# Hydrodynamic interactions can induce jamming in flow-driven systems

Eric Cereceda-López  Departament de Física de la Matèria Condensada,
Universitat de Barcelona, 08028, Spain  Institut de Nanociència i
Nanotecnologia, Universitat de Barcelona (IN2UB), 08028, Barcelona, Spain
Dominik Lips  Universität Osnabrück, Fachbereich Physik, Barbarastraße 7,
D-49076 Osnabrück, Germany  Antonio Ortiz-Ambriz<EMAIL_ADDRESS>Departament de Física de la Matèria Condensada, Universitat de Barcelona,
08028, Spain  Institut de Nanociència i Nanotecnologia, Universitat de
Barcelona (IN2UB), 08028, Barcelona, Spain  University of Barcelona Institute
of Complex Systems (UBICS), 08028, Barcelona, Spain  Artem Ryabov
<EMAIL_ADDRESS>Charles University, Faculty of Mathematics and
Physics, Department of Macromolecular Physics, V Holešovičkách 2, CZ-18000
Praha 8, Czech Republic  Philipp Maass<EMAIL_ADDRESS>Universität Osnabrück,
Fachbereich Physik, Barbarastraße 7, D-49076 Osnabrück, Germany  Pietro Tierno
Departament de Física de la Matèria Condensada, Universitat de Barcelona,
08028, Spain  Institut de Nanociència i Nanotecnologia, Universitat de
Barcelona (IN2UB), 08028, Barcelona, Spain  University of Barcelona Institute
of Complex Systems (UBICS), 08028, Barcelona, Spain

###### Abstract

Hydrodynamic interactions between fluid-dispersed particles are ubiquitous in
soft matter and biological systems and they give rise to intriguing collective
phenomena. While it was reported that these interactions can facilitate force-
driven particle motion over energetic barriers, here we show the opposite
effect in a flow-driven system, i.e. that hydrodynamic interactions hinder
transport across barriers. We demonstrate this result by combining experiments
and theory. In the experiments, we drive colloidal particles using rotating
optical traps, thus creating a vortex flow in the corotating reference frame.
We observe a jamming-like decrease of particle currents with density for large
barriers between traps. The theoretical model shows that this jamming arises
from hydrodynamic interactions between the particles. The impact of
hydrodynamic interactions is reversed compared to force-driven motion,
suggesting that our findings are a generic feature of flow-driven transport.

Collective transport of microscale particles in fluid media can occur either
due to external forces or to a flow that drags the particles. Prominent
examples include driven motion of particles through narrow channels [1, 2, 3],
in micro- and nanofluidic devices [4, 5, 6], in pores of zeolites [7], and
through carbon nanotubes with relevance to biotechnological and biomedical
applications [8]. Hydrodynamic interactions (HI) are always present in viscous
fluids but only a few studies so far have tackled their influence on the
collective transport behavior [9, 10, 11, 12, 13, 14, 15]. However, most of
these studies have considered force- rather than flow-driven systems where HI
were found to facilitate particle motion. In particular, it was reported that
HI make it easier to surmount potential barriers when particles are force-
driven across an optical sawtooth potential [16]. Here we show that the
opposite is true for flow-driven transport of particles through periodic
potentials. Using a combined experimental and theoretical approach we show
that HI can lead to an effective enhancement of potential barriers, causing a
slowing down of particle motion and a jamming at high density.

To experimentally realize a well controlled flow-driven system it is necessary
to overcome several difficulties. For example, the pressure field should be
precisely controllable, and one should be able to vary the number of particles
and the height of the potential barriers. Usually, flow-driven systems are
realized in lithographically designed chambers, where the flow is produced by
connecting a microfluidic channel to two particle reservoirs at different
pressures. However, for studying many-particle dynamics, such system could
introduce unwanted effects, including fluctuations of the particle number in
the channel and, even more importantly, the collective dynamics may be
affected by strong channel-reservoir coupling effects. These couplings can
lead to nonequilibrium steady states, where the particle number density is
determined by uncontrollable details [17]. We avoid such complications by
experimentally generating a flow in a confined system with periodic boundary
conditions. This is a typical setup considered in theoretical studies, which
we realize here by driving particles dispersed in a liquid via a traveling-
wave like potential along a ring. In a reference frame co-moving with the
traveling wave, the particle transport then corresponds to that in a flow-
driven system.

Figure 1:  (a) Image of 15 particles (black circles) confined to a ring of
radius $R$ with 27 equidistantly placed optical traps (contrast was enhanced
by standard gamma correction). The ring rotates with angular velocity
$\omega$. The lines mark isolines of the optical potential $U(r,\varphi)$.
Along the azimuthal direction, the potential is given by
$U_{\varphi}(\varphi,t_{0})$ in Eq. (1) for a fixed time $t_{0}$ and $r=R$.
(b) Potential $U_{\varphi}(\varphi,t_{0})$ as a function of $\varphi$. The
faded line shows the potential at a later instant $t_{0}+\Delta t$, and the
dashed black lines indicate the potential amplitude modulation. Experimental
data (markers) are determined by averaging the position increments of a single
particle measured at a sequence of times $t_{n}=t_{0}+2\pi n/\omega$,
$n=0,1,2,...$ The red line is a fit of Eq. (1) to these experimental data. (c)
Mean barrier height $U_{0}$ and modulation parameter $\xi$ as a function of
the laser power. (d) Average single-particle velocity $v_{0}$ normalized to
the flow velocity $\omega R$ as a function of the mean barrier height $U_{0}$.
Experimental values (symbols) are compared to simulations (line) for the
potential in Eq. (1).

Specifically, $N_{\rm tr}=27$ optical traps are positioned along a ring of
radius $R=20.22\,$\mu\mathrm{m}$$ in the $xy$-plane, see Fig. 1. We created
the traps by passing an infrared continuous wave laser through two acousto-
optic deflectors (AODs) that are capable to deflect the beam to a different
position every $20\,$\mu\mathrm{s}$$, thus each trap is generated once every
$0.54\,$\mathrm{m}\mathrm{s}$$. A fluid cell with an aqueous solution of
spherical polystyrene colloids of radius $a=2\,$\mu\mathrm{m}$$ (CML,
Molecular Probes) is sealed by two coverslips separated by $\sim
100$\mu\mathrm{m}$$ and placed on a custom-built inverted optical microscope.
The particles sediment by gravity close to the bottom cell and float there at
a surface to surface distance of $\sim$200nm. Thus, they are far from the top
plate and also from the in-plane boundaries located a few centimeters away.
The microscope is equipped with a CMOS camera (Ximea MQ003MG-CM) and tracking
is done using the Crocker-Grier method [18]. Note that the particle diameter
$2a=4\,$\mu\mathrm{m}$$ is comparable to the distance $\lambda=2\pi R/N_{\rm
tr}\cong 4.7\,$\mu\mathrm{m}$$ between neighboring traps.

Due to the fast deflection of the laser beam, all traps appear as simultaneous
because the typical self-diffusion time of the particles is $D_{0}/a^{2}\sim
30$s, where $D_{0}\cong 0.1295\,$\mu\mathrm{m}^{2}\mathrm{s}^{-1}$$ is the
particle diffusion coefficient. We independently obtained $D_{0}$ by measuring
the time-dependent mean-square displacement in the absence of the optical
ring.

Figure 1(a) illustrates the optical potential landscape $U(\bm{r})$, which
confines the particles to a ring with potential valleys at the trap centers.
Expressed in polar coordinates, $U(r,\varphi)$ has a deep minimum along the
radial direction at $r=R$. Along the azimuthal direction it has $N_{\rm tr}$
pronounced minima at the trap positions shown by the dark red lines in Fig.
1(a). By changing the phase of the circulating beam linearly in time, the
traps move at a constant angular velocity of
$\omega=0.63\,$\mathrm{r}\mathrm{a}\mathrm{d}\,\mathrm{s}^{-1}$\cong
6\,\textrm{rpm}$ and the potential becomes time-dependent,
$U=U(r,\varphi-\omega t)$. All of the following observations are done in the
reference frame where the trap positions are stationary:
$\varphi\rightarrow\varphi-\omega t$.

Figure 2: Fundamental diagrams for (a) experiments and (b), (c) for
simulations based on Eqs. (2). The current $J(\rho)$ is normalized with
respect to the single-particle current $J_{\rm sp}=v_{0}/2\pi R$ where $v_{0}$
is the single-particle velocity from Fig. 1(d). Filled circles/solid lines and
open circles/dashed-dotted lines refer to simulations with and without HI,
respectively. In (b) results are shown for the time-dependent potential in Eq.
(1) with amplitude modulation ($\xi=0.22$). In (c) results are shown for the
ideal periodic potential ($\xi=0$), and for a force-driven system
(squares/dotted lines). The legend in (b) applies also to (c). In all graphs
the solid black line marks the behavior for independent particles and the thin
dotted line indicates the function $\rho(1-\rho)$ as a reference to jamming
(see text).

From our setup depicted in Fig. 1(a), one should expect the potential to be
periodic along the azimuthal direction with a period $2\pi/N_{\rm tr}$,
corresponding to a wavelength $\lambda=2\pi R/N_{\rm tr}$. To check whether
this is the case, and to obtain parameters for our simulations, we measured
the optical forces by dragging a single particle along the ring and analyzed
particle displacements between successive frames, similarly as in Ref. [19].
Videos S1 and S2 of the Supplemental Material [20] show that the particles
exhibit negligible radial displacements, and thus we can consider the dynamics
to proceed only along the ring through a one-dimensional potential
$U_{\varphi}(\varphi)=U(R,\varphi)$. However, the potential turned out not to
be perfectly $\lambda$-periodic, because the AOD response is not flat along
the sample, causing the deflected laser power to vary weakly with $\varphi$.
This leads to a static modulation of the potential amplitude with a relative
strength $\xi$. In the corotating frame, the potential is periodically varying
with angular frequency $\omega$, yielding a time-dependent potential

$U_{\varphi}(\varphi,t)=\frac{U_{0}}{2}[1+\xi\sin(\varphi+\omega
t)]\cos\left(N_{\rm tr}\varphi\right)\,.$ (1)

The parameters of Eq. (1) were obtained by fitting the forces for various
laser powers in the range $11-40\,$\mathrm{m}\\!\mathrm{W}$$. Figure 1(b)
shows a typical outcome, where the dashed line represents the modulation
caused by the AOD’s response. As shown in Fig. 1(c), the modulation strength
$\xi=0.22\pm 0.02$ is almost independent of the laser power, while the mean
barrier height $U_{0}$ between the traps increases linearly with the laser
power from 70 to 150$\,k_{\rm B}T$, where $k_{\rm B}T$ is the thermal energy.

To check the parameters $U_{0}$, $\xi$, and $D_{0}$, we performed Brownian
dynamics simulations (see below) and compared simulated with measured drag
velocities $v_{0}$ for the amplitudes $U_{0}$ applied in the experiment. The
results in Fig. 1(d) show an excellent agreement between simulated and
measured data.

We now study the fundamental diagram [21] of the many-particle dynamics, i.e.
the relation between the current $J$ along the azimuthal direction and the
particle density $\rho$. To determine the current, we first calculated the
instantaneous velocities of each particle in the stationary state from changes
of the particle positions in small time steps (successive frames) along the
azimuthal direction. We then averaged these velocities over time and all
particles. The resulting mean velocity $\langle v\rangle$ gives the current
$J=N\langle v\rangle/(2\pi R)$. For the density, we use the fraction of traps
occupied by the particles, $\rho=N/N_{\rm tr}$.

The current $J(\rho)$ is shown in Fig. 2(a) for various barrier heights
$U_{0}$. To see the impact of the particle interactions, we normalized
$J(\rho)$ with respect to the current of a single-particle, $J_{\rm
sp}=v_{0}/(2\pi R)$. For independent particles, we would expect a linear
function $J(\rho)/J_{\rm sp}=\rho$, represented by the straight black line in
the figure. All curves $J(\rho)/J_{\rm sp}$ approach this line in the limit
$\rho\to 0$, while for $\rho>0$ the current is smaller, and as $U_{0}$ is
increased, the current suppression is larger.

When $U_{0}\lesssim 80k_{\rm B}T$, the suppression of the current is
relatively weak for all $\rho$, while at larger $U_{0}\gtrsim 100k_{\rm B}T$,
we find a strong suppression at large $\rho$. A local maximum in $J(\rho)$
occurs, which is a signature of jamming, i.e. a transition from a fluid-like
continuous motion to a thermally activated behavior with blocking effects. A
prominent simple model for this jamming is the asymmetric simple exclusion
process [22, 23] where the current follows, $J(\rho)/J_{\rm sp}=\rho(1-\rho)$,
which we included in Fig. 2 as a reference (black dotted line). However, the
dynamics in our experiment are more complex as witnessed by the more
complicated shapes of the current-density relations and their strong
dependence on $U_{0}$.

The jamming-like behavior seen in Fig. 2(a) suggests that it arises from the
strong confinement of the particles along the ring, which hinders them from
overtaking each other (single-file transport). Is this jamming originating
solely from a hard-sphere type interaction between the polystyrene colloids?
Or is the combined effect of this interaction with the time-dependence of the
potential in Eq. (1) essential? And what is the impact of HI?

To answer these questions, we performed Brownian dynamics simulations of hard-
sphere interacting particles. The optical forces acting on the particles at
positions $\bm{r}_{i}$ are described by the potential
$U(\bm{r}_{i}-\bm{u}_{i}t)$, where $\bm{u}_{i}=\bm{\omega}\times\bm{r}_{i}$
are the azimuthal velocities of the particles
($\bm{\omega}=\omega\hat{\bm{z}}$, where $\hat{\bm{z}}$ is the unit vector in
$z$ direction).

In our reference frame, which corotates with the traps, the translational
motion of $N$ particles in the presence of HI can be described by the Langevin
equations [24]

$\displaystyle\dot{\bm{r}_{i}}$ $\displaystyle=$
$\displaystyle-\bm{\omega}\times\bm{r}_{i}+\sum_{j=1}^{N}\bigl{[}k_{\rm
B}T\bm{\nabla}_{j}\bm{\mu}_{ij}+\bm{\mu}_{ij}\bm{f}_{i}\bigr{]}+\bm{\eta}_{i},$
(2a) $\displaystyle\bm{f}_{i}$ $\displaystyle=$
$\displaystyle-\bm{\nabla}_{i}U(\bm{r}_{i})+\bm{f}_{i}^{\rm int}\,,$ (2b)

where $\bm{f}_{i}^{\rm int}$ is the interaction force exerted on particle $i$
by the other particles, and
$\bm{\mu}_{ij}=\bm{\mu}_{ij}(\bm{r}_{1},\ldots,\bm{r}_{N})$ is the mobility
tensor, which accounts for HI by the mobility method [25]. The vector
$\bm{\eta}_{i}$ is a Gaussian white noise with zero mean and covariance matrix
in accordance with the fluctuation-dissipation theorem, i.e.
$\langle\bm{\eta}_{i}(t)\otimes\bm{\eta}_{j}(t^{\prime})\rangle=2k_{\rm
B}T\bm{\mu}_{ij}\delta(t-t^{\prime})$.

Equation (2a) shows that our experiment indeed corresponds to a flow-driven
system of interacting particles. The term $\bm{\omega}\times\bm{r}_{i}$ equals
the driving in a radially symmetric vortex flow field. When averaging
$U_{\varphi}(\varphi,t)$ from Eq. (1) over one time period $2\pi/\omega$, it
becomes time-independent and periodic in $\varphi$ with period $2\pi/N_{\tr}$.
Accordingly, when averaging the force of the time-averaged potential over one
period $2\pi/N_{\tr}$ along the azimuthal direction, it is zero. Shortly
speaking, in a fluid at rest, there would be no particle current on average
111For asymmetric potentials as those considered in Brownian motors, there can
be a net driving also if forces are zero after period-averaging but this does
not apply here because of lack of asymmetry..

To take the HI into account, we used the procedure developed in [27], where
the mobilities $\bm{\mu}_{ij}$ are given by the Rotne-Prager form, both for
the reflective fluid flows resulting from the coverslip underneath the
particles and the fluid flows induced by the movements of the particles. This
consideration of HI constitutes a minimal model, where we neglect lubrication
effects, possible translation-rotation couplings and expansions of the
mobilities beyond the Rotne-Prager form for particles coming close to each
other. In all simulations we included the reflective fluid flow and
constrained the particle movement to the azimuthal direction. When we refer to
simulations with and without HI in the following, we mean the particle-
particle HI, which we calculated in full three-dimensional space.

Figure 2(b) shows the simulated normalized current $J(\rho)/J_{\rm sp}$
obtained for the potential (1) with amplitude modulation as in the experiment
($\xi=0.22$). The open circles connected by the dashed-dotted lines refer to
the simulations without HI. In contrast to a suppression of the current, they
show an enhancement at larger densities. This enhancement is due to the fact
that with increasing density, regions of large driving force are more strongly
populated. The behavior changes drastically when including the HI (filled
circles connected by solid lines). The normalized current now decreases at
large $\rho$ in qualitative agreement with the experiments. In particular, the
jamming-like behavior becomes stronger with increasing $U_{0}$. The details of
the behavior differ from the experiments in Fig. 2(a), and we attribute this
to the limitations of our minimal model of HI.

To clarify whether the amplitude modulation plays a crucial role for the
jamming, we performed additional simulations for the ideal case when the
periodic potential is time-independent ($\xi=0$ in Eq. (1)). The results shown
in Fig. 2(c) are very similar to those in Fig 2(b). Without HI, $J(\rho)$
exceeds the single-particle current. In the presence of HI, the current is
smaller than that of independent particles and decreases with $\rho$ at large
densities, reflecting jamming.

In order to explore if the jamming would occur in a force-driven system, we
solved the Langevin equations (2) for particles driven by the external torque
$\bm{f}_{\rm ext}(\bm{\hat{}}{\bm{\varphi}})=-\omega R\hat{\bm{\varphi}}$,
where $\hat{\bm{\varphi}}$ denotes the unit vector along the azimuthal
direction; this means that Eq. (2a) becomes
$\dot{\bm{r}_{i}}=\sum_{j}\left\\{k_{\rm
B}T\bm{\nabla}_{j}\bm{\mu}_{ij}+\bm{\mu}_{ij}\left[\bm{f}_{i}+\bm{f}_{\rm
ext}(\hat{\bm{\varphi}}_{i})\right]\right\\}+\bm{\eta}_{i}$. In contrast to
the flow-driven case, the results for the force-driven one show a strong
current enhancement in agreement with previous findings [9], see the squares
connected by dotted lines in Fig. 2(c).

We now provide an argument for the current suppression in flow-driven
transport. To this end, we consider the equation of motion of a single
particle in the potential given by Eq. (1),

$\dot{\varphi}=-\frac{\mu_{0}}{R^{2}}\frac{\partial}{\partial\varphi}\left[\frac{\omega
R^{2}}{\mu_{0}}\varphi+U_{\varphi}(\varphi,t)\right]+\eta_{\varphi}\,,$ (3)

where
$\langle\eta_{\varphi}(t)\eta_{\varphi}(t^{\prime})\rangle=2D_{0}R^{-2}\delta(t-t^{\prime})$
with $D_{0}=k_{\rm B}T\mu_{0}$. Hence, $U_{\varphi}(\varphi,t)$ is tilted by
the linear potential $\omega R^{2}\varphi/\mu_{0}$, resulting in the effective
potential $U_{\varphi}^{\rm eff}(\varphi,t)=U_{\varphi}(\varphi,t)+\omega
R^{2}\varphi/\mu_{0}$. For small $U_{0}$, this effective potential exhibits no
barriers, implying that a single particle is essentially dragged by the flow.
The part $U_{\varphi}$ in $U_{\varphi}^{\rm eff}$ can be viewed as creating a
resistance for the flow-driven particle motion, causing $v_{0}$ to be smaller
than the flow velocity $\omega R$ for $U_{0}>0$ and to decrease with $U_{0}$.

When $U_{0}$ becomes larger than a critical amplitude $U_{0{\rm c}}$, the
single-particle motion becomes thermally activated. For determining $U_{0{\rm
c}}$, we take the temporally period-averaged potential $\bar{U}_{\varphi}^{\rm
eff}(\varphi)=(\omega/2\pi)\int_{0}^{2\pi/\omega}U_{\varphi}(\varphi,t)\differential
t$, which is also the effective potential for the ideal case $\xi=0$ [time-
independent periodic potential, see Eq. (1)]. The barriers in
$\bar{U}_{\varphi}^{\rm eff}(\varphi)$ emerge when $U_{0}$ passes the critical
amplitude $U_{0{\rm c}}=2\omega R^{2}/\left(\mu_{0}N_{\rm tr}\right)\cong
147\,k_{\rm B}T$.

The above shows that all experiments are below the critical amplitude, and
therefore one would expect linear current-density relations with no pronounced
jamming effect. This is indeed confirmed by the simulated data without HI
shown in Fig. 2(b). However, the HI leads to an effective increase of the
potential barrier. Within the Rotne-Prager level of description, the terms
$\bm{\mu}_{ij}\bm{f}_{j}$ contain the part
$(\bm{\mu}_{ij})_{\varphi\varphi}\partial U_{\varphi}/\partial\varphi$, where
$(\bm{\mu}_{ij})_{\varphi\varphi}$ is the $\varphi\varphi$-component of the
tensor $\bm{\mu}_{ij}$ in cylindrical coordinates. In the absence of HI, only
the term $\mu_{0}\partial U_{\varphi}/\partial\varphi$ for $j=i$ contributes
to the sum over $j$. In the presence of HI, the additional contributions for
$j\neq i$ are dominated by the particles $j$ closest to particle $i$. For a
particle $j$ located at a neighboring trap of particle $i$, in particular, the
corresponding additional contribution is
$\mu_{0}[(3a/2\lambda)-(a/\lambda)^{3}]\partial U_{\varphi}/\partial\varphi$
($a$: particle size, $\lambda$: wavelength of the potential).

This can be viewed as an effective enhancement of the mean barrier height
$U_{0}$ by HI to a value

$U_{0}^{\rm\scriptscriptstyle
HI}=\left(1+\frac{3a}{2\lambda}-\frac{a^{3}}{\lambda^{3}}\right)U_{0}\,.$ (4)

Because $a<\lambda$, the additional contribution is always positive, i.e.
$U_{0}^{\rm\scriptscriptstyle HI}>U_{0}$. Using Eq. (4) with $\lambda=2\pi
R/N_{\rm tr}\cong 4.71\,$\mu\mathrm{m}$$ and $a\cong 2\,$\mu\mathrm{m}$$,
$U_{0}$ is increased by about 56%. For large $U_{0}$ in experiment, this gives
$U_{0}^{\rm HI}>U_{0{\rm c}}$, which implies that the effective potential
$U_{\varphi}^{\rm eff}$ (now for one particle in the many-particle system)
exhibits barriers. The dynamics thus becomes thermally activated and strongly
slows down. This barrier enhancement effect should become stronger with larger
occupation probabilities of neighboring traps, i.e. density. In addition,
blocking effects can lead to a further slowing down with increasing $\rho$
[28, 29]. Indeed, we have seen indications of a hopping motion and jamming in
the measured trajectories for large $U_{0}$ and high densities, see videos in
the Supplemental Material [20].

Our analysis can be made more precise by refining the description beyond the
Rotne-Prager approximation. This can include higher order terms in the
expansion of mobilities in powers of the particle radius to interparticle
distance ratio $a/\lambda$, lubrication effects, and an additional
consideration of the rotational dynamics of the particles. One can imagine to
reach a quantitative agreement between experiments and modeling with large-
scale simulation methods, as, for example, by implementing multiparticle
collision dynamics [30]. However, our model is able to qualitatively reproduce
the experimental findings and it provides an understanding of the mechanisms
governing the current suppression in our system.

To conclude, we have found that HI in flow-driven many-particle systems can
lead to an effective barrier enhancement, which induces a jamming-like
behavior. We support this conclusion by combining experiments with numerical
simulations and we provide a minimal approach for exploring the impact of HI
on the translational motion. The flow-driving is essential for the observed
phenomena and the reported effect is present regardless of imperfections of
the external potential, which makes our findings relevant for non-ideal
situations in nature.

Particle transport over energetic barriers occurs in many soft matter and
biological systems. We expect that the phenomena uncovered here, namely the
HI-induced barrier enhancement and jamming effects will be of general
importance for further studies and applications of flow-driven many-particle
systems.

###### Acknowledgements.

We sincerely thank G. Nägele, H. Stark for advice, and the members of the DFG
Research Unit FOR 2692 for fruitful discussions. E. C.-L., A. O.-A and P. T.,
acknowledge support from the ERC Consolidator Grant (Grant agreement number
811234). P. T. acknowledges support from Ministerio de Ciencia, Innovación y
Universidades (PID2019-108842GB-C21), AGAUR (2017-SGR-1061) and Generalitat de
Catalunya under Program “ICREA Acadèmia”. A.R., P.M., and D.L. gratefully
acknowledge financial support by the Czech Science Foundation (Project No.
20-24748J) and the Deutsche Forschungsgemeinschaft (Project No. 432123484).

## References

  * Mirzaee-Kakhki  _et al._ [2020] M. Mirzaee-Kakhki, A. Ernst, D. de las Heras, M. Urbaniak, F. Stobiecki, A. Tomita, R. Huhnstock, I. Koch, J. Gördes, A. Ehresmann, D. Holzinger, M. Reginka, and T. M. Fischer, Colloidal trains, Soft Matter 16, 1594 (2020).
  * Lutz  _et al._ [2004] C. Lutz, M. Kollmann, and C. Bechinger, Single-File Diffusion of Colloids in One-Dimensional Channels, Phys. Rev. Lett. 93, 026001 (2004).
  * Wei  _et al._ [2000] Q.-H. Wei, C. Bechinger, and P. Leiderer, Single-File Diffusion of Colloids in One-Dimensional Channels, Science 287, 625 (2000).
  * Rodriguez-Villarreal  _et al._ [2020] A. I. Rodriguez-Villarreal, L. Ortega-Tana, J. Cid, A. Hernandez-Machado, T. Alarcon-Cor, P. Miribel-Catala, and J. Colomer-Farrarons, An integrated detection method for flow viscosity measurements in microdevices, IEEE Transactions on Biomedical Engineering , 1 (2020).
  * Petit  _et al._ [2016] J. Petit, I. Polenz, J.-C. Baret, S. Herminghaus, and O. Bäumchen, Vesicles-on-a-chip: A universal microfluidic platform for the assembly of liposomes and polymersomes, Eur. Phys. J. E 39, 59 (2016).
  * Ma  _et al._ [2015] M. Ma, F. Grey, L. Shen, M. Urbakh, S. Wu, J. Z. Liu, Y. Liu, and Q. Zheng, Water transport inside carbon nanotubes mediated by phonon-induced oscillating friction, Nat. Nanotechnol. 10, 692 (2015).
  * Van de Voorde and Sels [2017] M. Van de Voorde and B. Sels, eds.,  _Nanotechnology in Catalysis: Applications in the Chemical Industry, Energy Development, and Environment Protection_ (Wiley-VCH, Weinheim, 2017).
  * Zeng  _et al._ [2018] S. Zeng, J. Chen, X. Wang, G. Zhou, L. Chen, and C. Dai, Selective transport through the ultrashort carbon nanotubes embedded in lipid bilayers, J. Phys. Chem. C 122, 27681 (2018).
  * Reichert and Stark [2004] M. Reichert and H. Stark, Circling particles and drafting in optical vortices, J. Phys.: Condens. Matter 16, S4085 (2004).
  * Misiunas and Keyser [2019] K. Misiunas and U. F. Keyser, Density-Dependent Speed-up of Particle Transport in Channels, Phys. Rev. Lett. 122, 214501 (2019).
  * Zahn  _et al._ [1997] K. Zahn, J. M. Méndez-Alcaraz, and G. Maret, Hydrodynamic Interactions May Enhance the Self-Diffusion of Colloidal Particles, Phys. Rev. Lett. 79, 175 (1997).
  * Rinn  _et al._ [1999] B. Rinn, K. Zahn, P. Maass, and G. Maret, Influence of hydrodynamic interactions on the dynamics of long-range interacting colloidal particles, Europhysics Letters (EPL) 46, 537 (1999).
  * Malgaretti  _et al._ [2012] P. Malgaretti, I. Pagonabarraga, and D. Frenkel, Running faster together: Huge speed up of thermal ratchets due to hydrodynamic coupling, Phys. Rev. Lett. 109, 168101 (2012).
  * Nagar and Roichman [2014] H. Nagar and Y. Roichman, Collective excitations of hydrodynamically coupled driven colloidal particles, Phys. Rev. E 90, 042302 (2014).
  * Grimm and Stark [2011] A. Grimm and H. Stark, Hydrodynamic interactions enhance the performance of Brownian ratchets, Soft Matter 7, 3219 (2011).
  * Lutz  _et al._ [2006] C. Lutz, M. Reichert, H. Stark, and C. Bechinger, Surmounting barriers: The benefit of hydrodynamic interactions, EPL 74, 719 (2006).
  * Dierl  _et al._ [2012] M. Dierl, P. Maass, and M. Einax, Classical driven transport in open systems with particle interactions and general couplings to reservoirs, Phys. Rev. Lett. 108, 060603 (2012).
  * Crocker and Grier [1996] J. C. Crocker and D. G. Grier, Methods of Digital Video Microscopy for Colloidal Studies, J. Colloid Interface Sci. 179, 298 (1996).
  * Juniper  _et al._ [2012] M. P. N. Juniper, R. Besseling, D. G. A. L. Aarts, and R. P. A. Dullens, Acousto-optically generated potential energy landscapes: Potential mapping using colloids under flow, Opt. Express 20, 28707 (2012).
  * [20] See EPAPS Document No.xxxx which includes two supplementary videos.
  * Schadschneider  _et al._ [2010] A. Schadschneider, D. Chowdhury, and K. Nishinari,  _Stochastic Transport in Complex Systems: From Molecules to Vehicles_, 3rd ed. (Elsevier Science, Amsterdam, 2010).
  * Derrida [1998] B. Derrida, An exactly soluble non-equilibrium system: The asymmetric simple exclusion process, Phys. Rep. 301, 65 (1998).
  * Schütz [2001] G. M. Schütz, Exactly solvable models for many-body systems far from equilibrium, in  _Phase Transitions and Critical Phenomena_, Vol. 19, edited by C. Domb and J. Lebowitz (Academic Press, London, 2001) pp. 1–251.
  * Ermak and McCammon [1978] D. L. Ermak and J. A. McCammon, Brownian dynamics with hydrodynamic interactions, J. Chem. Phys. 69, 1352 (1978).
  * Kim and Karrila [1991] S. Kim and S. J. Karrila,  _Microhydrodynamics: Principles and Selected Appliacations_ (Butterworth-Heinemann, Boston, 1991).
  * Note [1] For asymmetric potentials as those considered in Brownian motors, there can be a net driving also if forces are zero after period-averaging but this does not apply here because of lack of asymmetry.
  * von Hansen  _et al._ [2011] Y. von Hansen, M. Hinczewski, and R. R. Netz, Hydrodynamic screening near planar boundaries: Effects on semiflexible polymer dynamics, J. Chem. Phys. 134, 235102 (2011).
  * Lips  _et al._ [2018] D. Lips, A. Ryabov, and P. Maass, Brownian Asymmetric Simple Exclusion Process, Phys. Rev. Lett. 121, 160601 (2018).
  * Lips  _et al._ [2019] D. Lips, A. Ryabov, and P. Maass, Single-file transport in periodic potentials: The Brownian asymmetric simple exclusion process, Phys. Rev. E 100, 052121 (2019).
  * Howard  _et al._ [2019] M. P. Howard, A. Nikoubashman, and J. C. Palmer, Modeling hydrodynamic interactions in soft materials with multiparticle collision dynamics, Curr. Opin. Chem. Eng. 23, 34 (2019), frontiers of Chemical Engineering: Molecular Modeling.