Browsing by Subject "Porous medium"
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Item Experimental analysis of evaporation driven emulsion flow in porous media(2013-05) Kulkarni, Akhil; Berberoglu, HalilIn some configurations of compact, biofilm based photobioreactors, algae grow on a porous substrate that acts as the support system for the cells providing them with the necessary water and nutrients as well as carrying away their secreted products. The flow in these porous media can be driven by evaporation, mimicking the function of a synthetic leaf. The surface properties of the porous medium as well as the presence of a second immiscible phase in the fluid transported can significantly alter the transport capability and evaporative performance of the porous medium. The focus of this study is to investigate these effects through an experimental study. A dilute, 1% emulsion of lauric acid (chemical formula: C₁₂H₂₄O₂) in water was prepared using Tween® 80 surfactant. Evaporation driven flow of deionized water and the emulsion through two porous media, a hydrophilic glass fiber membrane and a less hydrophilic poly(vinylidene) fluoride (PVDF) membrane were studied. Experiments were conducted to determine the effect of porous medium and fluid properties on the rate of evaporation. The parameters investigated were the hydrophilicity of the porous medium and the area of the porous medium available for evaporation for both water and emulsion. During the experiment, the mass flow rate of the fluid as well as the temperature and the relative humidity of the ambient air were monitored. The results showed that for dilute emulsions, the rate of evaporation observed was the same as that for water and was dictated by the governing laws of convection applicable to the situation based on the geometry of the setup and the ambient conditions. The response of the porous medium to flow of dilute emulsion showed that the highly hydrophilic glass fiber porous medium rejected any accumulation of the oil phase in the pores, and ejected it out, whereas the lesser hydrophilic PVDF porous medium allowed the pores to be clogged by the oil phase, resulting in change in the properties of the medium. However, the dependence of this observation solely on surface properties of the medium cannot be ascertained as the glass fiber medium had a larger pore diameter than the PVDF medium, and this factor could be of effect. The relative humidity of ambient air affected the rate of evaporation, which implied that the flow was limited by evaporation rather than by the viscous losses in the porous medium. The response of change in rate of evaporation to change in relative humidity showed a high time lag. Also, it was seen that there was a maximum area over which evaporation occurred which was dictated by the capillary pressure generated by the porous medium and the viscous losses for the fluid flow through the medium. Any excess area available for evaporation did not have any effect on the rate of evaporation. Electrospinning, as a simple and effective process for generating fibrous porous media was presented and a sample porous medium was prepared using this method. A parametric analysis of the effect of the potential difference applied between the syringe tip and the collector electrode, and the distance between the tip and the collector on the diameter of fibers produced, was performed.Item Multiscale mortar mixed finite element methods for flow problems in highly heterogeneous porous media(2013-12) Xiao, Hailong; Arbogast, Todd James, 1957-We use Darcy's law and conservation of mass to model the flow of a fluid through a porous medium. It is a second order elliptic system with a heterogeneous coefficient. We consider the equations written in mixed form. In the heterogeneous case, we define a new multiscale mortar space that incorporates purely local information from homogenization theory to better approximate the solution along the interfaces with just a few degrees of freedom. In the case of a locally periodic heterogeneous coefficient of period epsilon, we prove that the new method achieves both optimal order error estimates in the discretization parameters and good approximation when epsilon is small. Moreover, we present numerical examples to assess its performance when the coefficient is not obviously locally periodic. We show that the new mortar method works well, and better than polynomial mortar spaces. On the other hand, we also propose to use multiscale mortars as a coarse component to construct a two-level preconditioner for the saddle point linear system arising from the fine scale discretization of the mixed finite element system. The two-level preconditioners are constructed based on the interfaces. We propose a framework to define the interpolation operators for the face based two-level preconditioners for different combination of coarse and fine scale mortar spaces for matching and nonmatching grids. In this dissertation, we show that for quasi-homogeneous problems and matching grids, the condition number of the preconditioned interface operator is bounded by (log(H/h))², which is the same as the traditional two-level preconditioners, for quasi-homogeneous problems. We show several numerical examples to demonstrate that for the strongly heterogeneous porous media, it is often desirable and even necessary to use a higher dimensional coarse mortar space to construct the coarse preconditioner to achieve convergence. We apply our ideas to study slightly compressible single phase and two-phase flow in a porous medium. We find that for the nonlinear single phase problem, the two-level preconditioners could be successfully applied to the symmetrized linear system. For the two-phase problem, using the fine scale, instead of multiscale, velocity solutions from the flow problem can greatly benefit the transport problem.