### Page Content

# Statistical Physics of Soft Matter and Biological Systems

We work on a broad spectrum of projects from statistical physics of soft condensed matter and biological systems. Besides problems in thermal equilibrium, we investigate systems that are kept in nonequilibrium either by external fields or

by an internal propulsion mechanism such as active Brownian particles.

The highly topical fields of microfluidics and (bio)fluiddynamics inspire us.

One current focus in our research is active motion of artificial and biological systems. We aim at understanding design principles for generating active

motion, its generic properties, and the emergent collective dynamics.

Our topics are:

- Soft matter: such as liquid crystals, colloidal dispersions, (bio)polymers
- Structure formation of soft matter at interfaces
- Soft Matter and biological systems in nonequilibrium, microfluidics
- Biofluiddynamics and locomotion of microorganisms, active motion
- Biomimetic materials and biomechanics

# News

**Seminar in the summer semester 2020**: Seminar Statistical Physics of Soft Matter and Biological SystemsThemen und Methoden der Statistischen Mechanik weicher Materie und biologischer Systeme

Introduction on Wednesday,**22.04.2020****Please register in the SAP system.**

Prof. Stark offers the following

**examination date**:Friday,

**29.05.2020**Please register in the SAP system.

- Brennpunkt-Artikel im Physik Journal:
**Die Körperform macht's**

Holger Stark

Physik Journal

**Emergent collective dynamics of bottom-heavy squirmers under gravity**

**by Felix Rühle and Holger Stark**

We present the results of hydrodynamic simulations using the method of multi-particle collision dynamics for a system of squirmer microswimmers moving under the influence of gravity at low Reynolds numbers. In addition, the squirmers are bottom-heavy so that they experience a torque which aligns them along the vertical. The squirmers interact hydrodynamically by the flow fields of a stokeslet and rotlet, which are initiated by the acting gravitational force and torque, respectively, and by their own flow fields. By varying the ratio of swimming to bulk sedimentation velocity and the torque, we determine state diagrams for the emergent collective dynamics of neutral squirmers as well as strong pushers and pullers. For low swimming velocity and torque we observe conventional sedimentation, while the sedimentation profile becomes inverted when their values are increased. For neutral squirmers we discover convective rolls of circulating squirmers between both sedimentation states, which sit at the bottom of the system and are fed by plumes made of collectively sinking squirmers. At larger torques porous clusters occur that spawn single squirmers. The two latter states can also occur transiently starting from a uniform squirmer distribution and then disappear in the long-time limit. For strong pushers and pullers only weak plume formation is observed.

Eur. Phys. J. E **43**, 26 (2020)

see also: *'Bottom-heavy' squirmers adopt characteristic group behaviours*, article as EPJE Highlight and at EurekAlert

**Capillary condensation in an active bath**

**by Milos Knezevic and Holger Stark**

e study capillary condensation in a bath of active Brownian particles (ABPs) and the forces acting on the capillary close to the motility-induced phase separation (MIPS). The capillary is modeled as two parallel rods, which are fixed in space. We consider a bath of ABPs having a self-propulsion speed much larger than the critical speed necessary for MIPS to occur.We gradually increase the packing fraction of ABPs, starting from a dilute phase of ABPs and going towards the binodal of MIPS. In stark contrast to conventional capillary condensation, we do not observe any hysteresis in the capillary packing fraction and attribute this to strong temporal fluctuations in the capillary packing fraction . Depending on the packing fraction of ABPs and capillary width, we find that the effective force between the capillary rods can be either attractive or repulsive. In fact,with increasing width it shows damped oscillations as long as capillary condensation occurs. We analyze them in detail by studying the distribution of particle distances from the inner and outer wall of the capillary, respectively. In addition, we examine the capillary in the active bath close to the critical point. We do not observe signs of the presence of long-range Casimir interactions.

Europhys. Lett. **128**, 40008 (2020)

**Optimal steering of a smart active particle**

**by Elias Schneider and Holger Stark**

We formulate the theory for steering an active particle with optimal travel time between two locations and apply it to the Mexican hat potential without brim. For small heights the particle can cross the potential barrier, while for large heights it has to move around it. Thermal fluctuations in the orientation strongly affect the path over the barrier. Then we consider a smart active particle and apply reinforcement learning. We show how the active particle learns in repeating episodes to move optimally. The optimal steering is stored in the optimized action-value function, which is able to rectify thermal fluctuations.

Europhys. Lett. **127**, 64003 (2019)

**Collective Dynamics in a Monolayer of Squirmers Confined to a Boundary by Gravity**

**by Jan-Timm Kuhr, Felix Rühle, and Holger Stark**

We present a hydrodynamic study of a monolayer of squirmer model microswimmers confined to aboundary by strong gravity using the simulation method of multi-particle collision dynamics. Thesquirmers interact with each other via their self-generated hydrodynamic flow fields and thereby form avariety of fascinating dynamic states when density and squirmer type are varied. Weak pushers, neutralsquirmers, and pullers have an upright orientation. With their flow fields they push neighbors away andthereby form a hydrodynamic Wigner fluid at lower densities. Furthermore, states of fluctuating chainsand trimers, of kissing, and at large densities a global cluster exist. Finally, pushers at all densities can tiltagainst the wall normal and their in-plane velocities align to show swarming. It turns into chaoticswarming for strong pushers at high densities. We characterize all these states quantitatively.

Soft Matter **15**, 5685 (2019)

**Traveling concentration pulses of bacteria in a generalized Keller–Segel model**

**by Maximilian Seyrich, Andrzej Palugniok, and Holger Stark**

We formulate a Markovian response theory for the tumble rate of a bacterium moving in a chemical field and use it in the Smoluchowski equation. Based on a multipole expansion for the one-particle distribution function and a reaction-diffusion equation for the chemoattractant field, we derive a polarization extended model, which also includes the recently discovered angle bias. In the adiabatic limit we recover a generalized Keller–Segel equation with diffusion and chemotactic coefficients that depend on the microscopic swimming parameters. Requiring the tumble rate to be positive, our model introduces an upper bound for the chemotactic drift velocity, which is no longer singular as in the original Keller–Segel model. Solving the Keller–Segel equations numerically, we identify traveling bacterial concentration pulses, for which we do not need a second, signaling chemical field nor a singular chemotactic drift velocity as demanded in earlier publications. We present an extensive study of the traveling pulses and demonstrate how their speeds, widths, and heights depend on the microscopic parameters. Most importantly, we discover a maximum number of bacteria that the pulse can sustain—the maximum carrying capacity. Finally, by tuning our parameters, we are able to match the experimental realization of the traveling bacterial pulse.

New J. Phys. **21, **103001 (2019)

**Chemotaxis in a binary mixture of active and passive particles**

**by Julian Stürmer , Maximilian Seyrich , and Holger Stark**

Mixtures of active and passive colloids show an intriguing dynamics of self-assembling, which is driven by the active component. Self-phoretic active colloids generate sinks in a chemical concentration field that cause passive colloids to drift toward active colloids by diffusiophoresis. The strength of this effective attraction is governed by the diffusiophoretic parameter, which determines the drift velocity. Simulating the Langevin dynamics of the colloids, we determine the state diagram for increasing diffusiophoretic strength and fixed active velocity. Three main states are distinguished. For weak attraction, passive particles are first scattered in the simulation box and then form a colloidal cloud around its center. Increasing the diffusiophoretic parameter further, passive particles oscillate between the cloud and a compact cluster, which embeds active colloids. Ultimately, in the third state, all particles collapse into a single stable cluster. In the collapse regime, the clustering dynamics of the largest cluster follows a logistic function and the mean cluster velocity vs cluster size decays with a power law. Throughout this article, we discuss our simulation results with regard to the experiments of Singh et al., Adv. Mater. **29** (32), 1701328 (2017).

J. Chem. Phys. **150**, 214901 (2019)

**A flowing pair of particles in inertial microfluidics**

**by Christian Schaaf, Felix Rühle and Holger Stark**

A flowing pair of particles in inertial microfluidics gives important insights into understanding and controlling the collective dynamics of particles like cells or droplets in microfluidic devices. They are applied in medical cell analysis and engineering. We study the dynamics of a pair of solid particles flowing through a rectangular microchannel using lattice Boltzmann simulations. We determine the inertial lift force profiles as a function of the two particle positions, their axial distance, and the Reynolds number. Generally, the profiles strongly differ between particles leading and lagging in flow and the lift forces are enhanced due to the presence of a second particle. At small axial distances, they are determined by viscous forces, while inertial forces dominate at large separations. We identify cross-streamline pairs as stable fixed points in the lift force profiles and argue that same-streamline configurations are only one-sided stable. Depending on the initial conditions, the two-particle lift forces in combination with the Poiseuille flow give rise to three types of unbound particle trajectories, called moving-apart, passing, and swapping, and one type of bound trajectory, where the particles perform damped oscillations towards the cross-stream line configuration. The damping rate scales with Reynolds number squared, since inertial forces are responsible for driving the particles to their steady-state positions.

Soft Matter **15**, 1988 (2019)

**Artificial Chemotaxis of Self-Phoretic Active Colloids: Collective Behavior**

**by Holger Stark**

Microorganisms use chemotaxis, regulated by internal complex chemical pathways, to swim along chemical gradients to find better living conditions. Artificial microswimmers can mimic such a strategy by a pure physical process called diffusiophoresis, where they drift and orient along the gradient in a chemical density field. Similarly, for other forms of taxis in nature such as photo- or thermotaxis the phoretic counterpart exists.

In this Account, we concentrate on the chemotaxis of self-phoretic active colloids. They are driven by self-electro- and diffusiophoresis at the particle surface and thereby acquire a swimming speed. During this process, they also produce nonuniform chemical fields in their surroundings through which they interact with other colloids by translational and rotational diffusiophoresis. In combination with active motion, this gives rise to effective phoretic attraction and repulsion and thereby to diverse emergent collective behavior. A particular appealing example is dynamic clustering in dilute suspensions first reported by a group from Lyon. A subtle balance of attraction and repulsion causes very dynamic clusters, which form and resolve again. This is in stark contrast to the relatively static clusters of motility-induced phase separation at larger densities.

To treat chemotaxis in active colloids confined to a plane, we formulate two Langevin equations for position and orientation, which include translational and rotational diffusiophoretic drift velocities. The colloids are chemical sinks and develop their long-range chemical profiles instantaneously. For dense packings, we include screening of the chemical fields. We present a state diagram in the two diffusiophoretic parameters governing translational, as well as rotational, drift and, thereby, explore the full range of phoretic attraction and repulsion. The identified states range from a gaslike phase over dynamic clustering states 1 and 2, which we distinguish through their cluster size distributions, to different types of collapsed states. The latter include a full chemotactic collapse for translational phoretic attraction. Turning it into an effective repulsion, with increasing strength first the collapsed cluster starts to fluctuate at the rim, then oscillates, and ultimately becomes a static collapsed cloud. We also present a state diagram without screening. Finally, we summarize how the famous Keller−Segel model derives from our Langevin equations through a multipole expansion of the full one-particle distribution function in position and orientation. The Keller−Segel model gives a continuum equation for treating chemotaxis of microorganisms on the level of their spatial density.

Our theory is extensible to mixtures of active and passive particles and allows to include a dipolar correction to the chemical field resulting from the dipolar symmetry of Janus colloids.

Acc. Chem. Res. **51**, 2681 (2018)

**Elastic turbulence in two-dimensional Taylor-Couette flows **

**by R. van Buel, C. Schaaf, and H. Stark**

We report the onset of elastic turbulence in a two-dimensional Taylor-Couette geometry using numerical solutions of the Oldroyd-B model generated with the program OpenFOAM®. Beyond a critical Weissenberg number, an elastic instability causes a supercritical transition from the laminar Taylor-Couette flow to a turbulent flow. The order parameter, the time average of secondary-flow strength, follows the scaling law Φ∝ Wi -Wi_{c}^{γ} with Wi_{c}=10 and γ= 0.45 . Additionally, the flow resistance increases beyond Wi_{c} . The temporal power spectra of the velocity fluctuations show a power-law decay with a characteristic exponent in the range 2< α < 4 , which strongly depends on the radial position. The characteristic exponent β for the spatial power spectra obeys the necessary condition β > 3 , associated with elastic turbulence, for all Wi > Wi_{c} .

Europhys. Lett. **124,** 14001 (2018)

**Feedback control of photoresponsive fluid interfaces**

**by Josua Grawitter and Holger Stark**

Photoresponsive surfactants provide a unique microfluidic driving mechanism. Since they switch between two molecular shapes under illumination and thereby affect surface tension of fluid interfaces, Marangoni flow along the interface occurs. To describe the dynamics of the surfactant mixture at a planar interface, we formulate diffusion–advection–reaction equations for both surfactant densities. They also include adsorption from and desorption into the neighboring fluids and photoisomerization by light. We then study how the interface responds when illuminated by spots of light. Switching on a single light spot, the density of the switched surfactant spreads in time and assumes an exponentially decaying profile in steady state. Simultaneously, the induced radial Marangoni flow reverses its flow direction from inward to outward. We use this feature to set up specific feedback rules, which couple the advection velocities sensed at the light spots to their intensities. As a result two neighboring spots switch on and off alternately. Extending the feedback rule to light spots arranged on the vertices of regular polygons, we observe periodic switching patterns for even-sided polygons, where two sets of next-nearest neighbors alternate with each other. A triangle and pentagon also show regular oscillations, while heptagon and nonagon exhibit irregular oscillations due to frustration. While our findings are specific to the chosen set of parameters, they show how complex patterns at photoresponsive fluid interfaces emerge from simple feedback coupling.

Soft Matter **14**, 1856 (2018)