Fig. 3: Phase map of the electroconvective viscous fingering and its relative finger width.
From: Electroconvective viscous fingering in a single polyelectrolyte fluid on a charge selective surface
a Differentiation of three EC morphologies (circular EC, straight, and ramified finger) by \({S}_{1}\) and \({S}_{2}\). b, Phase map with four regimes as (i) circular EC (orange), (ii) straight finger (yellow), (iii) ramified finger (green), and (iv) no EC (red). The experimental cases cover the ranges of \({{Ra}}_{E}\) (186–6.91\(\times {10}^{6}\)), \({Sc}\) (555–3520), and \(M\) (0.0041–7.12\(\times {10}^{3}\)), as adjusting the applied voltage (1–50 V) and the polyelectrolyte concentrations (0–2.0 wt% PAA and 0.5 wt% PQ-10). Boundaries of each regime are drawn on dotted lines (\({M}^{*}=1\), \({M}^{*\ast }=1.5\), \(R{a}_{E}^{*}={10}^{4}\), and \(\sqrt{R{a}_{E}}/{ScM}=0.0047\)). c The relative finger width \(\lambda\) according to \(\sqrt{R{a}_{E}}/{ScM}\). The best fitting line is \(\lambda \,=52.56{(\sqrt{R{a}_{E}}/{ScM})}^{-0.0011}-51.9563\)(\({R}^{2}=0.88\)).
