Transition to irreversibility in sheared suspensions: An analysis based on a mesoscopic entropy production

Abstract

We study the shear-induced diffusion effect and the transition to irreversibility in suspensions under oscillatory shear flow by performing an analysis of the entropy production associated to the motion of the particles. We show that the Onsager coupling between different contributions to the entropy production is responsible for the scaling of the mean square displacement on particle diameter and applied strain. We also show that the shear-induced effective diffusion coefficient depends on the volume fraction and use Lattice-Boltzmann simulations to characterize the effect through the power spectrum of particle positions for different Reynolds numbers and volume fractions. Our study gives a thermodynamic explanation of the the transition to irreversibility through a pertinent analysis of the second law of thermodynamics.

Transition to irreversibility in sheared suspensions

“…The dynamics of N spherical particles of radius a and mass m suspended in a Newtonian fluid at constant temperature T and subjected to the non-stationary flow v 0 ( r,t) can be described by using the Gibbs entropy postulate and the second law of thermodynamics [7,6].…”

“…[7] that these interactions can be represented through a tensor of the form The form of the friction tensor reflects the anisotropic nature of the hydrodynamic interactions.…”

“…In this article, we use a Fokker-Planck equation, derived from the Gibbs entropy postulate by using the rules of mesoscopic nonequilibrium thermodynamics (MNET) [6,7,8], to show that both the transition to irreversibility and the shear-induced diffusion effect in suspensions of non-Brownian particles are compatible with the second principle of thermodynamics. In particular, we show that the origin of the irreversibility is due to an Onsager coupling containing hydrodynamic interactions and leading to a breaking down of the fluctuation-dissipation relation.…”

Mesoscopic Thermodynamics in the Presence of Flow

“…Specifically, the existence of a nonequilibrium temperature in sheared systems lead to a considerable theoretical (Criado-Sancho, 2005;Mauri & Leporini, 2006), numerical (Kurchan, 2005;O'Hern, 2004;Sarman, 1992) and experimental works with particular emphasis to the nonequilibrium properties of colloidal suspensions (Abou & Gallet, 2004;Bellon, 2001). These studies are relevant to us because kinetic nonequilibrium temperatures may not follow equipartition and are usually related to the breakdown of the fluctuation-dissipation theorem, a central relation of Langevin descriptions (Criado-Sancho, 2005;Santamaría Holek, 2001;Subramanian & Brady, 2004). Suspended objects diffuse in and are convected by the fluid; their motion may eventually be influenced by the presence of external fields.…”

“…where the superscript s stands for the symmetric part of a tensor, m is the mass of the molecule, β is the the friction tensor of the particles proportional to the corresponding Stokes coefficient (Santamaría Holek, 2001), and L ur is an Onsager coefficient. Notice that in contrast with Eqs.…”