Cavitation: Testing the Eulerian and Lagrangian Descriptions of the Dynamics of Soft Materials
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Cavitation: Testing the Eulerian and Lagrangian Descriptions of the Dynamics of Soft Materials

Abstract

The systems encountered in biophysics typically straddle the line between solidand fluid, and are thus subject to large deformations even at modest stress val- ues. This, along with the presence of material properties such as visco-elasticity and strain hardening, necessitate the use of non-linear elasticity when describ- ing the physics of these systems. In this dissertation, we explore the use of non-linear elasticity theory in describing soft matter physics, with a focus on the specific example of cavitation in polymer gels and similar systems. We first look at cavitation in the context of equilibrium mechanics. In sim- ple materials that obey neo-Hookean elasticity, we show that compressibility effects strongly enhance cavitation. On the other hand, cavitation phenom- ena in gels of flexible polymers in a binary solvent that phase separates are surprisingly similar to those of incompressible materials. We find that, as a function of the interfacial energy between the two solvent components, there is a sharp transition between cavitation and classical nucleation-and-growth. Fi- nally, biopolymer gels are characterized by strain hardening, and even very low levels of strain hardening are shown to suppress cavitation in polymer gel that obey Flory-Huggins theory in the absence of strain hardening. Next, we explore the dynamics of cavitation in non-linear incompressible mate- rials. We find that, while purely elastic systems can be described entirely within either a Lagrangian or Eulerian frame of reference, and viscous fluids with no elasticity can be described entirely within an Eulerian frame, visco-elastic ma- terials such a Maxwell materials cannot be fully described without making use both frames, translating between the two using a known deformation mapping.

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