arXiv subjects

Andrej Vilfan

Publications and source records attributed to Andrej Vilfan.

At least 19 recordsLinked to original sources

arXiv2026

Mixing induced by microswimmers as probed by mutual information

We investigate fluid mixing induced by microswimmers using mutual information as a global, information-theoretic measure of mixing efficiency. For a two-dimensional squirmer model in a confined domain, we compute numerically the swimmer-generated flows and solve the advection-diffusion equation for the transport of tracer particles in the fluid. We show that the spatial distribution of swimmers strongly affects mixing, which is suppressed by swimmer aggregation and enhanced by positional and orientational disorder. At fixed energy dissipation, mixing efficiency depends non-monotonically on the squirmer parameter, with an optimal finite value arising from the balance between swimmer translation and dipolar flow generation. When hydrodynamic interactions are included, pushers outperform pullers. The mutual information as a function of time decays in three stages: an initial diffusion-dominated stage, an intermediate advection enhanced regime, and a final relaxation stage controlled by system size. Our results demonstrate that mutual information, previously validated as a measure of mixing efficiency only in simplified model systems, can equally be used in complex flows. Its application reveals that mixing by microswimmers is subject to a trade-off between the generation of strong shear flows and achieving optimal dispersion across the fluid domain.

cond-mat.soft↗

arXiv2026

Self-phoretic colloids in chiral active fluids

Autonomous and driven transport in chiral active fluids have been shown to exhibit features that cannot be accommodated within the classical formulation of fluid mechanics, due to the role of odd viscosity. We generalize the theory of phoretic active matter to fluid environments with odd viscosity and derive expressions for translational and rotational self-propulsion velocities in the case of a spherical swimmer with arbitrary activity and mobility surface profiles. We discuss specific examples of chemically active colloids with axisymmetric and non-axisymmetric coatings and the resulting interplay between symmetry and chirality. Our results can be applied to study the emergent collective dynamics of phoretic particles in fluid media with broken time-reversal and parity symmetries.

cond-mat.soft↗

arXiv2025

Asymptotic limits of the axisymmetric solution of the Brinkman equation for a point force near a no-slip wall

We derive the far-field and near-field solutions for the Green's function of a point force acting perpendicular to a no-slip wall in a Brinkman fluid, focusing on the regime where the distance between the force and the wall is much smaller than the screening length. The general solution is obtained in closed form up to a single integral and can be systematically expanded in a Taylor series in both the far-field and near-field limits. The flow can then be expressed as a series of source-multipole singularities with an additional, analytically known, correction in the proximity of the wall. Comparisons with numerical integration demonstrate the accuracy and reliability of the asymptotic expansions. The results are also applicable to the unsteady Stokes flow driven by a localized assembly of forces, such as a beating cilium protruding from a flat surface.

physics.flu-dyn↗

arXiv2025

Stokes drag on a sphere in a three-dimensional anisotropic porous medium

We study the hydrodynamic drag force exerted on a sphere in a static anisotropic porous medium. This problem is analysed using the Brinkman-Debye-Bueche equations with an axisymmetric shielding (or permeability) tensor. Using the exact Green's functions for this model fluid within a single-layer boundary element formulation, we numerically compute the friction tensor for a translating sphere subjected to stick boundary conditions. Furthermore, we derive approximate analytical expressions for small anisotropy using the Lorentz reciprocal theorem. By benchmarking this result against the numerical solutions, we find that a linear approximation is valid in a broad parameter regime. Our results are important for studying self-diffusion in general anisotropic porous media, but can also be applied to small tracers in nematic fluids composed of disk- or rod-like crowders.

cond-mat.soft↗

arXiv2025

Information-optimal mixing at low Reynolds number

Mutual information between particle positions before and after mixing provides a universal assumption-free measure of mixing efficiency at low Reynolds number which accounts for the kinematic reversibility of the Stokes equation. For a generic planar shear flow with time-dependent shear rate, we derive a compact expression for the mutual information as a nonlinear functional of the shearing protocol and solve the associated extremisation problem exactly to determine the optimal control under both linear and non-linear constraints, specifically total shear and total dissipation per unit volume. Remarkably, optimal protocols turn out to be universal and time-reversal symmetric in both cases. Our results establish a minimum energetic cost of erasing information in a broad class of non-equilibrium drift-diffusive systems.

cond-mat.stat-mech↗

arXiv2025

Hydrodynamic flow field and frictional resistance coefficient of a disk rotating steadily in a compressible fluid layer with odd viscosity on a rigid substrate

We analyze the hydrodynamics of a rotating disk in a two-dimensional compressible fluid layer with odd viscosity. Unlike conventional fluids, odd viscosity introduces a radial flow component that can be directed either inward or outward, depending on its sign. This phenomenon is expected to significantly impact the hydrodynamic interactions between two rotating disks, potentially causing effective attraction or repulsion depending on the sign of the odd viscosity and the direction of rotation. Furthermore, we calculate the rotational resistance coefficient and find that odd viscosity increases this coefficient, regardless of its sign.

physics.flu-dyn↗

arXiv2025

On force balance in Brinkman fluids under confinement

A point force acting on a Brinkman fluid in confinement is always counterbalanced by the force on the porous medium, the force on the walls and the stress at open boundaries. We discuss the distribution of those forces in different geometries: a long pipe, a medium with a single no-slip planar boundary, a porous sphere with an open boundary and a porous sphere with a no-slip wall. We determine the forces using the Lorentz reciprocal theorem and additionally validate the results with explicit analytical flow solutions. We discuss the relevance of our findings for cellular processes such as cytoplasmic streaming and centrosome positioning.

physics.flu-dyn↗

arXiv2025

Analytical solution for the hydrodynamic resistance of a disk in a compressible fluid layer with odd viscosity on a rigid substrate

Chiral active fluids can exhibit odd viscosity, a property that breaks the time-reversal and parity symmetries. Here, we examine the hydrodynamic flows of a rigid disk moving in a compressible 2D fluid layer with odd viscosity, supported by a thin lubrication layer of a conventional fluid. Using the 2D Green's function in Fourier space, we derive an exact analytical solution for the flow around a disk of arbitrary size, as well as its resistance matrix. The resulting resistance coefficients break the Onsager reciprocity, but satisfy the Onsager-Casimir reciprocity to any order in odd viscosity.

physics.flu-dyn↗

arXiv2024

Chirotactic response of microswimmers in fluids with odd viscosity

Odd viscosity is a property of chiral active fluids with broken time-reversal and parity symmetries. We show that the flow of such a fluid around a rotating axisymmetric body is exactly solvable and use this solution to determine the orientational dynamics of surface-driven microswimmers. Swimmers with a force-dipole moment exhibit precession around the axis of the odd viscosity. In addition, pushers show bimodal chirotaxis, i.e., alignment parallel or antiparallel to the axis, while pullers orbit in a plane perpendicular to it. A chiral swimmer that itself has a broken parity symmetry can exhibit unimodal chirotaxis and always align in the same direction.

cond-mat.soft↗

arXiv2024

Hydrodynamic efficiency limit on a Marangoni surfer

A Marangoni surfer is an object embedded in a gas-liquid interface, propelled by gradients in surface tension. We derive an analytical theorem for the lower bound on the viscous dissipation by a Marangoni surfer in the limit of small Reynolds and capillary numbers. The minimum dissipation can be expressed with the reciprocal difference between drag coefficients of two passive bodies of the same shape as the Marangoni surfer, one in a force-free interface and the other in an interface with surface incompressibility. The distribution of surface tension that gives the optimal propulsion is given by the surface tension of the solution for the incompressible surface and the flow is a superposition of both solutions. For a surfer taking the form of a thin circular disk, the minimum dissipation is $16μa V^2$, giving a Lighthill efficiency of $1/3$. This places the Marangoni surfers among the hydrodynamically most efficient microswimmers.

physics.flu-dyn↗

arXiv2023

Mutual information as a measure of mixing efficiency in viscous fluids

Because of the kinematic reversibility of the Stokes equation, fluid mixing at the microscale requires an interplay between advection and diffusion. Here we introduce mutual information between particle positions before and after mixing as a measure of mixing efficiency. We demonstrate its application in a Couette flow in an annulus and show that non-uniform rotation sequences can lead to more efficient mixing. We also determine mutual information from Brownian dynamics simulations using data compression algorithms. Our results show that mutual information provides a universal and assumption-free measure of mixing efficiency in microscale flows.

physics.flu-dyn↗

arXiv2023

Lorentz Reciprocal Theorem in Fluids with Odd Viscosity

The Lorentz reciprocal theorem -- that is used to study various transport phenomena in hydrodynamics -- is violated in chiral active fluids that feature odd viscosity with broken time-reversal and parity symmetries. Here we show that the theorem can be generalized to fluids with odd viscosity by choosing an auxiliary problem with the opposite sign of the odd viscosity. We demonstrate the application of the theorem to two categories of microswimmers. Swimmers with prescribed surface velocity are not affected by odd viscosity, while those with prescribed active forces are. In particular, a torque-dipole can lead to directed motion.

cond-mat.soft↗

arXiv2023

Energetic cost of microswimmer navigation: the role of body shape

We study the energetic efficiency of navigating microswimmers by explicitly taking into account the geometry of their body. We show that, as their shape transitions from prolate to oblate, non-steering microswimmers rotated by flow gradients naturally follow increasingly time-optimal trajectories. At the same time, they also require larger dissipation to swim. The coupling between body geometry and hydrodynamics thus leads to a generic trade-off between the energetic costs associated with propulsion and navigation, which is accompanied by the selection of a finite optimal aspect ratio. We derive from optimal control theory the steering policy ensuring overall minimum energy dissipation, and characterize how navigation performances vary with the swimmer shape. Our results highlight the important role of the swimmer geometry in realistic navigation problems.

cond-mat.soft↗

arXiv2023

Axisymmetric monopole and dipole flow singularities in proximity of a stationary no-slip plate immersed in a Brinkman fluid

Green's function plays an important role in many areas of physical sciences and is a prime tool for solving diverse hydrodynamic equations in the linear regime. In the present contribution, the axisymmetric low-Reynolds-number Brinkman flow induced by monopole and dipole singularities in proximity of a stationary plate of circular shape is theoretically investigated. The flow singularities are directed along the central axis of the plate. No-slip boundary conditions are assumed to hold at the surface of the plate. The Green's functions are determined to a large extent analytically, reducing the solution of the linear hydrodynamic equations to well-behaved one-dimensional integrals amenable to numerical computation. In our approach, the Brinkman flow problem is formulated as a mixed boundary value problem that is subsequently mapped in the form of dual integral equations on the domain boundaries. Thereupon, the solution of the equations of fluid motion is eventually reduced to the solution of two independent Fredholm integral equations of the first kind. The overall flow structure and emerging eddy patterns are found to strongly depend on the magnitude of the relevant geometrical and physical parameters of the system. Moreover, the effect of the confining plate on the dynamics of externally driven or force-free particles is assessed through the calculation of the relevant hydrodynamic reaction functions. The effect of the plate on the locomotory behavior of a self-propelling active dipole swimmer is shown to be maximum when the radius of the plate is comparable to the distance separating the swimmer from the plate. Our results may prove useful for characterizing transport processes in microfluidic devices and may pave the way toward understanding and controlling of small-scale flows in porous media.

cond-mat.soft↗

arXiv2023

Minimum Entropy Production by Microswimmers with Internal Dissipation

The energy dissipation and entropy production by self-propelled microswimmers differ profoundly from passive particles pulled by external forces. The difference extends both to the shape of the flow around the swimmer, as well as to the internal dissipation of the propulsion mechanism. Here we derive a general theorem that provides an exact lower bound on the total, external and internal, dissipation by a microswimmer. The problems that can be solved include an active surface-propelled droplet, swimmers with an extended propulsive layer and swimmers with an effective internal dissipation. We apply the theorem to determine the swimmer shapes that minimize the total dissipation while keeping the volume constant. Our results show that the entropy production by active microswimmers is subject to different fundamental limits than the entropy production by externally driven particles.

cond-mat.soft↗

arXiv2023

Nonreciprocal interactions give rise to fast cilium synchronisation in finite systems

Motile cilia beat in an asymmetric fashion in order to propel the surrounding fluid. When many cilia are located on a surface, their beating can synchronise such that their phases form metachronal waves. Here, we computationally study a model where each cilium is represented as a spherical particle, moving along a tilted trajectory with a position-dependent active driving force and a position-dependent internal drag coefficient. The model thus takes into account all the essential broken symmetries of the ciliary beat. We show that taking into account the near-field hydrodynamic interactions, the effective coupling between cilia can become nonreciprocal: the phase of a cilium is more strongly affected by an adjacent cilium on one side than by a cilium at the same distance in the opposite direction. As a result, synchronisation starts from a seed at the edge of a group of cilia and propagates rapidly across the system, leading to a synchronisation time that scales proportionally to the linear dimension of the system. We show that a ciliary carpet is characterised by three different velocities: the velocity of fluid transport, the phase velocity of metachronal waves and the group velocity of order propagation. Unlike in systems with reciprocal coupling, boundary effects are not detrimental for synchronisation, but rather enable the formation of the initial seed.

cond-mat.soft↗

arXiv2021

Diffusiophoretic propulsion of an isotropic active colloidal particle near a finite-sized disk embedded in a planar fluid-fluid interface

Breaking spatial symmetry is an essential requirement for phoretic active particles to swim at low Reynolds number. This fundamental prerequisite for swimming at the micro-scale is fulfilled either by chemical patterning of the surface of active particles or alternatively by exploiting geometrical asymmetries to induce chemical gradients and achieve self-propulsion. In the present manuscript, a far-field analytical model is employed to quantify the leading-order contribution to the induced phoretic velocity of a chemically homogeneous isotropic active colloid near a finite-sized disk of circular shape resting on an interface separating two immiscible viscous incompressible Newtonian fluids. To this aim, the solution of the phoretic problem is formulated as a mixed-boundary-value problem which is subsequently transformed into a system of dual integral equations on the inner and outer domains. Depending on the ratio of different involved viscosities and solute solubilities, the sign of phoretic mobility and chemical activity, as well as the ratio of particle-interface distance to the radius of the disk, the isotropic active particle is found to be either repelled from the interface, attracted to it, or reach a stable hovering state and remains immobile near the interface. Our results may prove useful in controlling and guiding the motion of self-propelled phoretic active particles near aqueous interfaces.

cond-mat.soft↗

arXiv2021

Optimal swimmer can be puller, pusher, or neutral depending on the shape

The ability of microswimmers to deploy optimal propulsion strategies is of paramount importance for their locomotory performance and survival at low Reynolds numbers. Although for perfectly spherical swimmers minimum dissipation requires a neutral type swimming, any departure from the spherical shape may lead the swimmer to adopt a new propulsion strategy, namely those of puller- or pusher-type swimming. In this study, by using the minimum dissipation theorem for microswimmers, we determine the flow field of an optimal nearly spherical swimmer, and show that indeed depending on the shape profile, the optimal swimmer can be a puller, pusher, or neutral. Using an asymptotic approach, we find that amongst all the modes of the shape function, only the third mode determines to leading order the swimming type of the optimal swimmer.

physics.flu-dyn↗