Bubble Assemblies in Ternary Systems with Long Range Interaction

A nonlocal diffuse interface model is used to study bubble assemblies in ternary systems. As model parameters vary, a large number of morphological phases appear as stable stationary states. One open question related to the polarity direction of double bubble assemblies is answered numerically. Moreover, the average size of bubbles in a single bubble assembly depends on the sum of the minority constituent areas and the long range interaction coefficients. One identifies the ranges for area fractions and the long range interaction coefficients for double bubble assemblies.