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 (3×10⁻⁴≤Ca_C≤7.6×10⁻²), Reynolds (0.1≤Re_C≤49) and Weber (7×10⁻⁴≤We≤1.5) numbers while continuous to dispersed viscosity ratio (μ_C/μ_D) spanned from 0.058 to23.2. To obtain these ranges, five distinct liquid-liquid fluid combinations were examined within a capillary of diameter 800 µm. 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.