arXiv subjects

Maria L. Ekiel-Jezewska

Publications and source records attributed to Maria L. Ekiel-Jezewska.

At least 19 recordsLinked to original sources

arXiv2026

Experimental and numerical study of the dynamics of sedimenting pairs of semi-flexible fibers close to attractive `aligned' relative configuration

Dynamics of two short semi-flexible fibers settling under gravity in a viscous fluid are investigated at Reynolds numbers Re << 1. We focus on fibers initially relatively close to each other, and we check if later they approach an aligned horizontal configuration, previously identified numerically (Bukowicki and Ekiel-Jezewska, Soft Matter 46 (2019) 9379) as attractive for symmetric initial conditions of moderately elastic filaments. In our experiments, two semi-flexible ball chains sediment in a highly viscous silicone oil. They are initially straight and close to a parallel horizontal relative configuration. Their motion and shape deformation are recorded using two synchronized cameras. For most of the trials, ball chains stay together, with damped oscillations around the symmetric aligned configuration. For a few initial conditions, the ball chains move away horizontally or vertically. To study the behavior over a longer time, we perform numerical simulations, modeling moderately elastic filaments as chains of identical beads, with the centers of consecutive beads connected by springs and with the fibers' elastic resistance to bending. Different initial positions and orientations are considered. Their dynamics are determined by the multipole expansion of the Stokes equations, implemented in the precise Hydromultipole numerical code. For short times, we observe the similar dynamics of semi-flexible ball chains and moderately elastic filaments. We provide examples of long-time numerical simulations illustrating that elastic filaments close to each other can move away horizontally or vertically, but after a long time, come back and perform damped oscillations while approaching the aligned configuration with almost touching filament ends. We confirm the attractive nature of the aligned configuration of very close semi-flexible sedimenting fibers, even if they are far away from each other.

physics.flu-dyn↗

arXiv2025

Sedimenting rigid particles of certain shapes approach a stationary orientation

This work investigates experimentally and numerically the dynamics of rigid particles settling under gravity in a highly viscous fluid. We demonstrate that certain shapes: cones, crescent moons, arrowheads, and open flat rings reorient and approach a stationary configuration. We determine the mobility coefficients and the characteristic reorientation times. We find out that the two rotational-translational mobility coefficients have opposite signs. Therefore, based on the equations of motion for rigid bodies with two orthogonal planes of symmetry, theoretically derived by Joshi and Govindarajan, Phys. Rev. Lett., 134, 2025, 014002 and Ekiel-Jezewska and Wajnryb, J. Phys. Condens. Matter, 21, 2009, 204102, we conclude that the approached stationary configurations are stable. Owing to the similarity principle, our experimental findings apply to micro-objects in water-based solutions. The reorientation of sedimenting rigid particles of certain shapes to a stationary stable configuration in a relatively short time might be used for biological, medical, or industrial applications.

cond-mat.soft↗

arXiv2024

Dynamical modes of highly elastic loops settling under gravity in a viscous fluid

The settling of highly elastic non-Brownian closed fibres (called loops) under gravity in a viscous fluid is investigated numerically. The loops are represented using a bead-spring model with harmonic bending potential and finitely extensible nonlinear elastic (FENE) stretching potential. Numerical solutions to the Stokes equations are obtained with the use of HYDROMULTIPOLE numerical codes, which are based on the multipole method corrected for lubrication to calculate hydrodynamic interactions between spherical particles with high precision. Depending on the elasto-gravitation number B, a ratio of gravitation to bending forces, the loop approaches different attracting dynamical modes, as described by Gruziel-Slomka et al. (Soft Matter, vol. 15, 2019, pp. 7262-7274) with the use of the Rotne-Prager mobility of the elastic loop made of beads. Here, using a more precise method, we find and characterise a new mode, analyse typical timescales, velocities, and orientations of all the modes, compare them, and investigate their coexistence. We analyse the transitions (bifurcations) to a different mode at certain critical values of the elasto-gravitation number B.

cond-mat.soft↗

arXiv2024

Scaling law for a buckled elastic filament in a shear flow

We analyze the three-dimensional buckling of an elastic filament in a shear flow of a viscous fluid at low Reynolds number and high Peclet number. We apply the Euler-Bernoulli beam (elastica) theoretical model. We show the universal character of the full 3D spectral problem for the small perturbation of the thin filament from a straight position of arbitrary orientation. We use the eigenvalues and eigenfunctions for the linearized elastica equation in the shear plane, found earlier by [Liu et al., 2024] with the Chebyshev spectral collocation method, to solve the full 3D eigenproblem. We provide a simple analytic approximation to the eigenfunctions, represented as Gaussian wavepackets. As the main result of the paper, we derive square-root dependence of the eigenfunction wavenumber on the parameter $\tildeχ=-η\sin 2ϕ\sin^2θ$, where $η$ is the elastoviscous number, and the filament orientation is determined by the zenith angle $θ$ with respect to the vorticity direction and the azimuthal angle $ϕ$ relative to the flow direction. We also compare the eigenfunctions with shapes of slightly buckled elastic filaments with a non-negligible thickness with the same Young's modulus, using the bead model and performing numerical simulations with the precise Hydromultipole numerical codes.

physics.flu-dyn↗

arXiv2023

Spectral analysis for elastica 3-dimensional dynamics in a shear flow

We present the spectral analysis of three-dimensional dynamics of an elastic filament in a shear flow of a viscous fluid at a low Reynolds number in the absence of Brownian motion. The elastica model is used. The fiber initially is almost straight at an arbitrary orientation, with small perpendicular perturbations in the shear plane and out-of-plane. To analyze the stability of both perturbations, equations for the eigenvalues and eigenfunctions are derived and solved by the Chebyshev spectral collocation method. It is shown that their crucial features are the same as in the case of the two-dimensional elastica dynamics in shear flow [Becker and Shelley, Phys. Rev. Lett. 2001] and the three-dimensional elastica dynamics in the compressional flow [Chakrabarti et al., Nat. Phys., 2020]. We find a similar dependence of the buckled shapes on the ratio of bending to hydrodynamic forces as in the simulations for elastic fibers of a nonzero thickness [Slowicka et al., New J. Phys., 2022].

physics.flu-dyn↗

arXiv2023

Dynamics of Ball-Chains and Very Elastic Fibres Settling under Gravity in a Viscous Fluid

We study experimentally the dynamics of one and two ball-chains settling under gravity in a very viscous fluid at a Reynolds number much smaller than unity. We demonstrate that single ball-chains in most cases do not tend to be planar and often rotate, not keeping the ends at the same horizontal level. Shorter ball-chains usually form shapes resembling distorted U, and longer ones in the early stage of the evolution form a shape resembling distorted W, and later deform non-symmetrically and significantly out of plane. This behaviour is reproduced in our numerical simulations for a single very elastic filament, with the use of the bead model and multipole expansion of the Stokes equations, corrected for lubrication and implemented in the precise Hydromultipole numerical codes. In our experiments, two ball-chains, initially one above the other, later move away or approach each other, for a larger or smaller initial distance, respectively.

physics.flu-dyn↗

arXiv2018

Periodic motion of sedimenting flexible knots

We study the dynamics of knotted deformable closed chains sedimenting in a viscous fluid. We show experimentally that trefoil and other torus knots often attain a remarkably regular horizontal toroidal structure while sedimenting, with a number of intertwined loops, oscillating periodically around each other. We then recover this motion numerically and find out that it is accompanied by a very slow rotation around the vertical symmetry axis. We analyze the dependence of the characteristic time scales on the chain flexibility and aspect ratio. It is observed in the experiments that this oscillating mode of the dynamics can spontaneously form even when starting from a qualitatively different initial configuration. In numerical simulations, the oscillating modes are usually present as transients or final stages of the evolution, depending on chain aspect ratio and flexibility, and the number of loops.

cond-mat.soft↗

arXiv2016

Note: Brownian motion of colloidal particles of arbitrary shape

The analytical expressions for the time-dependent cross-correlations of the translational and rotational Brownian displacements of a particle with arbitrary shape are derived. The reference center is arbitrary, and the reference frame is such that the rotational-rotational diffusion tensor is diagonal.

cond-mat.soft↗

arXiv2015

Periodic and quasiperiodic motions of many particles falling in a viscous fluid

Dynamics of regular clusters of many non-touching particles falling under gravity in a viscous fluid at low Reynolds number are analysed within the point-particle model. Evolution of two families of particle configurations is determined: 2 or 4 regular horizontal polygons (called `rings') centred above or below each other. Two rings fall together and periodically oscillate. Four rings usually separate from each other with chaotic scattering. For hundreds of thousands of initial configurations, a map of the cluster lifetime is evaluated, where the long-lasting clusters are centred around periodic solutions for the relative motions, and surrounded by regions of the chaotic scattering,in a similar way as it was observed by Janosi et al. (1997) for three particles only. These findings suggest to consider the existence of periodic orbits as a possible physical mechanism of the existence of unstable clusters of particles falling under gravity in a viscous fluid.

cond-mat.soft↗

arXiv2015

Dynamics of flexible fibers in shear flow

Dynamics of flexible non-Brownian fibers in shear flow at low-Reynolds-number are analyzed numerically for a wide range of the ratios A of the fiber bending force to the viscous drag force. Initially, the fibers are aligned with the flow, and later they move in the plane perpendicular to the flow vorticity. A surprisingly rich spectrum of different modes is observed when the value of A is systematically changed, with sharp transitions between coiled and straightening out modes, period-doubling bifurcations from periodic to migrating solutions, irregular dynamics and chaos.

cond-mat.soft↗

arXiv2015

Brownian motion of a particle with arbitrary shape

Brownian motion of a particle with an arbitrary shape is investigated theoretically. Analytical expressions for the time-dependent cross-correlations of the Brownian translational and rotational displacements are derived from the Smoluchowski equation. The role of the particle mobility center is determined and discussed.

cond-mat.stat-mech↗

arXiv2015

Dynamics and Topology of Flexible Chains: Knots in Steady Shear Flows

We use numerical simulations of a bead-spring model chain to investigate the evolution of the conformation of long and flexible elastic fibers in a steady shear flow. In particular, for rather open initial configurations, and by varying a dimensionless elastic parameter, we identify two distinct conformational modes with different final size, shape, and orientation. Through further analysis we identify slipknots in the chain. Finally, we provide examples of initial configurations of an "open" trefoil knot that the flow unknots and then knots again, sometimes repeating several times. These changes in topology should be reflected in changes in bulk rheological and/or transport properties.

cond-mat.soft↗

arXiv2014

Dynamics of elastic dumbbells sedimenting in a viscous fluid: oscillations and hydrodynamic repulsion

Hydrodynamic interactions between two identical elastic dumbbells settling under gravity in a viscous fluid at low-Reynolds-number are investigated within the point-particle model. Evolution of a benchmark initial configuration is studied, in which the dumbbells are vertical and their centres are aligned horizontally. Rigid dumbbells and pairs of separate beads starting from the same positions tumble periodically while settling down. We find that elasticity (which breaks time-reversal symmetry of the motion) significantly affects the system's dynamics. This is remarkable taking into account that elastic forces are always much smaller than gravity. We observe oscillating motion of the elastic dumbbells, which tumble and change their length non-periodically. Independently of the value of the spring constant, a horizontal hydrodynamic repulsion appears between the dumbbells - their centres of mass move apart from each other horizontally. The shift is fast for moderate values of the spring constant k, and slows down when k tends to zero or to infinity; in these limiting cases we recover the periodic dynamics reported in the literature. For moderate values of the spring constant, and different initial configurations, we observe the existence of a universal time-dependent solution to which the system converges after an initial relaxation phase. The tumbling time and the width of the trajectories in the centre-of-mass frame increase with time. In addition to its fundamental significance, the benchmark solution presented here is important to understand general features of systems with larger number of elastic particles, at regular and random configurations.

physics.flu-dyn↗

arXiv2014

A class of periodic and quasi-periodic trajectories of particles settling under gravity in a viscous fluid

We investigate regular configurations of a small number of particles settling under gravity in a viscous fluid. The particles do not touch each other and can move relative to each other. The dynamics is analyzed in the point-particle approximation. A family of regular configurations is found with periodic oscillations of all the settling particles. The oscillations are shown to be robust under some out-of-phase rearrangements of the particles. In the presence of an additional particle above such a regular configuration, the particle periodic trajectories are horizontally repelled from the symmetry axis, and flattened vertically. The results are used to propose a mechanism how a spherical cloud, made of a large number of particles distributed at random, evolves and destabilizes.

physics.flu-dyn↗

arXiv2014

Hydrodynamic interactions between a sphere and a number of small particles

Exact expressions are derived for the pair and three-body hydrodynamic interactions between a sphere and a number of small particles immersed in a viscous incompressible fluid. The analysis is based on the Stokes equations of low Reynolds number hydrodynamics. The results follow by a combination of the solutions for flow about a sphere with no-slip boundary condition derived by Stokes and Kirchhoff, and the result derived by Oseen for the Green tensor of Stokes' equations in the presence of a fixed sphere.

physics.flu-dyn↗

arXiv2014

Hydrodynamic radius approximation for spherical particles suspended in a viscous fluid: influence of particle internal structure and boundary

Systems of spherical particles moving in Stokes flow are studied for a different particle internal structure and boundaries, including the Navier-slip model. It is shown that their hydrodynamic interactions are well described by treating them as solid spheres of smaller hydrodynamic radii, which can be determined from measured single-particle diffusion or intrinsic viscosity coefficients. Effective dynamics of suspensions made of such particles is quite accurately described by mobility coefficients of the solid particles with the hydrodynamic radii, averaged with the unchanged direct interactions between the particles.

cond-mat.soft↗

arXiv2012

Lateral migration of flexible fibers in Poiseuille flow between two parallel planar solid walls

Dynamics of non-Brownian flexible fibers in Poiseuille flow between two parallel planar solid walls is evaluated from the Stokes equations, solved numerically by an accurate multipole code HYDROMULTIPOLE. Fibers migrate towards a critical distance from the wall zc, which depends significantly on the fiber length N and bending stiffness A. Therefore, the calculated values of zc can be used to sort fibers. Three modes of the dynamics are found, depending on a shear-to-bending parameter Gamma. In the first mode, stiff fibers deform only a little and accumulate close to the wall, as the result of a balance between the tendency to drift away from the channel and the repulsive hydrodynamic interaction with the wall. This mechanism is confirmed by simulations in the unbounded Poiseuille flow. In the second mode, flexible fibers deform significantly and accumulate far from the wall. In both modes, the tumbling pattern is repeatable. In the third mode, the fibers are even more curved, and their tumbling is irregular.

cond-mat.soft↗

arXiv2012

Short-time dynamics and high-frequency rheology of core-shell suspensions with thin-shells

Short-time dynamics and high-frequency rheology for suspensions of non-overlapping core-shell particles with thin shells were analyzed. In the thin-shell limit, the single-particle scattering coefficients were derived and shown to define a unique effective radius. This result was used to justify theoretically (in the thin-shell limit) the accuracy of the annulus approximation with the inner radius equal to the effective hydrodynamic radius of the core-shell particle. The two-particle virial expansion of the translational & rotational self-diffusion, sedimentation and viscosity was performed. The virial coefficients were evaluated and shown to be accurately approximated by the effective annulus model, in contrast to the imprecise effective hard sphere model.

cond-mat.soft↗