A wide range of mesoscale phenomena, both natural and technological, involve multiphase flows and phase separation. Examples range from fundamental processes (e.g., boiling, droplet nucleation, emulsions, dynamics of thin films and particulate flows) to complex scenarios such as phase separation of polymer mixtures and intracellular biological processes. A key feature of these problems is that the dynamics occurs on nanometer to micrometer scales.
At those scales, thermal fluctuations play an important role in the overall dynamics and are expected to have significant impact on the overall behaviour of the system, particularly for problems that are far from equilibrium. In order to capture the effects of thermal fluctuations, Landau and Lifshitz proposed a modified version of the Navier-Stokes equations, referred to as fluctuating hydrodynamics (FHD) that incorporates stochastic flux terms designed to represent the effect of fluctuations. These stochastic fluxes are constructed so that the FHD equations are consistent with equilibrium fluctuations from statistical mechanics. Here, we generalize fluctuating hydrodynamics to a model for multiphase, multicomponent mixtures based on an N-component form of the Flory-Huggins extension to regular solution theory. The thermodynamics of the system is described by a free energy that includes entropy and enthalpy of mixing as well as non-local terms representing interfacial tension. The multiphase model is incorporated into a fluctuating hydrodynamics (FHD) model for nonideal liquid mixtures. The presentation will discuss the basic formulation of the model and sketch the derivation of the equations of motion. Numerical results will be presented validating the model and illustrating the range of phenomena that it can represent. Finally, we will show how fluctuations shift the stability region of the Rayleigh-Plateau instability that describes the breakup of fluid threads.
About the speaker
Dr John Bell is a Senior Scientist at Lawrence Berkeley National Laboratory and Chief Scientist of Berkeley Lab’s Computational Research Division. His research focuses on the development and analysis of numerical methods for partial differential equations arising in science and engineering. He has made contributions in the areas of finite volume methods, numerical methods for low Mach number flows, adaptive mesh refinement, stochastic differential equations, interface tracking and parallel computing.
He has also worked on the application of these numerical methods to problems from a broad range of fields, including combustion, shock physics, seismology, atmospheric flows, flow in porous media, mesoscale fluid modelling and astrophysics. He is a Fellow of the Society of Industrial and Applied Mathematics and a member of the National Academy of Sciences.
Register here for the FREE talk.
Monday 6 March
13:00 – 14:00
JJ Thomson seminar room
JJ Tomson Ave, Cambridge
Or join us on Zoom:
Meeting ID: 835 5747 5574
Find your local number: https://us06web.zoom.us/u/kdmQtIKdbI
Monday, 6 March, 2023 – 13:00 to 14:00
Hybrid – Maxwell Centre, Cambridge & Zoom