In this work, we investigate the fiber orientation dependent viscosity of fiber suspensions using a computational homogenization method. To improve computational prediction capabilities for the viscosity of fiber suspensions, we extend an existing, Fast Fourier Transform based computational approach for fiber suspensions with linear viscous, i.e., Newtonian, matrix behavior to nonlinear viscous matrix behavior. Specifically, a Cross-type shear-thinning rheology is assumed for the matrix fluid. We employ composite voxels to lower resolution requirements and find through resolution studies that the resolution error decreases for certain shear rates. Furthermore, we conduct a volume element study and find that the representative volume element sizes for engineering considerations in a specific Newtonian case and the investigated Cross-type case are highly similar. For shear rates of engineering process interest we visualize the effective suspension viscosity in three dimensions and study the effects of the fiber volume fraction and the imposed macroscopic shear rate tensor on the suspension viscosity. We find that the elongational viscosity and the degree of anisotropy of the suspension viscosity vary stronger with the shear rate for higher fiber volume fractions. In a comparison with an analytical mean-field model for the suspension viscosity, the deviations between the computational and analytical results turn out to be substantial. 

Homogenizing the viscosity of shear-thinning fiber suspensions with an FFT-based computational method

Accelerated computational micromechanics for solute transport in porous media

Reactive transport in permeable porous media is relevant for a variety of applications, but poses a significant challenge due to the range of length and time scales. Multiscale methods that aim to link microstructure with the macroscopic response of geo-materials have been developed, but require the repeated solution of the small-scale problem and provide the motivation for this work. We present an efficient computational method to study fluid flow and solute transport problems in periodic porous media. Fluid flow is governed by the Stokes equation, and the solute transport is governed by the advection-diffusion equation. We follow the accelerated computational micromechanics approach that leads to an iterative computational method where each step is either local or the solution of a Poisson's equation. This enables us to implement these methods on accelerators like graphics processing units (GPUs) and exploit their massively parallel architecture. We verify the approach by comparing the results against established computational methods and then demonstrate the accuracy, efficacy, and performance by studying various examples. This method efficiently calculates the effective transport properties for complex pore geometries.

Accelerated Computational Micromechanics for Reactive Flow in Porous Media

A numerical scheme which is a combination of FFT and Galerkin methods is proposed for calculating the effective permeability of periodic porous material. First, a periodic stress field whose divergence is equal to the subtraction of body force from prescribed pressure gradient is introduced to reformulate the governing equations. Then, an auxiliary problem is established to replace the prescribed pressure gradient with the resulting initial prescribed stress. An FFT‐based Galerkin method of stress control type, the associated projection operator for zero divergence condition and the treatment of composite pixels/voxels are presented for solving the viscous flow in periodic porous material. Finally, numerical examples of viscous flows in 2D parallel fissured medium, 2D medium with regularly packed squares, 2D medium with regularly packed and rotated squares, 3D medium with regularly packed ellipsoids, and 3D medium with randomly packed ellipsoids are implemented. Numerical results calculated by FFT‐based Galerkin method agree well with analytical solutions and finite element results. The proposed FFT‐based Galerkin method is effective for predicting the macro permeability of porous material with complex meso structures.

An FFT‐based Galerkin method for the effective permeability of porous material

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An FFT‐based Galerkin method for the effective permeability of porous material