Topic: surface tension

The one-phase Muskat problem models the boundary between wet and dry regions in a porous material under Darcy’s law. Including surface tension is physically important but makes the analysis more difficult. Hyunwoo Kwon presents a proof of global well-posedness for small initial data in the subcritical regime, together with convergence of the solution to zero in Lipschitz norm at long times. The work is presented as the first global well-posedness result for this version of the problem with surface tension. Time permitting, the talk also includes a numerical experiment. The research is joint wi

An equation of state is something you hear about in introductory thermodynamics, for example, the Ideal gas equation. The ideal gas equation relates the pressure, volume, and the number of particles of the gas, to its temperature, uniquely defining its state. This description is possible in physics when the system under investigation is in equilibrium or near equilibrium. In biology, a tissue is modeled as a fluid composed of cells. These cells are constantly interacting with each other through mechanical and chemical signaling, driving them far from equilibrium. Can an equation of state exist

At small length-scales, capillary effects are significant, and thus the mechanics of soft material interfaces may be dominated by solid surface stresses or liquid surface tensions. The balance between surface and bulk properties is described by an elasto-capillary length-scale, in which equilibrium interfacial energies are constant. However, at small length-scales in biological materials, including living cells and tissues, interfacial energies are not constant but are actively regulated and driven far from equilibrium. Thus, the balance between surface and bulk properties depends upon the