Abstract:

I shall describe Direct Numerical Simulations (DNS) of multiphase flows, with particular emphasis on two phenomena: a large scale, large Reynolds case, the atomization of liquid jets, and a small scale case, the moving contact line. Atomization is a striking fluid phenomenon in which a liquid stream is broken in a large number of much smaller droplets. It occurs in wave breaking on the ocean as in an array of industrial situations. We work on a simplified setup to investigate the possibility of detailed modeling .  The motivation of our numerical modeling of this simplified setup is 1) to use a simple setup to investigate the possibility of converged simulations, 2) to examine the physical causes of the observed frequency of oscillation and its relation to the viscous stability theory of shear flows and 3)  to shed light on the statistics of droplet formation and the log-normal distribution observed, which plays an analogous role to the Kolmogorov k^-5/3 spectrum in single phase turbulence. Numerically, “well balanced” Volume-of-Fluid methods for surface tension coupled with accurate curvature estimates by “height functions” are used. Care is taken to enhance the stability of the method in presence of large density ratios by using a consistent transport of momentum and Volume-of-Fluid around the interface  (also categorized as a “momentum conserving” method ). Several test cases are described that discriminate various variants of the method as regards their stability. In particular, the fall of a raindrop and the sudden acceleration of a drop with a large density ratio are studied.  Large scale simulations are then performed that yield a statistical distribution of droplet sizes. The influence of upstream turbulence is studied.  Care is taken to have sufficiently small Reynolds and Weber numbers so that a DNS is attainable.

The moving contact line is another phenomenon that makes detailed simulations difficult. We describe an attempt to model the contact line with the Navier-Stokes equations coupled with adequate boundary conditions, which may involve slip, the numerical imposition of an apparent contact angle, and possibly the Generalized Navier Boundary Conditions. These simulations will be compared to the result of molecular dynamics using potentials with hydrogen bonding adapted to the no-slip tendency of water. Applications to wettability in microfluidic and porous environments will be discussed.

Biography:

Stéphane Zaleski is Professor at Sorbonne Université. After his doctorate at Ecole Normale Supérieure (ENS) in Paris and early years at the Physics Laboratory of ENS he joined the Mechanics group at UPMC – Paris 6. He investigates  numerical methods for multiphase flow with applications to atomization, cavitation, porous media flow, boiling, hydrometallurgy, contact lines and droplet impact, including several variants of the Volume of Fluid method, the diffuse interface method and molecular dynamics. He has written several computer codes for the simulation of two-phase flow including PARIS Simulator (with D. Fuster, Y. Ling, R. Scardovelli and G. Tryggvason). He is Associate Editor of J. Comput. Phys. and of Computers and Fluids.