Plastocapillarity: Partial and full Newtonian drop embedding into immiscible yield stress substrates

Recent advances have been made in elastocapillarity; reversible 3D deformations of solid substrates with low elastic moduli from the surface tension of deposited drops. This study explores permanent deformations caused by liquid drops on immiscible yield stress substrates. We hypothesize that the substrate's rheological properties play a major role in determining the shape and stability of the drop-substrate interface, and govern partial or full embedding into the substrate.

Substrate yield stress magnitudes are modified through altering the mixture ratios of petroleum jelly to paraffin oil. Water drops are deposited on substrates and deformation profiles of the deformed interface are quantified.

Above a critical Bingham-Capillary number, which characterizes the ratio of yield stress magnitude to surface tension, deposited water drops deform the substrate surface permanently, but minimally. Below this value, drops become increasingly embedded as the substrate yield stress magnitude decreases, with larger indentation depths and increased circumferential ridge heights. With sufficiently low yield stress magnitudes, where surface tension forces dominate over yield stress forces, the plastically deformed ridges fully encapsulate the liquid drop surface, resulting in full drop embedding within the substrate. These results advance knowledge of interfacial wetting on soft yield stress substrates and has implications for binary fluids, functional materials, and new drug delivery systems.