Electroconvective Viscous Fingering in a Polyelectrolyte solution on a Charge Selective Surface

Viscous fingering is one of the most widely observed phenomenon of interfacial instabilities, which occurs at the interfaces of two fluids when a low viscous fluid displaces a highly viscous one. Despite its generality in Nature and engineering applications, viscous fingering has rarely been observed in a single fluid system. In this study, we describe the first observation of viscous fingering within a single polyelectrolyte solution on a charge selective surface. The fingering in a single fluid is realized by developing of ion concentration polarization and electroconvection (EC) on an ion exchange membrane, via applying an external electric field. Combining experiment and scaling analysis, we successfully described the onset and pattern of this electroconvective viscous fingering according to Ra_E (electric Rayleigh number), M (viscosity ratio) and Sc (Schmidt number), including (i) transition of the conventional to finger-like EC and (ii) transition of a single finger pattern to ramified one. Also, we investigate that the number of single and ramified fingers has a single curve relation with Ra_E, which is comparable to the relation of the conventional viscous fingering between the finger width and Ca (capillary number) despite in the zero interfacial tension limit.