Immiscible Liquid-Liquid Displacement in Capillary Tubes

Abstract

We analyze the liquid-liquid displacement in capillary tubes. The goal is to determine the amount of displaced liquid that remains attached to the tube wall and the configuration of the liquid-liquid interface at different operating parameters. The study encompasses both numerical and experimental approaches. The finite element method is used to solve the governing equations and, in order to validate the predictions, visualization experiments are performed to capture images of the interface. The numerical results were obtained for the assumption of negligible inertia, and the effects of viscosity ratio and capillary number are investigated. The predictions and experimental observations are in good agreement.

Shapes and dynamics of miscible liquid/liquid interfaces in horizontal capillary tubes

“…Similar experiments were also fulfilled by Soares et al [36] with the use of two immiscible liquids. They noted that air (or an injected liquid in the case of Soares et al) breaks through the center part of the tube's cross-section, and some amount of the liquid, that initially occupied the tube, remains on the tube's walls.…”

Numerical investigation on gas-displacement of a shear-thinning liquid and a visco-plastic material in capillary tubes

“…Fig. 5 also shows a comparison for the shear-thinning power-law liquid with behavior index n = 0.652 with two different meshes: one with 240 elements, 1035 nodes and 4860 degrees of freedom generated in a previous work by Soares et al [21] and another with 900 elements, 3801 nodes and 17,904 degrees of freedom generated in the present work. The results obtained with the finer mesh show a continuous tendency of departure from the Newtonian behavior as the capillary number is decreased.…”

“…In this method, the physical domain is mapped onto a computational fixed reference frame where the partial differential equations for each dimension considered are solved. Recent examples of interesting complex problems in which this technique has been applied are found in Romero et al [20], who studied the problem of the low-flow limit in slot coating, and Soares et al [21], who studied the liquid-liquid displacement of Newtonian fluids, among others.…”

Gas displacement of viscoplastic liquids in capillary tubes

“…They observed that the layer thickness decreases as the yield stress of the displaced liquid is increased. More recently, Soares et al [19] analyzed, using finite-element simulations and experiments, the steady displacement of a viscous liquid by a long drop of another viscous liquid in a capillary tube, for a wide range of the capillary number and viscosity ratio. Their theoretical predictions and flow visualization experiments showed the effect of different parameters on the interface configuration and on the thickness of the layer of the displaced liquid left on the walls.…”