WIAS Preprints

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Browsing WIAS Preprints by Author "Ahnert, Tobias"

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    Gradient structures for flows of concentrated suspensions
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Peschka, Dirk; Thomas, Marita; Ahnert, Tobias; Münch, Andreas; Wagner, Barbara
    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 twohomogeneous term to the dissipation potential, which creates a normal pressure even for pure shear flows.
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    Models for the two-phase flow of concentrated suspensions
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Ahnert, Tobias; Münch, Andreas; Wagner, Barbara
    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.
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    Stability of concentrated suspensions under Couette and Poiseuille flow
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Ahnert, Tobias; Münch, Andreas; Niethammer, Barbara; Wagner, Barbara
    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.
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    Two-phase flow model for concentrated suspensions
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Ahnert, Tobias; Münch, Andreas; Wagner, Barbara
    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.