Tyler Lutz successfully defends thesis: “Frictional, Large-Deformation Poroelastic Flow: Theory and Experiments”

Tyler Lutz, Yale University
April 7, 2021

On March 26, 2021 Tyler Lutz successfully defended the thesis: “Frictional, Large-Deformation Poroelastic Flow: Theory and Experiments” (Advisor: John Wettlaufer).

Lutz explained “Squishing a wet kitchen sponge causes water to gush out, while holding the sponge under a running tap will cause it to compress. This two-way relationship between solid and fluid dynamics in soft porous materials underlies a number of interesting—and often surprising—effects in geophysical and biological flows. Natural analogs to the kitchen sponge typically exist in contact with other materials that they might rub against during compression; this friction alters the behavior of the solid-fluid feedback. By running water through a latex foam confined in a tube, we study how the fluid compresses the foam in a regime where friction can not be ignored. Consistent with earlier work on flow-compressed foams, we find that the rate of fluid flow through the foam eventually saturates at high fluid pressures, while the foam compresses nonuniformly. We develop a theoretical framework that not only accurately predicts quantities like the fluid pressure in the sponge and the amount of flow through it but also fully captures the effects of friction.”

Lutz will be joining the Division of Theoretical Soft Matter and Biophysics at the University of Magdeburg in Germany as a postdoc.

Thesis Abstract: Fluid flow through deformable, porous materials is seemingly ubiquitous in the natural world—spanning length scales from the cellular to the planetary—and offers a phenomenologically rich setting in which to study the generally nonlinear coupling between solid- and fluid-mechanics in multiphase materials. As much as we might like to study such flows in strict isolation from their environment, this thesis argues that properly accounting for forces that arise on the boundaries of such flows is essential to understanding the behavior of realistic soft porous media flows. Building on an experimental program initiated more than half a century ago, we demonstrate a novel empirical method for simultaneously measuring the pore pressure and medium deformation profiles alongside the volume flux in uniaxial porous media flow. We perform a suite of experiments studying the flow-compaction of a foam sample in a regime in which the friction between the sample and boundaries of the experimental cell cannot be ignored. By opposing the motion of the foam, the wall friction leads to a demonstrable hysteresis in all of the measured quantities, a path-dependence which is difficult to account for in conventional theoretical models of large-deformation poroelasticity. Our experimental measurements constrain the material constitutive relations of our foam sample and thus enable us to formulate a mathematically closed theory of its poroelastic dynamics. Informed by these closures, we develop a particle-based theoretical framework that accounts for both static and kinetic frictional effects, and we demonstrate that our model quantitatively captures the full friction-induced phenomenology evinced in our experiments.