Cahn-Hilliard-Navier-Stokes Investigations of Droplet Dynamics in Turbulence
by
Nairita Pal(Indian Institute of Science, Bangalore)
→
Europe/Stockholm
Description
We study the challenging problem of turbulence in dynamics of
binary-fluid mixtures via extensive Direct Numerical Simulations
(DNSs) of the coupled Cahn-Hilliard-Navier-Stokes (CHNS) equations.
These CHNS allow us to study the dynamics of droplets elegantly via
gradients in a scalar-order-parameter field; therefore, we do not have
to enforce complicated boundary conditions at the moving interface
between the two fluids; this feature of the CHNS system helps us to
track the interface between the two fluids in great detail, and in a
computationally efficient manner. We begin with a study of the
dynamics of droplets in statistically homogeneous and isotropic
turbulent flow in two dimensions. We identify three parameter regimes
in which we find qualitatively different turbulent, but statistically
steady, states. In the first regime, the coalescence of droplets leads
finally to the mergers of all droplets leaving a a single droplet in a
turbulent flow;in the second regime, we obtain a statistically steady
droplet-size distribution because of continual surface-tension driven
coalescence and turbulence-induced break up of droplets; in the third
regime, the two fluids eventually mix to yield a single-phase fluid
that is turbulent.
We elucidate the important differences in the statistical properties
of binary-fluid turbulence in these three regimes. We investigate, in
detail,the mechanisms of droplet coalescence, and the various
statistical properties of droplet motion and deformation in
two-dimensional (2D), homogeneous,isotropic turbulence. We also
present illustrative DNSs for three-dimensional (3D) binary-fluid
turbulence in the CHNS system. We then show that the CHNS equations
provide a simple and natural theoretical basis for the study of the
gravity-driven dynamics of antibubbles. which have two surfaces, i.e.,
a shell of the light, minority phase inside the heavy,majority phase.
By carrrying out extensive DNSs, both in 2D and 3D, we obtain the
dependence of the antibubble lifetime on parameters like the viscosity
and the surface tension. We also study, in 50-50 binary-fluid
mixtures, the turbulence-induced suppression of phase separation in a
binary-fluid mixture by DNSs of the 2D CHNS equations.
The CHNS equations describe a phase-field model. Our results show that
these phase-field models can describe the dynamics of binary-fluids
efficiently.
