Ligand-mediated adhesive mechanics of two static, deformed spheres.

A self-consistent model is developed to investigate attachment/detachment kinetics of two static, deformable microspheres with irregular surface and coated with flexible binding ligands. The model highlights how the microscale binding kinetics of these ligands as well as the attractive/repulsive potential of the charged surface affects the macroscale static deformed configuration of the spheres. It is shown that in the limit of smooth, neutrally charged surface (i.e., the dimensionless inverse Debye length, [Formula: see text]), interacting via elastic binders (i.e., the dimensionless stiffness coefficient, [Formula: see text]) the adhesion mechanics approaches the regime of application of the JKR theory, and in this particular limit, the contact radius, Rc, scales with the particle radius, R, according to the scaling law, [Formula: see text]. We show that static, deformed, highly charged, ligand-coated surface of micro-spheres exhibit strong adhesion. Normal stress distribution within the contact area adjusts with the binder stiffness coefficient, from a maximum at the center to a maximum at the periphery of the region. Although reported in some in vitro experiments involving particle adhesion, until now a physical interpretation for this variation of the stress distribution for deformable, charged, ligand-coated microspheres is missing. Surface roughness results in a diminished adhesion with a distinct reduction in the pull-off force, larger separation gap, weaker normal stress and limited area of adhesion. These results are in agreement with the published experimental findings.

Surface deformation and shear flow in ligand mediated cell adhesion.

We present a unified, multiscale model to study the attachment/detachment dynamics of two deforming, charged, near spherical cells, coated with binding ligands and subject to a slow, homogeneous shear flow in a viscous, ionic fluid medium. The binding ligands on the surface of the cells experience both attractive and repulsive forces in an ionic medium and exhibit finite resistance to rotation via bond tilting. The microscale drag forces and couples describing the fluid flow inside the small separation gap between the cells, are calculated using a combination of methods in lubrication theory and previously published numerical results. For a selected range of material and fluid parameters, a hysteretic transition of the sticking probability curves (i.e., the function [Formula: see text]) between the adhesion phase (when [Formula: see text]) and the fragmentation phase (when [Formula: see text]) is attributed to a nonlinear relation between the total nanoscale binding forces and the separation gap between the cells. We show that adhesion is favoured in highly ionic fluids, increased deformability of the cells, elastic binders and a higher fluid shear rate (until a critical threshold value of shear rate is reached). Within a selected range of critical shear rates, the continuation of the limit points (i.e., the turning points where the slope of [Formula: see text] changes sign) predict a bistable region, indicating an abrupt switching between the adhesion and the fragmentation regimes. Although, bistability in the adhesion-fragmentation phase diagram of two deformable, charged cells immersed in an ionic aqueous environment has been identified by some in vitro experiments, but until now, has not been quantified theoretically.

Sticky surface: sphere-sphere adhesion dynamics.

We present a multi-scale model to study the attachment of spherical particles with a rigid core, coated with binding ligands and suspended in the surrounding, quiescent fluid medium. This class of fluid-immersed adhesion is widespread in many natural and engineering settings, particularly in microbial surface adhesion. Our theory highlights how the micro-scale binding kinetics of these ligands, as well as the attractive/repulsive surface potential in an ionic medium affects the eventual macro-scale size distribution of the particle aggregates (flocs). The bridge between the micro-macro model is made via an aggregation kernel. Results suggest that the presence of elastic ligands on the particle surface lead to the formation of larger floc aggregates via efficient inter-floc collisions (i.e. non-zero sticking probability, g). Strong electrolytic composition of the surrounding fluid favours large floc formation as well. The kernel for the Brownian diffusion for hard spheres is recovered in the limit of perfect binding effectiveness (g→1) and in a neutral solution with no dissolved salts.

Impact of flow on ligand-mediated bacterial flocculation.

To understand the adhesion-fragmentation dynamics of bacterial aggregates (i.e., flocs), we model the aggregates as two ligand-covered rigid spheres. We develop and investigate a model for the attachment/detachment dynamics in a fluid subject to a homogeneous planar shear-flow. The binding ligands on the surface of the flocs experience attractive and repulsive surface forces in an ionic medium and exhibit finite resistance to rotation (via bond tilting). For certain range of material and fluid parameters, our results predict a nonlinear or hysteretic relationship between the binding/unbinding of the floc surface and the net floc velocity (translational plus rotational velocity). We show that the surface adhesion is promoted by increased fluid flow until a critical value, beyond which the bonds starts to yield. Moreover, adhesion is not promoted in a medium with low ionic strength, or flocs with bigger size or higher binder stiffness. The numerical simulations of floc-aggregate number density studies support these findings.

Influence of the standard free energy on swelling kinetics of gels.

Classical theories of gel swelling employ the mixing free energy, thereby ignoring any effects of the free energy of the pure phases,i.e., the polymer standard free energy. In this paper we present a model for the swelling kinetics of gels that incorporates the free energy, including the polymer standard free energy. We provide a complete analysis of how the swelling kinetics and stable states and sizes of the swelled gel depends on the free energy parameters and show that theories that use only the mixing free energy cannot correctly describe equilibrium states or the swelling kinetics.

Shear-induced mesostructures in biaxial liquid crystals.

We study nematodynamics of a mesoscopic system consisting of sheared biaxial liquid crystalline polymers using a hydrodynamical kinetic theory. We solve the governing Smoluchowski equation using the Galerkin method in selected regions of the material parameter space and a range of accessible shear rates to investigate stable mesoscopic states and robust structures. The imposed shear flow breaks the rotational symmetry in the quiescent state to induce truly biaxial flow-aligning steady states, logrolling states, out-of-plane steady states, exotic time-periodic motions, and chaotic motions in different regimes of material parameters and shear rates.