Darcy Law

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Patrice Bacchin - One of the best experts on this subject based on the ideXlab platform.

  • Membranes: A Variety of Energy Landscapes for Many Transfer Opportunities
    Membranes, 2018
    Co-Authors: Patrice Bacchin
    Abstract:

    A membrane can be represented by an energy landscape that solutes or colloids must cross. A model accounting for the momentum and the mass balances in the membrane energy landscape establishes a new way of writing for the Darcy Law. The counter-pressure in the Darcy Law is no longer written as the result of an osmotic pressure difference but rather as a function of colloid-membrane interactions. The ability of the model to describe the physics of the filtration is discussed in detail. This model is solved in a simplified energy landscape to derive analytical relationships that describe the selectivity and the counter-pressure from ab initio operating conditions. The model shows that the stiffness of the energy landscape has an impact on the process efficiency: a gradual increase in interactions (such as with hourglass pore shape) can reduce the separation energetic cost. It allows the introduction of a new paradigm to increase membrane efficiency: the accumulation that is inherent to the separation must be distributed across the membrane. Asymmetric interactions thus lead to direction-dependent transfer properties and the membrane exhibits diode behavior. These new transfer opportunities are discussed.

  • Membranes: A Variety of Energy Landscapes for Many Transfer Opportunities
    Membranes, 2018
    Co-Authors: Patrice Bacchin
    Abstract:

    A membrane can be represented by an energy landscape that solutes or colloids must cross. A model accounting for the momentum and the mass balances on the membrane energy landscape establishes a new way of writing for the Darcy Law. The counter pressure in the Darcy Law is no longer written as the result of an osmotic pressure difference but rather as a function of colloid-membrane interactions. The ability of the model to describe the physics of the filtration is discussed in detail. This model is solved on a simplified energy landscape to derive analytical relationships that describe the selectivity and the counter pressure from ab-initio operating conditions. The model shows that the stiffness of the energy landscape has an impact on the process efficiency: a gradual increase in interactions (like with hourglass pore shape) can reduce the separation energetic cost. It allows the introduction of a new paradigm to increase membrane efficiency: the accumulation that is inherent to the separation must be distributed across the membrane. Asymmetric interactions thus lead to direction-dependent transfer properties and the membrane exhibits diode behavior. These new transfer opportunities are discussed.

M. Sheikholeslami - One of the best experts on this subject based on the ideXlab platform.

Mohsen Sheikholeslami - One of the best experts on this subject based on the ideXlab platform.

Nicola Zamponi - One of the best experts on this subject based on the ideXlab platform.

F Duval - One of the best experts on this subject based on the ideXlab platform.

  • A Darcy Law for the drift velocity in a two-phase flow model
    Journal of Computational Physics, 2007
    Co-Authors: Herve Guillard, F Duval
    Abstract:

    This work deals with the design and numerical approximation of an Eulerian mixture model for the simulation of two-phase dispersed flows. In contrast to the more classical two-fluid or Drift-flux models, the influence of the velocity disequilibrium is taken into account through dissipative second-order terms characterized by a Darcy Law for the relative velocity. As a result, the convective part of the model is always unconditionally hyperbolic. We show that this model corresponds to the first-order equilibrium approximation of classical two-fluid models. A finite volume approximation of this system taking advantage of the hyperbolic nature of the convective part of the model and of the particular structural form of the dissipative part is proposed. Numerical applications are presented to assess the capabilities of the model. © 2007 Elsevier Inc. All rights reserved.

  • a Darcy Law for the drift velocity in a two phase flow model
    Journal of Computational Physics, 2007
    Co-Authors: Herve Guillard, F Duval
    Abstract:

    This work deals with the design and numerical approximation of an Eulerian mixture model for the simulation of two-phase dispersed flows. In contrast to the more classical two-fluid or Drift-flux models, the influence of the velocity disequilibrium is taken into account through dissipative second-order terms characterized by a Darcy Law for the relative velocity. As a result, the convective part of the model is always unconditionally hyperbolic. We show that this model corresponds to the first-order equilibrium approximation of classical two-fluid models. A finite volume approximation of this system taking advantage of the hyperbolic nature of the convective part of the model and of the particular structural form of the dissipative part is proposed. Numerical applications are presented to assess the capabilities of the model.