Mathematical and Numerical Analysis

The properties and collective response to stimuli of biological and chemical systems often depend on physico-chemical and/or biological interactions that occur at disparate length and time scales. For instance, when a macromolecule (say a polymer with radius of gyration ~ nm) in solution is subjected to flow deformation, it can uncoil and orient in the flow direction. This causes the solution itself to behave differently in a macroscopic sense, e.g., flow aligned molecules can “slide” past each other more easily, hence the viscosity of the solution could decrease as flow deformation (shear rate) is increased. The purpose of Multiscale Modeling and Simulation (MMS) in this context is to device a self-consistent numerical simulation that would combine say a mesoscopic or “micro” simulator (e.g. Brownian Dynamics) that would “track” polymer configurations with a continuum-level or “macro” solver (e.g. Finite Element) for the conservation laws that represent the overall mass and momentum balance for the flowing system. The advantage of such an approach is that one can predict the additional stresses produced by the polymers without resorting to ad hoc closure approximations from the knowledge of polymer configurations obtained from the micro simulation. This information is then used in the overall force balance in the macro solver. The macro solver in turn updates the micro on the velocity distribution. Hence the method is self-consistent. Such numerical simulations together with sound theoretical framework for bridging the behavior of a system at one length or time scale to the dynamics at other scale is the key to understanding and predicting behavior of complex systems. Further, MMS is important to modern process and product design since it allows one to establish structure-processing-property relationships.

MMS can link different scales ranging from the quantum-mechanical, atomistic, molecular, mesoscopic and the continuum: see Figure above for a hierarchy of computational techniques. In the BMCE department Sureshkumar, Sangani and coworkers focus on developing efficient algorithms to explore the structure and dynamics of polymeric fluids, self-assembled phases of surfactants (micelles), bacterial biofilms, bubbly liquids and particulate/fiber/colloidal suspensions.

Representative publications

  1. Koppol, R. Sureshkumar & B. Khomami, Anomalous friction drag behavior of mixed kinematics flows of viscoelastic polymer solutions: a multiscale simulation approach, J. Fluid Mech., 631, 231-253 (2009).