Models for the two-phase flow of concentrated suspensions

A new two-phase model for concentrated suspensions is derived that incorporates a constitutive law combining the rheology for non-Brownian suspension and granular flow. The resulting model exhibits a yield-stress behavior for the solid phase depending on the collision pressure. This property is investigated for the simple geometry of plane Poiseuille flow, where an unyielded or jammed zone of finite width arises in the center of the channel. For the steady states of this problem, the governing equations are reduced to a boundary value problem for a system of ordinary differential equations and the conditions for existence of solutions with jammed regions are investigated using phase-space methods. For the general time-dependent case a new drift-flux model is derived using matched asymptotic expansions that takes into account the boundary layers at the walls and the interface between the yielded and unyielded region. The drift-flux model is used to numerically study the dynamic behavior of the suspension flow including the appearance and evolution of an unyielded or jammed region

Models for the two-phase flow of concentrated suspensions

A new two-phase model for concentrated suspensions is derived that incorporates a constitutive law combining the rheology for non-Brownian suspension and granular flow. The resulting model naturally exhibits a Bingham-type flow property. This property is investigated in detail for the simple geometry of plane Poiseuille flow, where an unyielded or jammed zone of finite width arises in the center of the channel. For the steady state of this problem, the governing equation are reduced to a boundary value problem for a system of ordinary differential equations and the dependence of its solutions are analyzed by using phase-space methods. For the general time-dependent case a new drift-flux model is derived for the first time using matched asymptotic expansions that take account of the boundary layers at the walls and the interface between the yielded and unyielded region. Using the drift-flux model, the behavior of the suspension flow, in particular the appearance and evolution of unyielded or jammed regions is then studied numerically for different choices of the parameters

Two-phase flow model for concentrated suspensions

A new two-phase model is derived that make use of a constitutive law combining non-Brownian suspension with granular rheology, that was recently proposed by Boyer et al. [PRL, 107(18),188301 (2011)]. It is shown that for the simple channel flow geometry, the stress model naturally exhibits a Bingham type flow property with an unyielded finite-size zone in the center of the channel. As the volume fraction of the solid phase is increased, the various transitions in the flow fields are discussed using phase space methods for a boundary value problem, that is derived from the full model. The predictions of this analysis is then compared to the direct finite-element numerical solutions of the full model

Two-phase flow model for concentrated suspensions

A new two-phase model is derived that make use of a constitutive law combining non-Brownian suspension with granular rheology, that was recently proposed by Boyer et al. [PRL, 107(18),188301 (2011)]. It is shown that for the simple channel flow geometry, the stress model naturally exhibits a Bingham type flow property with an unyielded finite-size zone in the center of the channel. As the volume fraction of the solid phase is increased, the various transitions in the flow fields are discussed using phase space methods for a boundary value problem, that is derived from the full model. The predictions of this analysis is then compared to the direct finite-element numerical solutions of the full model

Stability of concentrated suspensions under Couette and Poiseuille flow

The stability of two-dimensional Poiseuille flow and plane Couette flow for concentrated suspensions is investigated. Linear stability analysis of the two-phase flow model for both flow geometries shows the existence of a convectively driven instability with increasing growth rates of the unstable modes as the particle volume fraction of the suspension increases. In addition it is shown that there exists a bound for the particle phase viscosity below which the two-phase flow model may become ill-posed as the particle phase approaches its maximum packing fraction. The case of two-dimensional Poiseuille flow gives rise to base state solutions that exhibit a jammed and unyielded region, due to shear-induced migration, as the maximum packing fraction is approached. The stability characteristics of the resulting Bingham-type flow is investigated and connections to the stability problem for the related classical Bingham-flow problem are discussed

Stability of concentrated suspensions under Couette and Poiseuille flow

The stability of two-dimensional Poiseuille flow and plane Couette flow for concentrated suspensions is investigated. Linear stability analysis of the two-phase flow model for both flow geometries shows the existence of a convectively driven instability with increasing growth rates of the unstable modes as the particle volume fraction of the suspension increases. In addition it is shown that there exists a bound for the particle phase viscosity below which the two-phase flow model may become ill-posed as the particle phase approaches its maximum packing fraction. The case of two-dimensional Poiseuille flow gives rise to base state solutions that exhibit a jammed and unyielded region, due to shear-induced migration, as the maximum packing fraction is approached. The stability characteristics of the resulting Bingham-type flow is investigated and connections to the stability problem for the related classical Bingham-flow problem are discussed

Stability of concentrated suspensions under Couette and Poiseuille flow

The stability of two-dimensional Poiseuille flow and plane Couette flow for concentrated suspensions is investigated. Linear stability analysis of the twophase flow model for both flow geometries shows the existence of a convectively driven instability with increasing growth rates of the unstable modes as the particle volume fraction of the suspension increases. In addition it is shown that there exists a bound for the particle phase viscosity below which the two-phase flow model may become ill-posed as the particle phase approaches its maximum packing fraction. The case of two-dimensional Poiseuille flow gives rise to base state solutions that exhibit a jammed and unyielded region, due to shear-induced migration, as the maximum packing fraction is approached. The stability characteristics of the resulting Bingham-type flow is investigated and connections to the stability problem for the related classical Bingham-flow problem are discussed

Numerical comparison of hybridized discontinuous Galerkin and finite volume methods for incompressible flow

A numerical comparison of a hybridizable discontinuous Galerkin method proposed by Nguyen et al. and the well established finite volume method of second order in space represented by the icoFoam and simpleFoam solver of OpenFOAM is given. The hybridizable discontinuous Galerkin method has been reformulated as Picard iteration, hybridized and implemented from scratch. The methods are introduced and four numerical standard simulations are used in order to benchmark and evaluate the solver - the Taylor-Green vortex, the 180 degrees fence case as well as a two-dimensional stationary and non-stationary DFG benchmark. The numerical examples suggests hybridized discontinuous Galerkin methods are a competitive alternative to finite volume solvers for incompressible fluid simulations due to high accuracy and better stability properties

Time-stepping methods for the simulation of the self-assembly of nano-crystals in MATLAB on a GPU

Partial differential equations describing the patterning of thin crystalline films are typically of fourth or sixth order, they are quasi- or semilinear and they are mostly defined on simple geometries such as rectangular domains. For the numerical simulation of these kind of problems spectral methods are an efficient approach. We apply several implicit-explicit schemes to one recently derived PDE that we express in terms of coefficients of trigonometric interpolants. While the simplest IMEX scheme turns out to have the mildest step-size restriction, higher order SBDF schemes tend to be more unstable and exponential time integrators are fastest for the calculation of very accurate solutions. We implemented a reduced model in the EXPINT package syntax and compared various exponential schemes. A convexity splitting approach was employed to stabilize the SBDF1 scheme. We show that accuracy control is crucial when using this idea, therefore we present a time-adaptive SBDF1/SBDF1-2-step method that yields convincing results reflecting the change in timescales during topological changes of the nanostructures. The implementation of all presented methods is carried out in MATLAB. We used the open source GPUmat package to gain up to 5-fold runtime benefits by carrying out calculations on a low-cost GPU without having to prescribe any knowledge in low-level programming or CUDA implementations and found comparable speedups as with MATLAB's PCT or with GPUmat run on Octave

Gradient structures for flows of concentrated suspensions

In this work we investigate a two-phase model for concentrated suspensions. We construct a PDE formulation using a gradient flow structure featuring dissipative coupling between fluid and solid phase as well as different driving forces. Our construction is based on the concept of flow maps that also allows it to account for flows in moving domains with free boundaries. The major difference compared to similar existing approaches is the incorporation of a non-smooth two-homogeneous term to the dissipation potential, which creates a normal pressure even for pure shear flow