Abstract
Velocity profiles of Newtonian immiscible liquids undergoing laminar flow between two horizontal plates under pressure gradient are investigated using a momentum balance equation. The differential equation describing the flow has been solved and equations for the velocity profiles of a two-layer and three-layer liquid systems are presented. As examples, we show flow patterns of two-layer water-crude oil system and three-layer system involving water, tetrachloromethane, xylene, cyclopentane and hexane. A distinctive pattern is noticeable between the velocity profiles of heavy (API 19.19) and light (API 40.89) Omani crude oils.
Highlights
Multi-layer fluid flows span a wide field covering a multitude of various technological perspectives and a broad range of engineering disciplines
Engineering applications of multi-layer flows of immiscible liquids are found in multi-layer extrusion of plastic films, multi-layer coating, lubricated squeezing flows and in the transportation of liquid hydrocarbon [1]
In the two-layer case, like an oil-water system, accurate prediction of flow characteristics, such as flow pattern, water holdup and pressure gradient is important in many engineering applications including petroleum engineering [2]
Summary
Multi-layer fluid flows span a wide field covering a multitude of various technological perspectives and a broad range of engineering disciplines. They observed stratified flow with some mixing at the interface at mixture velocity of 0.50 m/s for all pipe inclinations In addition to these applications in chemical and petroleum engineering, the flow of multi-layered immiscible fluids is important in the study of the evolution of magma within the Earth. It has been suggested [4] that non-ideal mixing of silicate melts is the cause of liquid immiscibility in simple and naturally occurring systems. In the present study we present exact solutions of the momentum balance equations involving velocity profiles for a three-layer liquid system having different viscosities and densities; this is one-step forward in understanding immiscible multi-layer fluid dynamics.
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