Spherical particle in Poiseuille flow between planar walls

Cargo Size Limits and Forces of Cell-Driven Microtransport

The integration of motile cells into biohybrid microrobots offers unique properties such as sensitive responses to external stimuli, resilience, and intrinsic energy supply. Here, biohybrid cell-cargo systems that are driven by amoeboid Dictyostelium discoideum cells are studied and how the cargo speed and the resulting viscous drag force scales with increasing radius of the spherical cargo particle are explored. Using a simplified geometrical model of the cell-cargo interaction, the findings toward larger cargo sizes, which are not accessible with the experimental setup, are extrapolated and a maximal cargo size is predicted beyond which active cell-driven movements will stall. The active forces exerted by the cells to move a cargo show mechanoresponsive adaptation and increase dramatically when challenged by an external pulling force, a mechanism that may become relevant when navigating cargo through complex heterogeneous environments.

Hydrodynamic force on a particle oscillating in a viscous fluid near a wall with dynamic partial-slip boundary condition

The hydrodynamic force on a particle oscillating in a viscous fluid near a wall with partial-slip boundary condition is studied on the basis of the linearized Navier-Stokes equations. Both incompressible and compressible fluids are considered. It is assumed that the slip length characterizing the partial-slip boundary condition depends on frequency. The consequences of this assumption for the spectrum of Brownian motion near a wall are investigated and compared with a recent experiment.

Colloidal diffusion inside a spherical cell

The hydrodynamic hindering of a single-particle dynamics under total confinement is measured by optical microscopy. The three-dimensional trajectories of single-colloidal particles confined in spherical water globules of sizes only a few times the particle's diameter are tracked as they sample the entire volume of the globule. The hydrodynamic interactions between the particle and the spherical wall produce a dependence of the short-time diffusion on the particle's distance to the surface and an asymmetry in the radial and tangential components of the local diffusion coefficient, with the diffusion along the tangential direction being faster than along the radial direction. The latter decreasing close to the wall while the former being practically constant.

Hydrodynamic coupling of spherical particles to a planar fluid-fluid interface: theoretical analysis

We have developed a new technique (based on our Cartesian-representation method) to describe hydrodynamic interactions of a spherical particle with an undeformable planar fluid-fluid interface under creeping-flow conditions. The interface can be either surfactant-free or covered with an incompressible surfactant monolayer. We consider the effect of surface incompressibility and surface viscosity on particle motion. The new algorithm allows to calculate particle mobility coefficients for hydrodynamically coupled particles, moving either on the same or on the opposite sides of the interface.

Mean first passage times for bond formation for a Brownian particle in linear shear flow above a wall

Motivated by cell adhesion in hydrodynamic flow, here the authors study bond formation between a spherical Brownian particle in linear shear flow carrying receptors for ligands covering the boundary wall. They derive the appropriate Langevin equation which includes multiplicative noise due to position-dependent mobility functions resulting from the Stokes equation. They present a numerical scheme which allows to simulate it with high accuracy for all model parameters, including shear rate and three parameters describing receptor geometry (distance, size, and height of the receptor patches). In the case of homogeneous coating, the mean first passage time problem can be solved exactly. In the case of position-resolved receptor-ligand binding, they identify different scaling regimes and discuss their biological relevance.

Effect of the wall on the velocity autocorrelation function and long-time tail of Brownian motion in a viscous compressible fluid

Brownian motion of a particle situated near a wall bounding the fluid in which it is immersed is affected by the wall. Specifically, it is assumed that a viscous compressible fluid fills a half space bounded by a plane wall, and that the fluid flow satisfies stick boundary conditions at the wall. The fluctuation-dissipation theorem shows that the velocity autocorrelation function of the Brownian particle can be calculated from the frequency-dependent admittance valid locally. The admittance can be found from the linearized Navier-Stokes equations. The t(-3/2) long-time tail of the velocity relaxation function, valid in bulk fluid, is obliterated by the wall and replaced by a t(-5/2) long-time tail of positive amplitude for motions parallel to the wall and by a t(-5/2) long-time tail of negative amplitude for motions perpendicular to the wall. In both cases the amplitude of the t(-5/2) long-time tail turns out to be independent of fluid compressibility and bulk viscosity.

Hindered mobility of a particle near a soft interface

The translational motion of a solid sphere near a deformable fluid interface is studied in the low Reynolds number regime. In this problem, the fluid flow driven by the sphere is dynamically coupled to the instantaneous conformation of the interface. Using a two-dimensional Fourier transform technique, we are able to account for the multiple backflows scattered from the interface. The correction to the mobility tensor is then obtained from the matrix elements of the relevant Green's function. Our perturbative analysis allows us to express the explicit position and frequency dependence of the mobility for small particles. We recover in the steady limit the result for a sphere near a perfectly flat interface. At intermediate time scales, the mobility exhibits an imaginary part which is a signature of the elastic response of the interface. In the short time limit, we find that the perpendicular mobility may, under some circumstances, become lower than the bulk value. All the results can be explained using the definition of the relaxation time of the soft interface.

Diffusion and velocity relaxation of a Brownian particle immersed in a viscous compressible fluid confined between two parallel plane walls

The diffusion tensor and velocity correlation function of a Brownian particle immersed in a viscous compressible fluid confined between two parallel plane walls are calculated in point approximation. The fluid is assumed to satisfy stick boundary conditions at the walls. It is found that the velocity correlation function decays asymptotically with a negative t(-2) long-time tail due to coupling to overdamped sound waves. The coefficient of the long-time tail is calculated and shown to be independent of fluid viscosity.

Rotational diffusion of colloidal particles near confining walls

We study the rotational diffusion of a spherical colloid confined in a narrow channel between parallel plane hard walls. The walls damp translational diffusion much more than rotational diffusion so that there is expected to be little translation-rotation coupling. Using a recent calculation of the nonisotropic rotational mobilities arising from the hydrodynamic interactions with the walls, we set up the rotational Smoluchowski equation for either a particle with a permanent dipole moment or a polarizable particle with axisymmetric polarizabilities subject to an external electric field. Using the Smoluchowski equation dynamics we calculate the time-correlation functions of orientation that are measured in depolarized light scattering for the cases of no external field, external field normal to the walls, and external field parallel to the walls. The decay of correlations is shown to be given by a weighted sum of decaying exponentials and can be characterized by an initial and a mean characteristic decay time. The weights and decay rates of each component and the characteristic decay times are studied numerically for a range of field strengths. The nonisotropic rotational mobilities make these decay times highly sensitive to the distance of the particle from the confining walls. This position dependence can be used as a method of measuring the rotational mobilities or, conversely, the rate of decay of correlations can be used as a probe of particle position between the confining walls.

Sedimentation of spheres at small Reynolds number

The effect of fluid inertia on the settling of spheres in a viscous incompressible fluid is studied in the limit of small Reynolds number. The kinetic energy of flow depends on the positions of the spheres, and gives rise to forces on the spheres. In the dilute limit it suffices to study the corresponding pair interaction. The interaction is calculated from the Stokes flow for two spheres settling between plane walls in the point particle limit. The dissipative interaction between a pair of spheres is calculated from the Proudman-Pearson [I. Proudman and J. R. A. Pearson, J. Fluid Mech. 2, 237 (1957)] solution of the Navier-Stokes equations for flow about a sphere in unbounded geometry. The combination of kinetic and dissipative interaction gives rise to a repulsive force of range of the order of the sphere diameter divided by the Reynolds number.