Interfaces as fields
Where two fluids meet, the interface is a field
A diffuse-interface (phase-field) description lets interfaces merge, split, and relax without being tracked explicitly — what we need for coating flows, bubbles, and three-phase contact.
Robust interpolation
A rheologically robust phase-field method
Standard interpolation lets material properties overshoot the physical bounds of the phase field. A hyperbolic-tangent scheme keeps them bounded — and stops elasticity from leaking into the Newtonian phase.
Early stage
Bubble rising under viscoelasticity — early stage
Stretching of aligned polymer resists the rise: stronger elasticity accumulates more polymer stress and stretches the bubble laterally.
Late stage
Bubble rising under viscoelasticity — late stage
Capillary and Weissenberg numbers, the polymeric viscosity ratio, and the dimensionless residence time together decide whether the bubble stays quasi-spherical, elongates, or splits.
Three phases
Ternary fluid flow
Extending to three immiscible fluids — triple-junction equilibrium and liquid–liquid–air interfaces under shear — for the multilayer problems industry actually has.
