Measurement of dynamic surface tension using helical flow of a viscous liquid in a pool of another viscous liquid inside a micro-channel

Measurement of surface tension (s.t.) and critical micelle concentration (c.m.c.) of a surfactant in dynamic condition is important for several engineering applications, for which, the interface between two or more different phases does not remain constant but alters and replenishes continuously with flow of the fluids so that equilibrium may not be reached between the bulk and the interface. There are however not many methods for measuring these quantities in dynamic experiments which mimics the real dynamic situations. In this report, we present a novel two-phase flow pattern inside a triple-helical micro-channel using which, we show that it may be possible to measure the dynamic s.t. of a liquid. When two immiscible liquids such as oil and water are pumped into it, at a certain range of flow rates, oil flows as the continuous phase, whereas water remains in it as a wavy filament, the wavelength of which varies with the flow rates of oil and water but also on the interfacial tension between these two liquids. We show that wavelength decreases with increase in concentration of a solute attaining a minima at the c.m.c. A simple scaling analysis captures most experimental observations.