CAPILLARY RISE AND DISPLACEMENT OF IMMISCIBLE VISCOUS FLUIDS AS FUNCTION OF TIME

ABSTRACT The analytical solutions describe the behavior of physical phenomenon in nature. Capillary force is one of them and it acts in different manners. Particularly, the rise of a fluid through a capillary path is a phenomenon constantly present in nature. The document presents an analytical solution to describe the rate of rise of a wetting phase (displacing fluid) through a capillary tube in presence of a non-wetting phase (displaced fluid), taking into consideration the viscosity term and tube length effect. The Lucas-Washburn equation (1921) predicts the fluid rise in function of time. The model is accurate in late times and in early times or transient conditions the model has a variation compared with experimental data due to fluid inertia, which is not considered. The model is solely applicable when the displaced fluid viscosity is negligible. The solution obtained is compared with experimental data from bibliography. Three scenarios are presented, identified by the ratio of displacing and displaced viscosities; µ_1/µ_2= 0,01, 1 and 5000. The error between measured and simulated height at 50 [s] for all the experiments were 24, 23,8 and 5% respectively. The solution, successfully describes the trend of the three different scenarios, mainly the linear trend of the capillary rise vs. time when µ_1/µ_2= 0,01. The measurement of experimental data was planned as part of the research in order to perform the comparison between measured and simulated results. Due to the lack of specialized equipment, constant conditions and a suitable laboratory where to perform the tests, the experiments were cancelled. As further work in this topic, the integration of the contact angle change in dynamic conditions and the solution obtained could derive to a more accurate solution and by using an inclination angle the effect of tortuosity can also be analyzed.