addition of an
arbitrary constant does not contradict them. Table 2 summarizes the fitted
values of $a$, $b$, $c_{1}$, and $c_{2}$ and predictions by the LSW theory.
The fitted $a$ and $b$ are a few times larger than the LSW predictions. This
is possibly because the effect of finite volume fraction increases the
coarsening speed, $a$ and $b$, from the values of the LSW theory. When
$\phi=4\pi N\langle R^{3}\rangle/3Sd$ shown in Fig. 3f is used as the volume
fraction, the volume fraction of the capillary $d=0.3\,$mm becomes larger than
that of $d=0.6\,$mm because the empty region in the middle is included in the
calculation. As shown in the inset of Fig. 5b, the normalized coarsening speed
$9a/4K$ is an increasing function of the volume fraction [47]. Therefore,
$\phi$ is not a good variable to characterize the effect of finite volume
fraction in our system, and we use the effective volume fraction
$\phi_{\mathrm{eff}}$ shown in Fig. 3g. In the beginning,
$\phi_{\mathrm{eff}}$ is the order of $10^{-1}$, whereas it decreases later to
the order of $10^{-2}$. The normalized coarsening speed $9a/4K$ in Fig. 5b is
$2.8$ for $d=0.3\,$mm and $3.4$ for $0.6\,$mm, and then these decrease with
time. These behaviors can be semi-quantitatively explained by the time
dependence of $\phi_{\mathrm{eff}}$ and the $\phi$ dependence of the
coarsening speed as follows. In the beginning, the relatively high volume
fraction, $\phi_{\mathrm{eff}}\sim 10^{-1}$, enhanced the speed of coarsening
to about three times of the LSW prediction, and later the relatively low
volume fraction $\phi_{\mathrm{eff}}\sim 10^{-2}$ slowed down the coarsening
speed. As a result, the range of linear growth was limited for the first ten
minutes. Assuming that the coarsening speed is affected by the effective
volume fraction as $a\sim\phi_{\mathrm{eff}}$, equating
$a\sim\phi_{\mathrm{eff}}\sim\langle R\rangle^{-1}\sim t^{-\alpha/3}$ and
$a\sim\langle R\rangle^{3}/t\sim t^{\alpha-1}$ yields $\alpha=0.75$, which is
very close to our fitted exponents of about $\alpha=0.7$. Because a theory for
randomly distributed coarsening particles in two-dimensional space is lacking,
we cannot compare the coarsening speed with a more suitable theory. Ostwald
ripening of organic liquid droplets in water exhibited the linear evolution of
$\langle R\rangle^{3}$ for the full range of the observation period of about
$100\,$min [28]. This can be explained by the small coarsening speed of that
system of about $10^{-1}\,\mu$m3/min.

###  III.5 Bubble shrinkage dynamics

Figure 6:  (a) Radii of small shrinking bubbles as a function of time. The
reference time $t=0$ is set at radius of each bubble by $4\,\mu$m. (b)
Shrinkage speed $-dR_{i}/dt$ of individual bubbles as a function of $R_{i}$
plotted by the colored solid lines. Raw data plotted in (a) were interpolated
by spline curves, and $-dR_{i}/dt$ was obtained by differentiation of the
spline curves. The black solid line is Eq. (11) where $\langle
R\rangle=25\,\mu$m was plugged in.

In this section, shrinkage dynamics of small bubbles in a bubble solution is
investigated. The shrinkage dynamics of a single bubble in water has been
studied using the Epstein-Plesset equation so far [6, 61, 8, 9], but not yet
in a bubble solution to the best of our knowledge. Fig. 6a shows the radius of
shrinking bubbles as a function of time. The images were taken by an objective
lens $\times 20$ at $10\,$fps, and the capillary thickness was $d=0.3\,$mm.
The approximate time after the injection is $2\,$min, and the mean radius is
about $25\,\mu$m, which is much larger than the radii of shrinking bubbles.
The reference time $t=0$ here is set at the time of $R_{i}=4\,\mu$m. These
experimental data exhibit anomalous shrinkage, which cannot be described by
Eq. (11), for example, the slowdown of the shrinkage speed and pinning of the
radius. A bubble, number 3 (green up-pointing triangle), was stable during the
observation period at the radius $R_{i}=1.3\,\mu$m. A bubble, number 1 (red
circle) shrank and disappeared as expected of Eq. (11), whereas other bubbles,
number 2, 4, and 5 (blue square, purple down-pointing triangle, and orange
pentagon), exhibited the slowdown of shrinkage and pinning of the radius for a
few seconds. Although most of bubbles disappeared ($R=0$) in the last frame in
Fig. 6a, it was not clear whether they actually disappeared or just escaped
detection by the microscope.

Fig. 6b shows the speed of shrinkage $-dR_{i}/dt$ of individual bubbles as a
function of $R_{i}$. The colored lines in Fig. 6b are calculated by the
numerical differentiation of the spline interpolation of the discrete data in
(a). Therefore, small windings of the lines in (b) are artifacts. The black
solid line represents Eq. (11) with $\langle R\rangle=25\,\mu$m, which shows
somewhat larger values than the experimental observations for $R>4\,\mu$m.
However, when the radius was smaller than $4\,\mu$m, the shrinkage speed of
some bubbles (number 2, 3, 4 and 5) was significantly slowed down, and then,
the radius was pinned for a few seconds. The reason for these anomalous
shrinkages is not clear. Similar slowdown was reported in a shrinking bubble
in partially degassed water [61]. Furthermore, this anomalous shrinkage is not
deterministic because we could not find any principle explaining it, implying
that this is controlled by uncontrolled factors such as the cleanness of the
glass surface and impurity at the bubble interfaces.

We speculate two scenarios for these anomalous shrinkage. The first scenario
is that the thin water film at the contact point between the bubble and glass
surface was ruptured by hydrophobic impurities on the glass surface. The
contact line dynamics is generally slower than the diffusion of gas molecules.
Therefore, when the size of dry contact area is few micrometers, the shrinkage
dynamics will be slow and possibly pinned at this length scale.

The second scenario is based on a mechanism of stabilizing nanobubbles
proposed recently [16]. During the shrinkage of a microbubble with few tens
micrometer radius, the absorbed ions at the interface are concentrated, and
the resultant electrostatic repulsion will reduce the shrinkage speed than the
prediction of Eq. (11) [16]. Restarting the shrinkage would be caused by
desorption of the adsorbed ions. We do not think that the adsorbed ions are
hydroxide ions but charged impurities because the adsorption of hydroxide ion
contradicts the surface tension measurement of basic electrolyte solutions
[64, 55].

Although these anomalous shrinkage behaviors must be important for the
stability of long-lived nanobubbles, further investigation regarding this is
beyond the scope of this paper because the paper clarifies that microbubble
solutions averagely undergo diffusion-limited Ostwald ripening.

##  IV conclusion

We performed experiments on the kinetics of radii in aqueous microbubble
solutions confined in a rectangular glass capillary and examined the theories
of Ostwald ripening using experimental data. The images of the bubbles were
analyzed to obtain the radii and total number of bubbles, and the distribution
function of bubble radii was calculated. The calculated radii distribution is
closer to the universal distribution with the effect of finite volume fraction
included, rather than that derived from the LSW theory, and the scaled
distribution does not change. We found that the growth and shrinkage speed of
each bubble are averagely governed by diffusion-limited Ostwald ripening. The
kinetic coefficient in the kinetic equation is calculated by the surface
tension, Henry constant, diffusion coefficient of gas in literature, and the
numerical factor representing the binding of bubbles on the glass surface. We
find a quantitative agreement of our experimental data without any fitting
parameters, suggesting that the inhomogeneous distribution of the bubble
positions is not relevant for the mean-field description. This demonstrates
that the coarsening of bubbles is driven by diffusion-limited Ostwald
ripening.

Furthermore, we revealed that the mean radius cubed and mean volume exhibit a
linear time evolution. The coefficients are slightly larger but in the same
order of magnitude as that predicted by LSW theory. The coarsening speed is
enhanced due to the effect of finite volume fraction. Because the coarsening
speed is theoretically calculated to be an increasing function of the volume
fraction [42, 43, 44, 45, 38, 39, 46, 40, 47, 48, 41], the effective volume
fraction where $d$ is replaced by $2\langle R\rangle$ is more reasonable to
characterize the finite volume effect in the two-dimensional distributed
bubble system. However, a theory of Ostwald ripening for such a special system
with a lateral particle position distribution has not been constructed,
limiting a quantitative comparison between theory and experiments.

Lastly, the decrease in the shrinkage speed and pinning of the radii of a
small microbubble in a microbubble solution are discussed in detail. These
kinetics cannot be described by the mean-field kinetic equation of Ostwald
ripening. Instead, we consider that they are influenced by uncontrolled
factors such as the cleanness of the glass surface and impurity at the bubble
interfaces. However, on average, these anomalous behaviors have minor effects
on the overall coarsening.

Bubbles/water system is unique to study the Oswald ripening because all the
relevant physicochemical properties such as the surface tension, Henry
constant, and diffusion constant are quantitatively known in literature. It
serves as a model experimental system for studying Ostwald ripening when an
improved theory includes the lateral distribution of their positions. In
addition, this study is the first step to understanding the stability of nano-
and microbubble solutions from a many-body effect perspective. Application of
this picture to bulk nanobubble solutions will be the focus of our future
work. We believe this paper will elucidate fundamental properties of bubble
solutions and stimulate further technological applications.

## Acknowledgements

This work was supported by JST, PRESTO Grant number JPMJPR21O2, JSPS KAKENHI
Grants 18KK0151 and 20K14430, a grant from the Kurita Water and Environment
Foundation (21E006), and support from the Qdai-jump Research Program from
Kyushu University (R3-01302). Y.U. thanks Kenichiro Koga, Toshihiko Eguchi,
and Akimi Serizawa for valuable discussions.

## Data Availability Statements

The data that support the findings of this study are available from the
corresponding author upon reasonable request.

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††footnotetext: * means that Junlong Jia, Ying Hu, Xi Weng, and Yiming Shi
contribute equally.††footnotetext: ${\dagger}$ means that Lei Huang and Ji Wu
are corresponding authors.

# TinyLLaVA Factory: A Modularized Codebase for Small-scale Large Multimodal
Models

Junlong Jia∗1, Ying Hu∗2, Xi Weng∗1, Yiming Shi∗2 Miao Li2, Xingjian Zhang1,
Baichuan Zhou1, Ziyu Liu2 Jie Luo1, Lei Huang†1, Ji Wu†2
1 {jiajunlong, winci, zhangxingjian, baichuanzhou, luojie,
<EMAIL_ADDRESS>
SKLCCSE, Institute of Artificial Intelligence
Beihang University
Beijing, China 2 {yinghu_yh, miao-li<EMAIL_ADDRESS>{sym23,
<EMAIL_ADDRESS>
Department of Electronic Engineering, College of AI
Tsinghua University
Beijing, China

###### Abstract

We present TinyLLaVA Factory, an open-source modular codebase for small-scale
large multimodal models (LMMs) with a focus on simplicity of code
implementations, extensibility of new features, and reproducibility of
training results. Following the design philosophy of the factory pattern in
software engineering, TinyLLaVA Factory modularizes the entire system into
interchangeable components, with each component integrating a suite of
cutting-edge models and methods, meanwhile leaving room for extensions to more
features. In addition to allowing users to customize their own LMMs, TinyLLaVA
Factory provides popular training recipes to let users pretrain and finetune
their models with less coding effort. Empirical experiments validate the
effectiveness of our codebase. The goal of TinyLLaVA Factory is to assist
researchers and practitioners in exploring the wide landscape of designing and
training small-scale LMMs with affordable computational resources.
Code: https://github.com/TinyLLaVA/TinyLLaVA_Factory
Documentation: https://tinyllava-factory.readthedocs.io/en/latest/

Keywords: Large Multimodal Models, Open Source, Modularization

##  1 Introduction

Large Language Models (LLMs) have unified various language understanding and
generation tasks (Brown et al., 2020), by using auto-regressive prediction
during training and instruction prompt during evaluation (Ouyang et al.,
2022). This paradigm of task unification has spread to the computer vision
community, giving rise to the Large Multimodal Models (LMMs) (Tsimpoukelli et
al., 2021; Awadalla et al., 2023; Liu et al., 2023; Zhu et al., 2023) that
treat visual inputs as conditional information and leverage powerful abilities
of LLMs. While the unification of LMMs in modeling various visual and
linguistic tasks shows great potential in building Artificial General
Intelligence (AGI), the training of LMMs gets quite complicated for
practitioners - it requires miscellaneous data preprocessing and careful
collaboration between model architectures and training recipes. Furthermore,
the scaling up of model sizes of LMMs requires expensive computational
resources and leads to unaffordable training and evaluation budget, which
restricts research access to only well-funded industries and organizations
(Zhou et al., 2024).

To address the above issues, this paper presents TinyLLaVA Factory, a
modularized codebase with standard training$\&$evaluating pipelines, flexible
data preprocessing$\&$model configurations, and easily extensible
architectures. TinyLLaVA Factory adheres to the design philosophy of the
factory pattern in software engineering, which modularizes the entire system
into interchangeable components, with each component integrating a suite of
cutting-edge models and methods. Keeping in line with factory pattern can
decompose complicated model architecture and training process, thus enabling
users to easily build their own LMMs with minimal coding effort and to prevent
coding mistakes. It also features standard data-preprocessing pipelines and
popular training recipes, providing friendly interfaces for user
customization.

For small-scale LMMs that can be trained with limited computational resources,
Tiny-LLaVA Factory integrates popular small-scale LLMs ranging from 450M to
2.7B, such as OpenELM-450M (Mehta et al., 2024), TinyLlama-1.1B (Zhang et al.,
2024), StableLM-2-1.6B (Jonathan Tow, 2023), Gemma-2B (Team et al., 2024),
Phi-2-2.7B (Mojan Javaheripi, 2023). Despite the fact that TinyLLaVA Factory
targets at small-scale LMMs, the codebase is applicable to large-scale LMMs by
simply scaling up LLMs. Finally, we provide empirical experiments using this
codebase among different small-scale LMMs.

##  2 Architecture and Key Components

TinyLLaVA Factory follows software principles of modularity, simplicity, and
extensibility to build an ecosystem for training and evaluating small-scale
LMMs, implemented in PyTorch (Paszke et al., 2019) and Hugging Face and
equipped with DeepSpeed (Rasley et al., 2020). The overall architecture of
TinyLLaVA Factory is illustrated in Figure 1. It leverages the standard deep
learning pipeline that starts from preparing data, preparing model, to
training and evaluating. TinyLLaVA Factory is broken down into five modules
that can be interchangeable and manageable: data, model, training recipe,
trainer, and evaluator. We endeavor to minimize the dependencies between these
modules, allowing each module to be scaled to new alternatives in a plug-and-
play fashion. Specifically, data, model, and training recipe are managed by
factory pattern that is responsible for registering new models or training
recipes. A factory goes hand-in-hand with a base class that offers basic and
universal properties and functions. Users’ customized modules can inherit from
the base class with minimal code changes. Note that though TinyLLaVA Factory
aims to train small-scale LMMs, the codebase is applicable to large-scale LMMs
by simply scaling up LLMs.

Figure 1: The overall architecture of TinyLLaVA Factory.

###  2.1 Key Components

Data. The datasets that are used for pretraining and finetuning should follow
LLaVA (Liu et al., 2023) data format. Data processing includes image and text
preprocessing. For image preprocessing, typical operations like resizing,
cropping, and normalizing are performed. For text preprocessing, chat template
is important because it is usually related to the instruction following
ability of models. Therefore, we design a base data class of chat template
providing functions of prompting text using system message, tokenizing text,
and making labels for ground truth answers. We provide subclasses of chat
templates for popular LLMs like Llama, Phi, and Gemma, which are inherited
from the base class.

Model. The model part of TinyLLaVA Factory is further modularized as three
components: small-scale LLM, vision tower, and intermediate connector. Each
component is associated with a factory for registering new models that can be
created based on the base class. For LLM and vision tower, we have provided a
suite of alternative cutting-edge models and allow users to easily replace
these models by simply specifying configuration files. For example, vision
tower supports Openai CLIP ViT, Google SigLIP ViT, Meta Dinov2, or MoF
combining both CLIP and Dinov2. LLM supports Phi, Gemma, OpenELM, among
others. (Table 2 in Appendix lists models and methods that have been
implemented in TinyLLaVA Factory.)

Training Recipe. Existing work (Ye et al., 2023; Liu et al., 2023; Chen et
al., 2023) favors in adopting multi-stage training procedures where the LLM,
vision tower, and connector component can be either frozen, fully tuned, or
LoRA tuned in different stages. TinyLLaVA Factory designs a class named
training recipe to control the tuning type of each component. Users can
customize their own training recipes for more complex needs by inheriting from
the base training recipe. Furthermore, the design of training recipes
facilitates the selection of appropriate methods for saving and loading models
according to tuning type and DeepSpeed mode.

Trainer. After specifying LMM components and training recipe, TinyLLaVA
Factory leverages a Hugging Face trainer for feature-complete training.
TinyLLaVA training is powered by features that are built in Hugging Face,
including gradient accumulation, DeepSpeed ZeRO, report logging to TensorBoard
or Wandb.

Evaluation, Testing, and Documentation. TinyLLaVA Factory currently provides
evaluations on 8 benchmarks, including SQA, GQA, POPE, MMMU, and more. For
testing, we conduct integration tests for training and evaluating across
multiple modules to verify that they function correctly together with a
coverage of around 92% of code lines, which guarantees the quality and
executability of the code. For documentation, we provide installation
instructions and descriptions of methods and functions and their parameters
and returned values.

###  2.2 Comparison to Related Codebase

TinyLLaVA Factory is related to the released codebase of LLaVA (Liu et al.,
2023), but has several merits: 1) Our codebase is modularized with standard
training$\&$evaluating pipelines and flexible data preprocessing$\&$model
configurations, while the codebase of LLaVA neglects these characteristics
from the perspective of software designing; 2) LLaVA treats vision tower and
connector as the property of a LLM, while our TinyLLaVA Factory views LLM,
vision tower and connector as the components of the LMMs, which is more
extensible to integrate more capabilities, such as adding the vision
generation component. We also note that the codebase released by prismatic-
vlms (Karamcheti et al., 2024) uses this design for LMMs and enjoys the
extensibility. Different from Prismatic-VLMs, our TinyLLaVA Factory adopts the
design philosophy of the factory pattern in software engineering, and
modularizes the entire system into interchangeable components, with each
component already integrating a suite of cutting-edge models, standard data-
processing pipelines, and popular training recipes.

Table 1: The reproduction results of TinyLLaVA variants. ”VT”, ”LLM”, and ”Recipe” respectively represent Vision Tower, small-scale Large Language Model, and Training recipe. VT | LLM | Recipe | Image Question Answering | Benchmark Toolkit
---|---|---|---|---
|  |  |  VQAv2 | GQA |  SQAI |  VQAT | MM-Vet | POPE | MME | MMMU-val
CLIP | OpenELM-450M | base | 69.5 | 52.1 | 50.6 | 40.4 | 20.0 | 83.6 | 1052.9 | 23.9
SigLIP | OpenELM-450M | base | 71.7 | 53.9 | 54.1 | 44.0 | 20.0 | 85.4 | 1118.8 | 24.0
CLIP | TinyLlama-1.1B | base | 73.7 | 58.0 | 59.9 | 46.3 | 23.2 | 85.5 | 1284.6 | 27.9
SigLIP | TinyLlama-1.1B | base | 75.5 | 58.6 | 64.0 | 49.6 | 23.5 | 86.3 | 1256.5 | 28.3
CLIP | StableLM-2-1.6B | base | 75.9 | 59.5 | 64.6 | 50.5 | 27.3 | 86.1 | 1368.1 | 31.8
SigLIP | StableLM-2-1.6B | base | 78.2 | 60.7 | 66.7 | 56.0 | 29.4 | 86.3 | 1319.3 | 32.6
SigLIP | Gemma-2B | base | 78.4 | 61.6 | 64.4 | 53.6 | 26.9 | 86.4 | 1339.0 | 31.7
CLIP | Phi-2-2.7B | base | 76.8 | 59.4 | 71.2 | 53.4 | 31.7 | 86.8 | 1448.6 | 36.3
SigLIP | Phi-2-2.7B | base | 79.2 | 61.6 | 71.9 | 57.4 | 35.0 | 87.2 | 1462.4 | 38.2
SigLIP | Phi-2-2.7B | share | 80.1 | 62.1 | 73.0 | 60.3 | 37.5 | 87.2 | 1466.4 | 38.4

##  3 Experiments

We conduct experiments (see detailed settings in Appendix A) to reproduce
several variants of TinyLLaVA and assess their performance on standard
benchmarks within our codebase, as outlined in Table 1, achieving slightly
superior overall performance compared to the performance reported in the
original paper (Zhou et al., 2024) that were trained with the LLaVA codebase.
These results highlight the reliability of our TinyLLaVA Factory and offer
valuable insights into the performance of TinyLLaVA.

##  4 Conclusion and Future Work

To facilitate the open research on small-scale LMMs, we introduce TinyLLaVA
Factory, an open-source codebase implemented in Pytorch and Hugging Face for
training small-scale LMMs, adhering to the design philosophy of modularity,
simplicity, and extensibility, meanwhile guaranteeing the reproducibility of
training results. In the future, we will integrate more efficient fine-tuning
techniques and will continuously keep up to date with state-of-the-art models.
We also encourage contributions from the open-source community.

#### Acknowledgment.

This work was partially supported by the National Key Research and Development
Plan of China under Grant 2022ZD0116310, National Natural Science Foundation
of China (Grant No. 62106012), the Fundamental Research Funds for the Central
Universities.

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##  Appendix A Experimental Settings

In Table 1, we conduct extensive experiments to evaluate various models and
key components within our codebase. The specific experimental settings are
described as follows.

#### Models.

We reproduce all the model types used in the original TinyLLaVA paper,
including small-scale LLMs (TinyLlama-1.1B, StableLM-2-1.6B, and Phi-2-2.7B),
Vision Towers (OpenAI CLIP ViT and Google SigLIP ViT), and the connector (a
two-layer MLP with GELU activation). Additionally, we implement the language
models OpenELM-450M and Gemma-2B in the codebase.

#### Training Recipes.

We follow the training recipes (base and share) used in the original TinyLLaVA
paper. Specifically, for the base recipe, during pre-training, only the
connector is updated while the rest of the model remains frozen. The model is
trained for one epoch with a learning rate of 1e-3 and a batch size of 256. In
the supervised fine-tuning stage, the vision tower is kept frozen while both
the connector and the small-scale LLM are updated. The model is tuned for one
epoch with a learning rate of 2e-5 and a batch size of 128.

During pre-training of the share recipe, the connector is initialized from the
base’s pretrained counterpart. Additionally, the vision tower is kept frozen
while the rest of the model is updated for one epoch with a learning rate of
2e-5 and a batch size of 256. The setup for supervised fine-tuning is the same
as the base recipe.

#### Training Data and Data Preprocessing.

By default, the LLaVA-1.5 dataset is utilized for training when using the base
recipe, whereas the ShareGPT4V dataset is employed for training with the share
recipe. We follow the data preprocessing settings outlined in the original
TinyLLaVA paper, with the exception that we configure the image_aspect_ratio
parameter to square in both pretraining and finetuning stage when using
SigLIP. This adjustment leads to slightly superior performance compared to the
results reported in the original paper.

#### Evaluating Benchmarks.

We evaluate our reproduced models on four image question-answering benchmarks:
VQA-v2 (Goyal et al., 2017), GQA (Hudson and Manning, 2019), ScienceQA-IMG (Lu
et al., 2022), and TextVQA (Singh et al., 2019), and four comprehensive
benchmark: MM-Vet (Yu et al., 2023), POPE (Yifan Li and Wen, 2023), MME (Fu et
al., 2023), and MMMU (Yue et al., 2023).

Table 2:  Small-scale LLMs, vision towers, connectors, and training recipes that have been implemented in TinyLLaVA Factory. Module |  Name |  Module |  Name
---|---|---|---
Small-scale LLM |  OpenELM-450M (Mehta et al., 2024) |  Vision Tower |  CLIP (Radford et al., 2021) SigLIP (Zhai et al., 2023) DinoV2 (Oquab et al., 2023) MoF (Tong et al., 2024)
TinyLlama-1.1B (Zhang et al., 2024)
StableLM-2-1.6B (Jonathan Tow, 2023)
Qwen-1.5-1.8B (Jinze Bai, 2024)
Gemma-2B (Team et al., 2024)
Phi-2-2.7B (Mojan Javaheripi, 2023)
Connector |  Identity |  Training Recipe |  Frozen/Full/Partially Tune  LoRA/QLoRA (Hu et al., 2021; Dettmers et al., 2024)
Linear
MLP
Q-former (Li et al., 2023)
Resampler (Awadalla et al., 2023)