Flow and transport of colloidal suspensions in porous media

by Frank Wirner

Institution: University of Stuttgart
Department: Fakult├Ąt Mathematik und Physik
Degree: PhD
Year: 2015
Record ID: 1100780
Full text PDF: http://elib.uni-stuttgart.de/opus/volltexte/2015/10020/


Porous media are encountered in several areas of science and technology. The list of examples where flow and transport processes inside complex pore structures are of importance is long and includes topics like groundwater flow, blood perfusion inside the human body and oil recovery. The common and interesting feature of all porous media is their highly complicated pore structure. As the Navier-Stokes equations in such a complex structure are not easily solvable, it is a demanding task to predict flow and transport properties of a porous medium. The present thesis deals with the effect of the pore geometry on the flow and transport properties of colloidal suspensions. The porous structures used in this work are created by soft lithography. Therefore, the precise microscopic structure of these porous media is known and can be varied in a controlled way. The aqueous colloidal suspensions are used, on one hand, to visualize the flow of the fluid and, on the other hand, to directly study the transport of individual colloids. First, the relation between the velocity of the colloids and the fluid is investigated. Since the particles are of finite size, they will alter the surrounding flow field and, thus, their velocity at their center of mass is, in general, different from the velocity of the fluid at that point. The determination of the permeability of porous structures is achieved by calibrating the relation between mean particle and mean fluid velocity by adding an additional reference channel with known permeability and, consequently, known mean fluid velocity. Second, this calibration method is used to measure the permeabilities of two series of porous structures which are composed of randomly placed overlapping circles or ellipses (following Boolean models). An empirical expression for the permeability which makes use of purely structural parameters, namely the Euler Characteristic and the critical pore diameter, is introduced. The values predicted by this expression agree very well with the measured permeabilities. The advantage of this expression is that it does rely neither on the conductivity nor on the percolation threshold of the structures. In order to test whether the proposed empirical expression can be applied universally, two more series of porous structures, where the conducting and obstacle phase have been exchanged, are measured. It is found that for this class of structures the agreement is worse and possible explanations for the deviations are given. Third, the distribution of transit times of small particles in porous media with different porosities is studied by a combination of experiment and simulation. Since the velocities in different parts of the porous medium vary widely and particles in structures with low porosities can also get trapped in stagnant parts from which they can only escape by diffusion, the resulting distributions can be very wide. The longest transit times of the distributions can be related to a mean escape time for the largest stagnant parts which implies that…