Coagulation of Particles in Shear Flow: Applications to Biological Cells

Abstract

A simplified model is developed which makes it possible to describe the shear-induced coagulation of particles with different types of attractive interactions. In this model the trajectories of particles are calculated without taking into account any nonhydrodynamic interactions, while the hydrodynamic interaction is described in terms of the lubrication theory. Coagulation is assumed to occur if the hydrodynamic stretching force exerted on the doublet of particles is smaller than the attractive force binding the particles together. If the nonhydrodynamic interaction is reduced to the Van der Waals forces of molecular attraction, calculations of capture efficiency in terms of our simplified analysis are shown to be in good agreement with those carried out by other authors on the basis of analysis of numerically calculated trajectories. Further applications of our model deal with the coagulation of some biological cells, namely blood platelets, which are responsible for thrombous formation. In the first approximation activated platelets can be described as spherical elastic particles interacting via the superposition of Van der Waals attraction and biochemically specific interactions, which are attributed to receptor-coreceptor bonds between cells. The specific interactions are considered to result from the interplay of two subsystems, chemical and mechanical ones. The analysis of the kinetics of formation of intercellular bonds is carried out, yielding a simple analytic representation for the force of biospecific interaction. The biospecific interaction is shown to affect the capture efficiency, ϵ, at intermediate range of shear rate G , so that a plateau appears in the curve ϵ( G), while beyond this range coagulation is governed by Van der Waals attraction and ϵ is a decreasing function of G. This type of dependence is in qualitative agreement with that observed for blood platelet aggregation. Quantitative agreement is achieved with reasonable choice of parameters of interaction. Our approach also makes it possible to take into account the perturbation of particles' trajectories and the corrections to the force of Van der Waals and biospecific interactions due to elastic deformation of particles, which is shown to increase the capture efficiency at low shear rates and decrease it at high shear rates.