Computational Rheology of Microscale Physical and Biological Systems

To be held at MATX 1100 and on Zoom: https://ubc.zoom.us/j/68285564037?pwd=R2ZpLy9uc2pUYldHT3laK3orakg0dz09
Meeting ID: 682 8556 4037
Passcode: 636252

Reception and refreshments at 15:30 in MATX 1100

Complex fluids—such as polymer solutions, crude oil, blood, foams, emulsions, and soft matter—exhibit nontrivial rheological properties, including viscoelasticity, plasticity, and time- dependent behavior. Understanding, predicting, and controlling their response is crucial for industrial processing, materials science, and bioengineering. However, modeling their motion in both industrial and biological settings presents fundamental mathematical challenges due to nonlinear constitutive behavior, moving boundaries, and multiscale interactions between microscopic structure and macroscopic flow.
In this talk, I will explore three case studies that illustrate the interplay between mathematical modeling, numerical simulations, and experiments in complex fluid dynamics. First, I will discuss the flow of viscoelastic fluids in porous media by analyzing their behavior past confined microcylinders, where elasticity and shear-thinning effects lead to unexpected flow asymmetries and bifurcations. Next, I will present our work on polymer melt extrusion, resolving a decades-old puzzle on the emergence of surface distortions in extrudates by linking them to intense polymer chain stretching and recoil. Finally, I will introduce in-silico rheological experiments on centrosomal asters, revealing how the cytoskeleton interacts with the intracellular environment to regulate cell division.
Throughout these examples, I will highlight key mathematical structures, including non-linear PDEs, bifurcation theory, fluid-structure interactions, and computational methods, that enable us to simulate and understand these systems. By bridging mathematics with materials science and biophysics, we uncover principles that advance both theoretical insights and real-world applications.