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Doctoral Dissertation Announcement
Candidate: Yongquing Peng
Doctor of Philosophy
Department: Mechanical and Aeronautical Engineering
Title: Analytical, Computational and Experimental Studies of Capillary Flow in Complex Geometries
Dr. William W. Liou, Chair
Dr. Peter Parker, Co-Chair
Dr. Parvis Merati
Dr. Tianshu Liu
Date: Friday, June 26, 2009 8:30 a.m. - 10:30 a.m.
D-202 Parkview Campus
The dynamic processes of the capillary flows in complex geometries are studied analytically, computationally and experimentally in this research. A general approach, based on the Navier-Stokes equations, for modeling the capillary flow in arbitrary irregular geometries with straight axis of symmetry is proposed. Using this approach, the governing equation to describe the dynamic capillary rising motion in capillaries with nonuniform elliptical cross-section is first derived under the assumptions of parabolic distribution of the axial velocity and constant contact angle. The derived nonlinear second order differential equation can be solved numerically using the Runge-Kutta method. The calculation results for the capillary flow in different tubes with irregular wall show that, in comparison with existing models tested, the present model can improve the underestimation of the nonuniformity effects.
Using the perturbation method, an asymptotic solution of the flow field in nonuniform circular tubes is obtained and is shown to be superior to the traditional Hagen-Poisuille solutions by comparing with the numerical FLUENT results. A new DCA (dynamic contact angle) model, combining the current velocity-dependent model based on molecularkinetic theory and empirical time-dependent model based on experiments, is proposed to describe the dynamic transition process of the gas liquid interface. The applicable scope of the new DCA model is extended to the entire process from the initial state to the equilibrium state. The capillary flow model is further developed by using the new velocity distribution and the DCA model. The proposed theoretical models are validated by a series of experiments of capillary flow in complex geometries.
The industrial application of the research work is explored by adopting the proposed model to describe the water flow passing through a multi-layer porous medium that is used in Procter & Gamble’s dewatering device for paper making industry. Comparing with the experimental data, the proposed model predicts well the dewatering performance of the device, and hence, can potentially be used as an industrial design optimization tool.