| This thesis is divided into two parts.In the first part, we study that the thermal-hydro-mass·transfer processes around the nuclear repository, induced by the long-time heat-emitting effect of the nuclear waste. This multi-physics processes are modeled as a coupled nonlinear system with oscillating coefficients, governing the fluid flow and thermal and contamination trans-fer. We establish the homogenization theory for this system. Firstly, by the technique of two-scale convergence, the homogenized equations are derived. Then, some error estimates are presented for the first order expansions.In the second part, we present some new perspectives on electrokinetics. Elec-trokinetics (EK) is a classic topic that is important not only in practical applications but also in the basic understanding of ionic fluid and its interaction with the solid. In this work we treat the Poisson-Nernst-Planck (PNP) equations as the starting point for deriving a consistent framework for the EK effects, under the constraint of overall charge neutrality. It is shown that the static limit of the PNP equations is given by the charge-conserving Poisson Boltzmann (CCPB) equation. As an accompanying inter-facial condition to the CCPB equation (or the PNP equations), we propose a surface potential trap model that, on the one hand, can trap a surface charge density σ and hence induce the EK effects, and, on the other hand, can accommodate the usually observed C variation with bulk ion density n∞. hence the average ion density n0=n∞+2σ/α for a cylindrical channel with radius a. The CCPB provides a consistent framework for the determination of both σ and μ from a single input n∞, for a given surface poten-tial trap. We show that the CCPB can be reduced to the form of the PB equation, but requires-μ(a) to be the accompanying boundary condition. Therefore both the PB form of the equation and its associated Gouy-Chapman physical picture can be repro-duced within the computational domain, with the implication that the surface charge density is in active equilibrium with the bulk and hence can vary as a function of a and n∞. Such variation is especially important for nanoscale channels. The resulting pre- diction of the Debye screening layer profile, for the static limit of the PNP equations or the CCPB equation, is in excellent agreement with that of the PB equation when the channel width is much larger than the Debye length; but they differ in the limit when the channel width approaches the nanometer scale. To delineate the behavior of the electro-osmotic (EO) effect, the PNP equations are coupled with the Navier-Stokes equation and solved numerically with the surface potential trap boundary condition, under an externally applied electric field. Owing to the charge neutrality condition, the net force exerted on the fluid by the electric field is zero. However, the EO effect arises from the difference in the flows associated with the ions and counter-ions. The EO effect is shown to exhibit an intrinsic time dependence. A potential difference applied across the sample can give rise to a convective current, but the subsequent diffusive counter-current necessarily tends to establish a new equilibrium of the system within a certain relaxation period. Thus a step function electric field is seen to result in a pulse of fluid flow, followed by a decay to a smaller flux as the ions approach a new steady state distribution. An optimal, sustained EO effect should therefore be best realized through a periodically pulsed operation mode. We have also numerically evaluated the coefficients associated with the EO effect, L21, and its reverse SP effect, L12, and show that L12=L21identically, in accordance with the Onsager relation. We conclude by noting some of the challenges ahead. |
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