Oscillating modes of driven colloids in overdamped systems

Nonequilibrium dynamics and entropy production of a trapped colloidal particle in a complex nonreciprocal medium

We discuss the two-dimensional motion of a Brownian particle that is confined to a harmonic trap and driven by a shear flow. The surrounding medium induces memory effects modeled by a linear, typically nonreciprocal coupling of the particle coordinates to an auxiliary (hidden) variable. The system's behavior resulting from the microscopic Langevin equations for the three variables is analyzed by means of exact moment equations derived from the Fokker-Planck representation, and numerical Brownian dynamics simulations. Increasing the shear rate beyond a critical value we observe, for suitable coupling scenarios with nonreciprocal elements, a transition from a stationary to a nonstationary state, corresponding to an escape from the trap. We analyze this behavior, analytically and numerically, in terms of the associated moments of the probability distribution, and from the perspective of nonequilibrium thermodynamics. Intriguingly, the entropy production rate remains finite when crossing the stability threshold.

Harnessing Viscoelasticity to Suppress Irreversibility Buildup in a Colloidal Stirling Engine

Typically, the rate at which a heat engine can produce useful work is constrained by the buildup of irreversibility with increasing operating speed. Here, using a recently developed reservoir engineering technique, we designed and quantified the performance of a colloidal Stirling engine operating in a viscoelastic bath. While the bath acts like a viscous fluid in the quasistatic limit, and the engine's performance agrees with equilibrium predictions, on reducing the cycle time to the bath's structural relaxation time, the increasingly elastic response of the bath aids suppress the buildup of irreversibility. We show that the elastic energy stored during the isothermal compression step of the Stirling cycle facilitates quick equilibration in the isothermal expansion step. This results in equilibriumlike efficiencies even for cycle times shorter than the equilibration time of the colloidal particle.

Sliding Dynamics of a Small Charged Ring Chain on the Diblock Polyelectrolyte in Poly[2]catenane in the Presence of Counterions

In this study, we investigate the sliding dynamics of small charged ring chains along the rigid central cyclic diblock polyelectrolyte of AnBn in radial charged poly[2]catenane in the presence of counterions using molecular dynamics simulations and the Lifson-Jackson formula, and our aim is to study the effects of electrostatical interaction strength, the size of the charged small ring chain, and the rigid block length of the diblock polyelectrolyte on the sliding dynamics of a small ring chain threaded on the rigid diblock polyelectrolyte. The mean-square displacement g3(t) of a small ring chain sliding along the rigid diblock polyelectrolyte of A10B10 exhibits oscillating behavior at short time scales for the moderate electrostatical interaction strength, while for the weak or strong electrostatic interactions, it is normal subdiffusion at short time scales. For n = 1, the diffusion coefficient D of the small ring chain sliding along the rigid diblock polyelectrolyte of A1B1 decreases monotonically as the relative electrostatic interaction strength A increases from A = 0.25-4. However, for n ≠ 1, the diffusion coefficient D of the small ring chain sliding along the rigid diblock polyelectrolyte of AnBn first decreases and then increases with the increase of A, and the nonmonotonous relationship between D and A becomes more obvious for larger n. In view of the free energy potential, the sliding diffusion of a small ring chain is governed by both the width of the free energy potential well and the height of the free energy potential barrier. According to the potential of mean force (PMF) of the small ring chain sliding along the rigid diblock polyelectrolyte, we find that our results are in good agreement with the theoretical analysis using the Lifson-Jackson formula. These results may help us to understand the diffusion motion of a ring chain in radial poly[n]catenanes from a fundamental point of view and control the sliding dynamics in molecular designs.

Memory-induced alignment of colloidal dumbbells

When a colloidal probe is forced through a viscoelastic fluid which is characterized by a long stress-relaxation time, the fluid is excited out of equilibrium. This is leading to a number of interesting effects including a non-trivial recoil of the probe when the driving force is removed. Here, we experimentally and theoretically investigate the transient recoil dynamics of non-spherical particles, i.e., colloidal dumbbells. In addition to a translational recoil of the dumbbells, we also find a pronounced angular reorientation which results from the relaxation of the surrounding fluid. Our findings are in good agreement with a Langevin description based on the symmetries of a director (dumbbell) as well as a microscopic bath-rod model. Remarkably, we find an instability with amplified fluctuations when the dumbbell is oriented perpendicular to the direction of driving. Our results demonstrate the complex behavior of non-spherical objects within a relaxing environment which are of immediate interest for the motion of externally but also self-driven asymmetric objects in viscoelastic fluids.

Optimum transport in systems with time-dependent drive and short-ranged interactions

We consider a one-dimensional lattice gas model of hardcore particles with nearest-neighbor interaction in presence of a time-periodic external potential. We investigate how attractive or repulsive interaction affects particle transport and determine the conditions for optimum transport, i.e., the conditions for which the maximum dc particle current is achieved in the system. We find that the attractive interaction in fact hinders the transport, while the repulsive interaction generally enhances it. The net dc current is a result of the competition between the current induced by the periodic external drive and the diffusive current present in the system. When the diffusive current is negligible, particle transport in the limit of low particle density is optimized for the strongest possible repulsion. But when the particle density is large, very strong repulsion makes particle movement difficult in an overcrowded environment and, in that case, the optimal transport is obtained for somewhat weaker repulsive interaction. Our numerical simulations show reasonable agreement with our mean-field calculations. When the diffusive current is significantly large, the particle transport is still facilitated by repulsive interaction, but the conditions for optimality change. Our numerical simulations show that the optimal transport occurs at the strongest repulsive interaction for large particle density and at a weaker repulsion for small particle density.

How are mobility and friction related in viscoelastic fluids?

The motion of a colloidal probe in a viscoelastic fluid is described by friction or mobility, depending on whether the probe is moving with a velocity or feeling a force. While the Einstein relation describes an inverse relationship valid for Newtonian solvents, both concepts are generalized to time-dependent memory kernels in viscoelastic fluids. We theoretically and experimentally investigate their relation by considering two observables: the recoil after releasing a probe that was moved through the fluid and the equilibrium mean squared displacement (MSD). Applying concepts of linear response theory, we generalize Einstein's relation and, thereby, relate recoil and MSD, which both provide access to the mobility kernel. With increasing concentration, however, MSD and recoil show distinct behaviors, rooted in different behaviors of the two kernels. Using two theoretical models, a linear two-bath particle model, and hard spheres treated by mode coupling theory, we find a Volterra relation between the two kernels, explaining differing timescales in friction and mobility kernels under variation of concentration.

Memory can induce oscillations of microparticles in nonlinear viscoelastic media and cause a giant enhancement of driven diffusion

We investigate analytically and numerically a basic model of driven Brownian motion with a velocity-dependent friction coefficient in nonlinear viscoelastic media featured by a stress plateau at intermediate shear velocities and profound memory effects. For constant force driving, we show that nonlinear oscillations of a microparticle velocity and position emerge by a Hopf bifurcation at a small critical force (first dynamical phase transition), where the friction's nonlinearity seems to be wholly negligible. They also disappear by a second Hopf bifurcation at a much larger force value (second dynamical phase transition). The bifurcation diagram is found in an analytical form confirmed by numerics. Surprisingly, the particles' inertial and the medium's nonlinear properties remain crucial even in a parameter regime where they were earlier considered entirely negligible. Depending on the force and other parameters, the amplitude of oscillations can significantly exceed the size of the particles, and their period can span several time decades, primarily determined by the memory time of the medium. Such oscillations can also be thermally excited near the edges of dynamical phase transitions. The second dynamical phase transition combined with thermally induced stochastic limit cycle oscillations leads to a giant enhancement of diffusion over the limit of vast driving forces, where an effective linearization of stochastic dynamics occurs.

Lane and band formation of oppositely driven colloidal particles in two-dimensional ring geometries

We study the segregation phenomena for oppositely driven colloidal particles in two-dimensional ring geometries by means of Brownian dynamics simulations without hydrodynamic interactions. The particles interact via a repulsive Yukawa potential and are confined to a two-dimensional circular channel by hard walls, in which half of the particles are driven clockwise and the other half are driven counterclockwise. In addition to lane formation, which is commonly found in oppositely driven systems, we found band formation along the angular direction in channels with a very large radius. This indicates that a formation of lanes is prevented in the limit of channels with an infinitely large inner radius. The dependency of this segregation has been examined for the two control parameters, the interaction strength between the particles and the width of the circular channel.

Topology mediates transport of nanoparticles in macromolecular networks

Diffusion transport of nanoparticles in confined environments of macromolecular networks is common in diverse physical systems and regulates many biological responses. Macromolecular networks possess various topologies, featured by different numbers of degrees and genera. Although the network topologies can be manipulated from a molecular level, how the topology impacts the transport of nanoparticles in macromolecular networks remains unexplored. Here, we develop theoretical approaches combined with simulations to study nanoparticle transport in a model system consisting of network cells with defined topologies. We find that the topology of network cells has a profound effect on the free energy landscape experienced by a nanoparticle in the network cells, exhibiting various scaling laws dictated by the topology. Furthermore, the examination of the impact of cell topology on the detailed behavior of nanoparticle dynamics leads to different dynamical regimes that go beyond the particulars regarding the local network loop. The results might alter the conventional picture of the physical origin of transport in networks.

Macromolecular networks relevant for biological processes and technological applications, are often characterized by complex architectures. The authors uncover the impact of topology on the properties of nanoparticle transport in macromolecular networks.

Active Brownian motion with memory delay induced by a viscoelastic medium

By now active Brownian motion is a well-established model to describe the motion of mesoscopic self-propelled particles in a Newtonian fluid. On the basis of the generalized Langevin equation, we present an analytic framework for active Brownian motion with memory delay assuming time-dependent friction kernels for both translational and orientational degrees of freedom to account for the time-delayed response of a viscoelastic medium. Analytical results are obtained for the orientational correlation function, mean displacement, and mean-square displacement which we evaluate in particular for a Maxwell fluid characterized by a kernel which decays exponentially in time. Further, we identify a memory-induced delay between the effective self-propulsion force and the particle orientation which we quantify in terms of a special dynamical correlation function. In principle, our predictions can be verified for an active colloidal particle in various viscoelastic environments such as a polymer solution.

Sustained order-disorder transitions in a model colloidal system driven by rhythmic crosslinking

Biological systems have the unique ability to self-organize and generate autonomous motion and work. Motivated by this, we investigate a 2D model colloidal network that can repeatedly transition between disordered states of low connectivity and ordered states of high connectivity via rhythmic binding and unbinding of biomimetic crosslinkers. We use Langevin dynamics to investigate the time-dependent changes in structure and collective properties of this system as a function of colloidal packing fractions and crosslinker oscillation periods and characterize the degree of order in the system by using network connectivity, bond length distributions, and collective motion. Our simulations suggest that we can achieve distinct states of this colloidal system with pronounced differences in microstructural order and large residence times in the ordered state when crosslinker kinetics and lifetimes depend directly on the oscillation period and this oscillation period is much larger than the colloidal diffusion time. Our results will provide insights into the rational design of smart active materials that can independently cycle between ordered and disordered states with desired material properties on a programmed schedule.

Viscoelasticity, Like Forces, Plays a Role in Mechanotransduction

Viscoelasticity and its alteration in time and space has turned out to act as a key element in fundamental biological processes in living systems, such as morphogenesis and motility. Based on experimental and theoretical findings it can be proposed that viscoelasticity of cells, spheroids and tissues seems to be a collective characteristic that demands macromolecular, intracellular component and intercellular interactions. A major challenge is to couple the alterations in the macroscopic structural or material characteristics of cells, spheroids and tissues, such as cell and tissue phase transitions, to the microscopic interferences of their elements. Therefore, the biophysical technologies need to be improved, advanced and connected to classical biological assays. In this review, the viscoelastic nature of cytoskeletal, extracellular and cellular networks is presented and discussed. Viscoelasticity is conceptualized as a major contributor to cell migration and invasion and it is discussed whether it can serve as a biomarker for the cells’ migratory capacity in several biological contexts. It can be hypothesized that the statistical mechanics of intra- and extracellular networks may be applied in the future as a powerful tool to explore quantitatively the biomechanical foundation of viscoelasticity over a broad range of time and length scales. Finally, the importance of the cellular viscoelasticity is illustrated in identifying and characterizing multiple disorders, such as cancer, tissue injuries, acute or chronic inflammations or fibrotic diseases.

The rise and fall of branching: A slowing down mechanism in relaxing wormlike micellar networks

A mean-field kinetic model suggests that the relaxation dynamics of wormlike micellar networks is a long and complex process due to the problem of reducing the number of free end-caps (or dangling ends) while also reaching an equilibrium level of branching after an earlier overgrowth. The model is validated against mesoscopic molecular dynamics simulations and is based on kinetic equations accounting for scission and synthesis processes of blobs of surfactants. A long relaxation time scale is reached with both thermal quenches and small perturbations of the system. The scaling of this relaxation time is exponential with the free energy of an end cap and with the branching free energy. We argue that the subtle end-recombination dynamics might yield effects that are difficult to detect in rheology experiments, with possible underestimates of the typical time scales of viscoelastic fluids.

Two step micro-rheological behavior in a viscoelastic fluid

We perform micro-rheological experiments with a colloidal bead driven through a viscoelastic worm-like micellar fluid and observe two distinctive shear thinning regimes, each of them displaying a Newtonian-like plateau. The shear thinning behavior at larger velocities is in qualitative agreement with macroscopic rheological experiments. The second process, observed at Weissenberg numbers as small as a few percent, appears to have no analog in macro-rheological findings. A simple model introduced earlier captured the observed behavior and implied that the two shear thinning processes correspond to two different length scales in the fluid. This model also reproduces oscillations, which have been observed in this system previously. While the system under macro-shear seems to be near equilibrium for shear rates in the regime of the intermediate Newtonian-like plateau, the one under micro-shear is thus still far from it. The analysis suggests the existence of a length scale of a few micrometres, the nature of which remains elusive.

Fluid Viscoelasticity Triggers Fast Transitions of a Brownian Particle in a Double Well Optical Potential

Thermally activated transitions are ubiquitous in nature, occurring in complex environments which are typically conceived as ideal viscous fluids. We report the first direct observations of a Brownian bead transiting between the wells of a bistable optical potential in a viscoelastic fluid with a single long relaxation time. We precisely characterize both the potential and the fluid, thus enabling a neat comparison between our experimental results and a theoretical model based on the generalized Langevin equation. Our findings reveal a drastic amplification of the transition rates compared to those in a Newtonian fluid, stemming from the relaxation of the fluid during the particle crossing events.

Bayesian inference of the viscoelastic properties of a Jeffrey's fluid using optical tweezers

Bayesian inference is a conscientious statistical method which is successfully used in many branches of physics and engineering. Compared to conventional approaches, it makes highly efficient use of information hidden in a measured quantity by predicting the distribution of future data points based on posterior information. Here we apply this method to determine the stress-relaxation time and the solvent and polymer contributions to the frequency dependent viscosity of a viscoelastic Jeffrey's fluid by the analysis of the measured trajectory of an optically trapped Brownian particle. When comparing the results to those obtained from the auto-correlation function, mean-squared displacement or the power spectrum, we find Bayesian inference to be much more accurate and less affected by systematic errors.

Active Brownian and inertial particles in disordered environments: Short-time expansion of the mean-square displacement

We consider an active Brownian particle moving in a disordered two-dimensional energy or motility landscape. The averaged mean-square displacement (MSD) of the particle is calculated analytically within a systematic short-time expansion. As a result, for overdamped particles, both an external random force field and disorder in the self-propulsion speed induce ballistic behavior adding to the ballistic regime of an active particle with sharp self-propulsion speed. Spatial correlations in the force and motility landscape contribute only to the cubic and higher-order powers in time for the MSD. Finally, for inertial particles two superballistic regimes are found where the scaling exponent of the MSD with time is α=3 and α=4. We confirm our theoretical predictions by computer simulations. Moreover, they are verifiable in experiments on self-propelled colloids in random environments.

Aging of living polymer networks: a model with patchy particles

Microrheology experiments show that viscoelastic media composed by wormlike micellar networks display complex relaxations lasting seconds even at the scale of micrometers. By mapping a model of patchy colloids with suitable mesoscopic elementary motifs to a system of worm-like micelles, we are able to simulate its relaxation dynamics, upon a thermal quench, spanning many decades, from microseconds up to tens of seconds. After mapping the model to real units and to experimental scission energies, we show that the relaxation process develops through a sequence of non-local and energetically challenging arrangements. These adjustments remove undesired structures formed as a temporary energetic solution for stabilizing the thermodynamically unstable free caps of the network. We claim that the observed scale-free nature of this stagnant process may complicate the correct quantification of experimentally relevant time scales as the Weissenberg number.

Negative friction memory induces persistent motion

We investigate the mean-square displacement (MSD) for random motion governed by the generalized Langevin equation for memory functions that contain two different time scales: In the first model, the memory kernel consists of a delta peak and a single-exponential and in the second model of the sum of two exponentials. In particular, we investigate the scenario where the long-time exponential kernel contribution is negative. The competition between positive and negative friction memory contributions produces an enhanced transient persistent regime in the MSD, which is relevant for biological motility and active matter systems.

Extremely Long-Range Light-Driven Repulsion of Porous Microparticles

The repulsive surface forces, such as electrostatic or steric, acting between particles explain why they remain well separated in aqueous electrolyte solutions and are responsible for the stability of colloidal dispersions. However, the effective range of these interactions is always well below hundreds of nanometers and typically can be controlled by advanced manipulations such as tuning the electrolyte concentration or modifying the particle surface or, in some more specific cases, via subjecting the suspension to an external electric or magnetic field. Here we employ solutions with small additives of a photosensitive ionic surfactant to investigate if a repulsive interaction of microsized particles sedimented at the solid surface can be remotely controlled simply by illuminating it with an appropriate wavelength. We show that interactions of conventional impermeable particles remain practically unaffected by light, but, in contrast, for porous particles, we observe a long-range repulsion, several orders of magnitude longer than any conceivable equilibrium surface force. This repulsion emerges due to the diffusio-osmotic flow generated near the porous particles that in this scenario are playing a role of micropumps. The diffusio-osmotic repulsion of porous particles can be used for a remote control of their two-dimensional assemblies at the solid wall, and in particular, we demonstrate that by simply using two different illumination wavelengths it is possible to reversibly switch the state of porous particle dispersion from densely packed surface aggregates to a periodic lattice of particles separated by distances on the order of tens of micrometers.

Cell viscoelasticity is linked to fluctuations in cell biomass distributions

The viscoelastic properties of mammalian cells can vary with biological state, such as during the epithelial-to-mesenchymal (EMT) transition in cancer, and therefore may serve as a useful physical biomarker. To characterize stiffness, conventional techniques use cell contact or invasive probes and as a result are low throughput, labor intensive, and limited by probe placement. Here, we show that measurements of biomass fluctuations in cells using quantitative phase imaging (QPI) provides a probe-free, contact-free method for quantifying changes in cell viscoelasticity. In particular, QPI measurements reveal a characteristic underdamped response of changes in cell biomass distributions versus time. The effective stiffness and viscosity values extracted from these oscillations in cell biomass distributions correlate with effective cell stiffness and viscosity measured by atomic force microscopy (AFM). This result is consistent for multiple cell lines with varying degrees of cytoskeleton disruption and during the EMT. Overall, our study demonstrates that QPI can reproducibly quantify cell viscoelasticity.

Mass-Dependent Solvent Friction of a Hydrophobic Molecule

We show by molecular dynamics simulations that the friction constant of a freely diffusing methane molecule in explicit water increases with the methane mass by a factor of up to 1.8 in the infinite mass limit compared to the massless limit. This effect is rationalized by the mass dependence of the friction memory kernel which is extracted from the simulation data by mapping on the generalized Langevin equation. On the basis of the mass-dependent memory kernels, we obtain perfect agreement between simulation results and analytic predictions for both mean-square displacements and force autocorrelation functions. The memory kernels, which account for methane interactions with the solvent, decay significantly slower with increasing methane mass. The mass-dependent friction is correlated with the mean escape time of water molecules from the first hydration shell, which increases monotonically with the methane mass by a factor of 3 over the mass range considered. Our proposed scaling expression allows the direct prediction of diffusion constants for stable methane isotopes, which will help to better understand bacterial methane isotope fractionation. Our scaling analysis suggests that mass-dependent friction will be relevant also for larger solutes in sufficiently viscous solvents.

Memory-kernel extraction for different molecular solutes in solvents of varying viscosity in confinement

The friction coefficient of molecular solutes depends on the solute, on the solvent, and on the solute-solvent interactions, but is typically assumed to not depend on an externally applied force that acts on the solute. In this paper we compute the friction memory function from molecular dynamics simulations and show that the friction coefficients of harmonically confined methane, water, Na^{+}, an artificial Na^{-} ion, and glycerol in water in fact increase with confinement strength. The results show that the friction increase with confinement strength is a fundamental effect that occurs for hydrophobic, hydrophilic, as well as charged molecules. We demonstrate that a parameter-free extraction of the running integral over the memory function yields the most robust results when compared to methods based on parametrization or Fourier transforms. In all systems, this friction increase is accompanied by a slowdown of the solvent dynamics in the first hydration shell of the solutes. By simulations of a confined glycerol molecule in water-glycerol mixtures, we furthermore demonstrate that the friction dependence on the confining potential is magnified in more viscous solvents, which suggests that this effect plays an important role for larger molecules in highly viscous solutions like polymer melts, in line with dynamic scaling arguments.

Non-Markovian barrier crossing with two-time-scale memory is dominated by the faster memory component

We investigate non-Markovian barrier-crossing kinetics of a massive particle in one dimension in the presence of a memory function that is the sum of two exponentials with different memory times, [Formula: see text] and [Formula: see text] . Our Langevin simulations for the special case where both exponentials contribute equally to the total friction show that the barrier-crossing time becomes independent of the longer memory time if at least one of the two memory times is larger than the intrinsic diffusion time. When we associate memory effects with coupled degrees of freedom that are orthogonal to a one-dimensional reaction coordinate, this counterintuitive result shows that the faster orthogonal degrees of freedom dominate barrier-crossing kinetics in the non-Markovian limit and that the slower orthogonal degrees become negligible, quite contrary to the standard time-scale separation assumption and with important consequences for the proper setup of coarse-graining procedures in the non-Markovian case. By asymptotic matching and symmetry arguments, we construct a crossover formula for the barrier crossing time that is valid for general multi-exponential memory kernels. This formula can be used to estimate barrier-crossing times for general memory functions for high friction, i.e. in the overdamped regime, as well as for low friction, i.e. in the inertial regime. Typical examples where our results are important include protein folding in the high-friction limit and chemical reactions such as proton-transfer reactions in the low-friction limit.

Dynamic ordering of driven spherocylinders in a nonequilibrium suspension of small colloidal spheres

The ordering effects of driven spherocylinder-shaped rods in a colloidal suspension of small spheres confined to a two-dimensional channel geometry are observed via Brownian dynamics simulations without hydrodynamics. To describe the ordering, an order parameter and an expression for a potential of mean force of an equivalent equilibrium system are defined and analyzed. By varying the application point of the external force along the rods and thus the resulting lever, a transition from a preferred orientation parallel to the direction of the force to a preferred orientation perpendicular to the direction of the force was observed. It is shown that this effect can only be found if the spheres and multiple rods are present. Furthermore, a dependency of the order parameter on the absolute value of the force was discovered. The analysis of the potential of mean force further indicates a transition between two different phases of mean orientation. An observation of the flow equilibrium mean velocity in channel direction led to a s-shaped progression regarding the lever dependency, also marking a transition between two states linked to the mean orientation of the rods. A finite size analysis was conducted. Its results indicate that the transition between the two orientation states is a general phenomenon of the observed rod-sphere mixture.

Tracer diffusion in crowded narrow channels

We summarise different results on the diffusion of a tracer particle in lattice gases of hard-core particles with stochastic dynamics, which are confined to narrow channels-single-files, comb-like structures and quasi-one-dimensional channels with the width equal to several particle diameters. We show that in such geometries a surprisingly rich, sometimes even counter-intuitive, behaviour emerges, which is absent in unbounded systems. This is well-documented for the anomalous diffusion in single-files. Less known is the anomalous dynamics of a tracer particle in crowded branching single-files-comb-like structures, where several kinds of anomalous regimes take place. In narrow channels, which are broader than single-files, one encounters a wealth of anomalous behaviours in the case where the tracer particle is subject to a regular external bias: here, one observes an anomaly in the temporal evolution of the tracer particle velocity, super-diffusive at transient stages, and ultimately a giant diffusive broadening of fluctuations in the position of the tracer particle, as well as spectacular multi-tracer effects of self-clogging of narrow channels. Interactions between a biased tracer particle and a confined crowded environment also produce peculiar patterns in the out-of-equilibrium distribution of the environment particles, very different from the ones appearing in unbounded systems. For moderately dense systems, a surprising effect of a negative differential mobility takes place, such that the velocity of a biased tracer particle can be a non-monotonic function of the force. In some parameter ranges, both the velocity and the diffusion coefficient of a biased tracer particle can be non-monotonic functions of the density. We also survey different results obtained for a tracer particle diffusion in unbounded systems, which will permit a reader to have an exhaustively broad picture of the tracer diffusion in crowded environments.

Optical Tweezers Microrheology: From the Basics to Advanced Techniques and Applications

Over the past few decades, microrheology has emerged as a widely used technique to measure the mechanical properties of soft viscoelastic materials. Optical tweezers offer a powerful platform for performing microrheology measurements and can measure rheological properties at the level of single molecules out to near macroscopic scales. Unlike passive microrheology methods, which use diffusing microspheres to extract rheological properties, optical tweezers can probe the nonlinear viscoelastic response, and measure the space- and time-dependent rheological properties of heterogeneous, nonequilibrium materials. In this Viewpoint, I describe the basic principles underlying optical tweezers microrheology, the instrumentation and material requirements, and key applications to widely studied soft biological materials. I also describe several sophisticated approaches that include coupling optical tweezers to fluorescence microscopy and microfluidics. The described techniques can robustly characterize noncontinuum mechanics, nonlinear mechanical responses, strain-field heterogeneities, stress propagation, force relaxation dynamics, and time-dependent mechanics of active materials.

Memory-Induced Transition from a Persistent Random Walk to Circular Motion for Achiral Microswimmers

We experimentally study the motion of light-activated colloidal microswimmers in a viscoelastic fluid. We find that, in such a non-Newtonian environment, the active colloids undergo an unexpected transition from enhanced angular diffusion to persistent rotational motion above a critical propulsion speed, despite their spherical shape and stiffness. We observe that, in contrast to chiral asymmetric microswimmers, the resulting circular orbits can spontaneously reverse their sense of rotation and exhibit an angular velocity and a radius of curvature that nonlinearly depend on the propulsion speed. By means of a minimal non-Markovian Langevin model for active Brownian motion, we show that these nonequilibrium effects emerge from the delayed response of the fluid with respect to the self-propulsion of the particle without counterpart in Newtonian fluids.

Long-time anomalous swimmer diffusion in smectic liquid crystals

The dynamics of self-locomotion of active particles in aligned or liquid crystalline fluids strongly deviates from that in simple isotropic media. We explore the long-time dynamics of a swimmer moving in a three-dimensional smectic liquid crystal and find that the mean-square displacement transverse to the director exhibits a distinct logarithmic tail at long times. The scaling is distinctly different from that in an isotropic or nematic fluid and hints at the subtle but important role of the director fluctuation spectrum in governing the long-time motility of active particles. Our findings are based on a generic hydrodynamic theory and Brownian dynamics computer simulation of a three-dimensional soft mesogen model.