Date of Award


Degree Name

Doctor of Philosophy


Mechanical and Aeronautical Engineering (to 2013)

First Advisor

Dr. William W. Liou

Second Advisor

Dr. Peter Parker

Third Advisor

Dr. Parviz Meratl

Fourth Advisor

Dr. Tianshi Liu


The dynamic processes of capillary flow in complex geometries have been studied analytically, computationally and experimentally in this research. A general approach 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 calculation results for the capillary flow in different tubes with irregular wall show that, in comparison with existing models that have been 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 in comparison to the numerical FLUENT results. A new DCA (dynamic contact angle) model, combining the current velocity-dependent model based on molecular-kinetic 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 was explored by adopting the proposed model to describe the water flow through a multi-layer porous medium that is used in Procter & Gamble's dewatering device for the paper making industry. Comparing with the experimental data, the proposed model has good predictions on the dewatering performance of the device, and hence, can potentially be used as an industrial design optimization tool.

Access Setting

Dissertation-Open Access