Complex fluids are often used as mixtures as in polymer blends and polymer-dispersed liquid crystals (PDLCs). The flow and rheology of such materials depend on two factors: the complex rheology of the components and the interfacial morphology. Both are a formidable tasks for modeling and simulation.
Our group has been working on this topic since 2004, when we developed a diffuse-interface model that handles these two factors in a unified theoretical framework. This led to finite-element algorithms AMPHI and AMPHI3D for simulation of complex flows, with adaptive mesh refinement to resolve the interface. The methodology has been applied to a host of problems, including drop deformation, breakup, coalescence and retraction in Newtonian, viscoelastic and liquid crystalline media, self-assembly of micro-particles and droplets, and even neutrophil transit in capillaries. An example on partial coalescence is shown at the bottom.
Ongoing work focuses on the dynamics of colloidal particles straddling an isotropic-nematic interface. The diffuse interface model couples the capillary forces on the interface with the elastic stresses in the nematic phase, while allowing a self-contained treatment of the three-phase contact line. An open question of great interest is how elasto-capillary forces may produce novel patterns of self-assembly on the isotropic-nematic interface.As an example for unusual interfacial dynamics of complex fluids, consider the intriguing partial coalescence phenomenon between a drop and an interface. Experimentally, we have shown that viscoelasticity tends to suppress partial coalescence. This is demonstrated by the comparison below: