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

Abstract

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.

Dynamics of suspensions of hydrodynamically structured particles: analytic theory and applications to experiments

“…In the experimentally common situation where L * h is small, curvature effects are negligible and the particlefluid interface can be described as flat. As it is explained in [23], the key point to notice is that the reduced slip length, L * h,f = 1 − a h,f /a, in the flat-interface approximation and its associated flat-interface hydrodynamic radius, a h,f , are independent of the single-particle transport properties D t 0 , D r 0 and [η] used in their definition. Since each of these transport properties is associated with a particular ambient velocity field, e.g.…”

“…The relation follows from Eqs. ( 13) and ( 14) in conjunction with a general scattering series expansion of the exact N -sphere translational mobility tensors [22,23]. Since the short-time transport properties are equilibrium averages of specific mobility tensor elements, it follows that…”

“…As discussed in [22][23][24], a simplifying concept allowing for abstracting from specific intraparticle structures is the so-called hydrodynamic radius model (HRM) which invokes the notion of an apparent no-slip hydrodynamic particle radius a h (see also [25,26]). The HRM amounts to approximating a globular particle of spherically symmetric hydrodynamic structure by a no-slip sphere of hydrodynamic radius a h while leaving the effective pair potential unchanged.…”

“…However, these simulations are numerically expensive, and in principle they must be performed separately for each particle model. In a recent series of papers, various short-time dynamic properties of dispersions of uniformly permeable spheres, [17][18][19][20] and of core-shell particles with uniformly permeable shell, [21][22][23] have been calculated using the HYDROMULTIPOLE method, as functions of particle concentration, reduced Darcy permeability, and shell-thickness to particle size ratio. The non-hydrodynamic direct particle interactions in these simulations have been taken for simplicity as pure hard-core interactions characterized by the excluded volume particle radius a ¼ s/2.…”

Intrinsic viscosity of macromolecules within the generalized Rotne–Prager–Yamakawa approximation

“…Furthermore, to calculate the intrinsic viscosity we need to assign an effective radius to such a conglomerate in order to estimate its volume as needed in (3.22). As shown by Cichocki, Ekiel-Jezewska & Wajnryb (2014), the correct procedure in such a case is to estimate v based on the hydrodynamic (Stokes) radius, defined as a hyd = (2πη 0 Trµ tt ) −1 . For an almost spherical shape, this approach leads to the correct value of the intrinsic viscosity, up to quadratic terms in surface roughness.…”