Experimentally investigating the pressure drop of liquid-liquid Taylor flows over varying viscosity ratios

Micro-capillary liquid-liquid Taylor flows have emerged as a promising new platform for achieving higher heat and mass transfer compared to single-phase flows. In any application benefiting from such flows, pressure drop is a fundamental characteristic in evaluating the required input power in order to achieve an optimum configuration. Despite several attempts to develop an all-encompassing model to estimate pressure drop in immiscible liquid-liquid flows, existing models are still limited to narrow ranges of Reynolds, Capillary and Weber numbers and are insufficiently accurate over a wide range of viscosity ratios. To push the limits, the present study proposes a new expression for interfacial pressure drop based on experimental investigations over a wide range of Capillary (3 x 10-4 <= CaC <= 7.6 x 10-2), Reynolds (0.1 <= ReC <= 49) and Weber (7 x 10-4 <= We <= 1.5) numbers while continuous to dispersed viscosity ratio (mu C/mu D) spanned from 0.058 to 23.2. To obtain these ranges, five distinct liquid-liquid fluid combinations were examined within a capillary of diameter 800 mu m. A novel experimental setup is employed in this study to ensure high accuracy and repeatability of the measurements. The strengths and weaknesses of existing models are identified and a more fundamental understanding of predicting pressure drop in Taylor flow regimes is developed. The new model uses standard Hagen-Poiseuille flow theory in combination with an empirical optimized term for predicting the effect of differential Laplace pressure between leading/trailing caps of dispersed phase droplets. This correlation fits the experimental data within +/- 20 % and can provide a prediction certainty for estimating pressure drop in applications that deal with such flows.