The role of sound propagation in concentrated colloidal suspensions

Abstract

In a suspension, the hydrodynamic interactions between particles can propagate by two mechanisms: relatively slowly, by the diffusion of transverse momentum, or relatively rapidly, by the propagation of sound waves. Here we describe computer simulation results for the collective and single particle dynamics of colloidal particles with the aim of clarifying the role of sound. We find that for single particle motion the effect is rather trivial. As for an isolated particle, compressibility modifies the decay of velocity fluctuations only at very short times. For collective correlations this is not true. Our results show that the multiple scattering of sound waves between particles can induce correlated collective motions on time scales comparable with the diffusion of transverse momentum. The effects of compressibility are no longer restricted to very short times and manifest themselves as rapid oscillations in the time dependence of the collective diffusion coefficient. We suggest that these oscillations can largely be explained in terms of ''effective'' incompressible hydrodynamic theory, the suspension bulk viscosity, kinematic viscosity, and speed of sound becoming the relevant parameters. The oscillations are furthermore centered on the ͑hypothetical͒ incompressible result. Thus, while the effects of sound propagation may extend to surprisingly long times, the net effect remains limited to very short times. We discuss where these sound-induced oscillations will be relevant experimentally.

Velocity autocorrelation function of a Brownian particle

“…The squareroot singularity in Eq. In simulations, however, the discontinuity is not observed due to the finite compressibility of the fluid [24,4,6]. In a compressible solvent, the sound propagation occurs with a finite speed, and the solvent surrounding the colloid is not instantly set in motion.…”

Hydrodynamic interactions and Brownian forces in colloidal suspensions: Coarse-graining over time and length scales

“…ref. [89]. Because t cs ≪ τ ν , the sound-wave contribution to the VACF decays much faster than the hydrodynamic contribution V (t)V (0) H or even than the Langevin approximation V (t)V (0) L (recall that τ ν = 9 2 τ B for neutrally buoyant colloids.)…”

“…For that reason, sound effects are often ignored for colloidal suspensions under the assumption that they will have dissipated so quickly that they have no noticeably influence on the dynamics. However, some experiments [88] and theory [89] do find effects from sound waves on colloidal hydrodynamics, so that this issue is not completely settled yet. The kinematic time, τ ν , defined in Eq.…”

Backtracking of Colloids: A Multiparticle Collision Dynamics Simulation Study

“…[15]. Computer simulations revealed that the origin of this phenomenon lies in multiple scattering of sound waves [16], implying that the role of sound effectively extends to times much longer than the sonic time. Such phenomena highlight the importance of a solid theoretical understanding of the interplay between the sonic and the viscous effects.…”