Shear-Induced Migration of Rigid Particles near an Interface between a Newtonian and a Viscoelastic Fluid

Simulations of rigid
particles suspended in two-phase shear flow
are presented, where one of the suspending fluids is viscoelastic,
whereas the other is Newtonian. The Cahn–Hilliard diffuse-interface
model is employed for the fluid–fluid interface, which can
naturally describe the interactions between the particle and the interface
(e.g., particle adsorption). It is shown that particles can migrate
across streamlines of the base flow, which is due to the surface tension
of the fluid–fluid interface and a difference in normal stresses
between the two fluids. The particle is initially located in the viscoelastic
fluid, and its migration is investigated in terms of the Weissenberg
number Wi (shear rate times relaxation time) and
capillary number Ca (viscous stress over capillary
stress). Four regimes of particle migration are observed, which can
roughly be described by migration away from the interface for Wi = 0, halted migration toward the interface for low Wi and low Ca, particle adsorption at the
interface for high Wi and low Ca, and penetration into the Newtonian fluid for high Wi and high Ca. It is found that the angular velocity
of the particle plays a large role in determining the final location
of the particle, especially for high Wi. From morphology
plots, it is deduced that the different dynamics can be described
well by considering a balance in the first-normal stress difference
and Laplace pressure. However, it is shown that other parameters,
such as the equilibrium contact angle and diffusion of the fluid,
are also important in determining the final location of the particle.