Modeling the Excess Velocity of Low-Viscous Taylor Droplets in Square Microchannels

Abstract

Microscopic multiphase flows have gained broad interest due to their capability to transfer processes into new operational windows and achieving significant process intensification. However, the hydrodynamic behavior of Taylor droplets is not yet entirely understood. In this work, we introduce a model to determine the excess velocity of Taylor droplets in square microchannels. This velocity difference between the droplet and the total superficial velocity of the flow has a direct influence on the droplet residence time and is linked to the pressure drop. Since the droplet does not occupy the entire channel cross section, it enables the continuous phase to bypass the droplet through the corners. A consideration of the continuity equation generally relates the excess velocity to the mean flow velocity. We base the quantification of the bypass flow on a correlation for the droplet cap deformation from its static shape. The cap deformation reveals the forces of the flowing liquids exerted onto the interface and allows estimating the local driving pressure gradient for the bypass flow. The characterizing parameters are identified as the bypass length, the wall film thickness, the viscosity ratio between both phases and the Ca-number. The proposed model is adapted with a stochastic, metaheuristic optimization approach based on high-speed camera measurements. In addition, our model is successfully verified with published empirical data.

Reconstruction of the 3D pressure field and energy dissipation of a Taylor droplet from a $$\upmu$$PIV measurement

“…While the gradient of the pressure inside the wall-layer points downstream as expected, we experimentally show a pressure gradient inversion with respect to the flow direction, and provide experimental evidence of the postulation of Abiev (2017). This reversed pressure gradient in the core of the flow drives the bypass flow of continuous phase through the corners (gutters) and gives rise to the Taylor droplet's relative velocity (Helmers et al 2019b). To quantify the driving pressure gradient along the gutter, the Taylor droplet interface approximation of Mießner et al (2019) is applied twice: to evaluate the experimental data of the pressure field directly at the interface position and subsequently to establish and verify an estimation method for the calculation of the gutter gradient.…”

“…At a constant volume flow rate and for a given surfactantfree material combination between two immiscible phases, only the droplet length determines its hydraulic resistance. The hydraulic resistance influences the actual droplet velocity, which finally determines the droplet residence time in a microchannel (Helmers et al 2019b). Thus, to control the flow stability of a Taylor droplet chain one needs to understand and control the pressure drop inside and outside the disperse phase.…”

“…This average velocity is derived from the total volume flow through the area of the channel cross-section A ch , where Q c and Q d are the volume flows of the continuous and the disperse phase, respectively. In this context, the droplet velocity u d is not useful for the definition of dimensionless numbers, since it is a flow dependent variable (Helmers et al 2019b): Continuous phase bypasses the droplet through the gutters from the droplet front to its back and causes a relative velocity u rel = u d −Ū of the Taylor droplet. Therefore, the droplet travels faster than the average flow Ū depending among other variables on the magnitude of the average flow velocity.…”

µPIV measurement of the 3D velocity distribution of Taylor droplets moving in a square horizontal channel

“…After a qualitative comparison of both results, we will propose two methods to estimate the pressure drop of the Taylor droplet and to estimate the driving pressure gradient for the bypass flow through the gutter of the Taylor droplet. The latter gives rise to the velocity difference between the mean flow and the Taylor droplet (Helmers et al 2019b).…”

Magnetic Resonance Imaging for Non‐invasive Study of Hydrodynamics Inside Gas‐Liquid Taylor Flows

“…These so‐called Taylor flows are the tool of choice for systematic studies when dealing with flow dynamics 5–9, mass transfer 10–12, and chemical reactions 13 within two‐phase flows. They are characterized by elongated, bullet‐shaped bubbles, the so‐called Taylor bubbles, moving along inside a capillary, with a well‐defined thin liquid film separating the bubble from the capillary wall.…”