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.

We developed a numerical algorithm AMPHI (and more recently AMPHI3D) that handles these two factors in a unified theoretical framework. It is based on a diffuse-interface model and employs adaptive mesh refinement to resolve the interface. So far, we have simulated drop deformation, coalescence and retraction in Newtonian, viscoelastic and liquid crystalline media. The same methodology has also been applied to study neutrophil transit in capillaries.

As an example, 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 comparison between a Newtonian system (click Fig. 1 below for video), where after initial film rupture, the drop transforms into a liquid column which then pinches off at the base to form the daughter drop, and a viscoelastic drop (click Fig. 2 for video), where the pinch-off is arrested by the polymer tensile stress.

Fig. 1: Video of partial coalescence in Newtonian liquids

Fig. 2: Video of the arrest of partial coalescence for a polymeric drop

This effect has been captured by simulations: Fig. 3 shows a partial coalescence cycle for a Newtonian drop, while Fig. 4 shows the arrest of partial coalescence for an Oldroyd-B drop. Click for details on the experimental and computational results.

Fig. 3: Simulation of a partial coalescence cycle for a Newtonian drop

Fig. 4: Simulation of an Oldroyd-B drop coalescencing with an interface