Rheological evaluation of colloidal dispersions using the smoothed profile method: formulation and applications

Abstract

The smoothed profile method is extended to study the rheological behaviour of colloidal dispersions under shear flow by using the Lees-Edwards boundary conditions. We start with a reformulation of the smoothed profile method, a direct numerical simulation method for colloidal dispersions, so that it can be used with the Lees-Edwards boundary condition, under steady or oscillatory-shear flow. By this reformulation, all the resultant physical quantities, including local and total shear stresses, become available through direct calculation. Three simple rheological simulations are then performed for (1) a spherical particle, (2) a rigid bead chain and (3) a collision of two spherical particles under shear flow. Quantitative validity of these simulations is examined by comparing the viscosity with that obtained from theory and Stokesian dynamics calculations. Finally, we consider the shear-thinning behaviour of concentrated colloidal dispersions.

Prediction of shear thickening of particle suspensions in viscoelastic fluids by direct numerical simulation

“…2008; Molina et al. 2016). In SPM, the continuum velocity field is defined in the entire domain, including the fluid and solids.…”

“…SPM has been applied to suspensions in Newtonian fluids to evaluate the shear viscosity (Iwashita & Yamamoto 2009; Kobayashi & Yamamoto 2011; Molina et al. 2016), complex modulus (Iwashita, Kumagai & Yamamoto 2010) and particle coagulation rate (Matsuoka et al. 2012) of Brownian suspensions up to .…”

“…2008; Molina et al. 2016), respectively, and is the inter-particle potential force due to the excluded volume that prevents particles from overlapping. The non-slip boundary condition for the velocity field is assigned at particle surfaces.…”

“…2008; Iwashita & Yamamoto 2009; Molina et al. 2016) where an identity for a second-rank tensor, is used for the derivation. In this study, the Reynolds stress term is not considered due to the small-Reynolds-number conditions.…”

Modeling the mechanosensitivity of fast-crawling cells on cyclically stretched substrates

“…Given the time-dependent deformation of the substrate, it is more convenient to solve the equations of motion in the body frame, which is by definition constant, than it is to solve them in the lab frame. This is a common strategy when solving flow or elasticity problems in the presence of time-dependent boundary conditions [40][41][42]. However, this requires careful consideration, particularly with regards to the definition of the time derivatives.…”