Actively deforming porous media in an incompressible fluid: A variational approach

PHYSICA D-NONLINEAR PHENOMENA

卷:426

Article

Farkhutdinov, Tagir^1,2  Gay-Balmaz, Francois³  Putkaradze, Vakhtang^1,2 

[1] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada

[2] ATCO SpaceLab, 5302 Forand St SW, Calgary, AB T3E 8B4, Canada

[3] Ecole Normale Super Paris, LMD, CNRS, F-75005 Paris, France

关键词: Porous media;    Variational principle;    Biological applications;    Active media;   

DOI  :  10.1016/j.physd.2021.132984

来源: Elsevier

【 摘 要 】

Many parts of biological organisms are comprised of deformable porous media. The biological media is both pliable enough to deform in response to an outside force and can deform by itself using the work of an embedded muscle. For example, the recent work (Ludeman et al., 2014) has demonstrated interesting 'sneezing' dynamics of a freshwater sponge, when the sponge contracts and expands to clear itself from surrounding polluted water. We derive the equations of motion for the dynamics of such an active porous media (i.e., a deformable porous media that is capable of applying a force to itself with internal muscles), filled with an incompressible fluid. These equations of motion extend the earlier derived equation for a passive porous media filled with an incompressible fluid. We use a variational approach with a Lagrangian written as the sum of terms representing the kinetic and potential energy of the elastic matrix, and the kinetic energy of the fluid, coupled through the constraint of incompressibility. We then proceed to extend this theory by computing the case when both the active porous media and the fluid are incompressible, with the porous media still being deformable, which is often the case for biological applications. For the particular case of a uniform initial state, we rewrite the equations of motion in terms of two coupled telegraph-like equations for the material (Lagrangian) particles expressed in the Eulerian frame of reference, particularly suitable for numerical simulations, formulated for both the compressible media/incompressible fluid case and the doubly incompressible case. We derive interesting conservation laws for the motion, perform numerical simulations in both cases and show the possibility of self-propulsion of a biological organism due to particular running wave-like application of the muscle stress. (C) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free