Suspensions of deformable particles in a Couette flow

Abstract

We consider suspensions of deformable particles in a Newtonian fluid by means of fully Eulerian numerical simulations with a one-continuum formulation. We study the rheology of the visco-elastic suspension in plane Couette flow in the limit of vanishing inertia and examine the dependency of the effective viscosity µ on the solid volume-fraction Φ, the capillary number Ca, and the solid to fluid viscosity ratio K. The suspension viscosity decreases with deformation and applied shear (shear-thinning) while still increasing with volume fraction. We show that µ collapses to an universal function, µ (Φ e ), with an effective volume fraction Φ e , lower than the nominal one owing to the particle deformation. This universal function is well described by the Eilers fit, which well approximate the rheology of suspension of rigid spheres at all Φ. We provide a closure for the effective volume fraction Φ e as function of volume fraction Φ and capillary number Ca and demonstrate it also applies to data in literature for suspensions of capsules and red-blood cells. In addition, we show that the normal stress differences exhibit a non-linear behavior, with a similar trend as in polymer and filament suspensions. The total stress budgets reveals that the particle-induced stress contribution increases with the volume fraction Φ and decreases with deformability.

Numerical simulations of vorticity banding of emulsions in shear flows

“…To ver-ify the independence of this result from the initial configuration we considered an additional case with bands of local volume fraction 30% and with a non-zero volume fraction, about 5%, between the bands so that the mean volume fraction in the domain is 15%, and also for this configuration the initial banded structure is stable (not reported here). Conversely to rigid 31 and deformable particles 32 , where the effective viscosity increases with the volume fraction, emulsions exhibit a rheological curve of the effective viscosity vs the volume fraction with a negative curvature, as shown in figure 5. To better understand this behavior, we computed the effective viscosity of an emulsion in a smaller domain, of size L x = L y = 16r, and same vertical distance between the walls δ.…”

Computational modeling of multiphase viscoelastic and elastoviscoplastic flows

“…In the case of deformable particles, we use the method described in the works of Rosti and Brandt . The solid is an incompressible viscous hyperelastic material undergoing only the isochoric motion, where the hyperelastic contribution is modeled as a neo‐Hookean material, thus satisfying the incompressible Mooney‐Rivlin law.…”

“…A very good agreement is found between our numerical results and those in the literature. Further validation and details of our implementation can be found in other works …”

“…In the case of deformable particles, we use the method described in the works of Rosti and Brandt. 74,85,86 The solid is an incompressible viscous hyperelastic material undergoing only the isochoric motion, where the hyperelastic contribution is modeled as a neo-Hookean material, thus satisfying the incompressible Mooney-Rivlin law. To numerically solve the fluid-structure interaction problem, we adopt the so called one-continuum formulation, 87 where only one set of equations is solved over the whole domain.…”

“…Further validation and details of our implementation can be found in other works. 74,85,86 Three-dimensional viscoelastic droplet. Verhulst et al 98 Figure 12A together with the numerical results by Verhulst et al 98 As expected, the drop deformation and alignment with the flow increase with Ca.…”