Abstract
We present a modification of a recently developed volume of fluid method for multiphase problems (Ii et al. in J Comput Phys 231(5):2328–2358, 2012), so that it can be used in conjunction with a fractional-step method and fast Poisson solver, and validate it with standard benchmark problems. We then consider emulsions of two-fluid systems and study their rheology in a plane Couette flow in the limit of vanishing inertia. We examine the dependency of the effective viscosity mu on the volume fraction varPhi (from 10 to 30%) and the Capillary number Ca (from 0.1 to 0.4) for the case of density and viscosity ratio 1. We show that the effective viscosity decreases with the deformation and the applied shear (shear-thinning) while exhibiting a non-monotonic behavior with respect to the volume fraction. We report the appearance of a maximum in the effective viscosity curve and compare the results with those of suspensions of rigid and deformable particles and capsules. We show that the flow in the solvent is mostly a shear flow, while it is mostly rotational in the suspended phase; moreover, this behavior tends to reverse as the volume fraction increases. Finally, we evaluate the contributions to the total shear stress of the viscous stresses in the two fluids and of the interfacial force between them.
Highlights
In the last decades, developments in colloidal science have proven to be crucial for fabrication of functional materials
The indicator function H can be reconstructed in various ways; here, we use the multi-dimensional tangent of hyperbola for interface capturing (MTHINC) method, developed by Ii et al [21], where a multi-dimensional hyperbolic tangent function is used as an approximated indicator function
We have implemented and validated a volume of fluid methodology based on the multi-dimensional THINC (MTHINC) method first proposed by Ii et al [21] which can be used to study multiphase problems
Summary
Developments in colloidal science have proven to be crucial for fabrication of functional materials. Different methodologies have been proposed to accurately recover the exact surface geometry from the discretized VOF function: the simple line interface calculation (SLIC) method [30] and the piecewise linear interface calculation (PLIC) [61,62], the latter being further modified by several authors [2,19,33,37,39] Another technique is the tangent of hyperbola for interface capturing (THINC) method [59], which avoids the explicit geometric reconstruction by using a continuous sigmoid function rather than the Heaviside function, allowing a completely algebraic description of the interface; this enables the computation of the numerical flux partially analytically. The scheme does not require the geometric reconstruction, and a curved (quadratic) surface can be constructed as well
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