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The linear stability analysis of vertical throughflow of power law fluid for double-diffusive convection with Soret effect in a porous channel is investigated in this study. The upper and lower boundaries are assumed to be permeable, isothermal and isosolutal. The linear stability of vertical through flow is influenced by the interactions among the non-Newtonian Rayleigh number (Ra), Buoyancy ratio (N), Lewis number (Le), Péclet number (Pe), Soret parameter (Sr) and power law index (n). The results indicate that the Soret parameter has a significant influence on convective instability of power law fluid. It has also been noticed that buoyancy ratio has a dual effect on the instability of fluid flow. Further, it is noticed that the basic temperature and concentration profiles have singularities at \(Pe = 0\) and \(Le = 1\), the convective instability is looked into for the limiting case of \(Pe\rightarrow 0\) and \(Le \rightarrow 1\). For the case of pure thermal convection with no vertical throughflow, the present numerical results coincide with the solution of standard Horton–Rogers–Lapwood problem. The present results for critical Rayleigh number obtained using bvp4c and two-term Galerkin approximation are compared with those available in the literature and are tabulated. 相似文献
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W. K. van Wijngaarden F. J. Vermolen G. A. M. van Meurs C. Vuik 《Transport in Porous Media》2012,92(3):847-866
Biogrout is a new method for soil reinforcement, which is based on microbial-induced carbonate precipitation. Bacteria and
reactants are flushed through the soil, resulting in calcium carbonate precipitation and consequent soil reinforcement. Bacteria
are crucially important in the Biogrout process since they catalyse the reaction. Hence, to control the process, it is essential
to know where the bacteria are located. The bacteria are possibly in suspension but can also be adsorbed or fixated on the
matrix of the porous structure. In this article, a model is derived for the placement of bacteria. The model contains three
phases of bacteria: bacteria in suspension, adsorbed bacteria and fixed bacteria. An analytical solution is derived for instantaneous
reactions between these three phases. The analytical solution is compared to numerical simulations for finite reaction rates.
For the numerical simulations the standard Galerkin Finite Element Method is used. 相似文献
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The existence of waiting times, before boundary motion sets in, for a diffusion-diffusion reaction equation with a discontinuous switch mechanism, is demonstrated. Limit cases of the waiting times are discussed in mathematical rigor. Further, analytic solutions for planar and circular wounds are derived. The waiting times, as predicted using these analytic solutions, are perfectly between the derived bounds. Furthermore, it is demonstrated by both physical reasoning and mathematical rigor that the movement of the boundary can be delayed once it starts moving. The proof of this assertion resides on continuity and monotonicity arguments. The theory sustains the construction of analytic solutions. The model is applied to simulation of biological processes with a threshold behavior, such as wound healing or tumor growth. 相似文献
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In this paper we analyse advective transport of polymers, crosslinkers and gel, taking into account non-equilibrium gelation, gel adsorption and crosslinker precipitation. In absence of diffusion/dispersion the resulting model consists of hyperbolic transport-reaction equations. These equations are studied in several steps using mainly analytical techniques. For simple cases, we obtain explicit travelling wave solutions, whereas for more complicated cases we rely on analytical techniques to analyse the problem qualitatively. Finally, a numerical solution for the full system of equations is obtained. The results developed in this study can be used to validate numerical solutions obtained from commercial simulators. 相似文献
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We provide travelling wave solutions of the equation for foam drainage in porous media, taking into account an additional
symmetry requirement. The method of solution used is reminescent of the approach developed to treat the Rapoport–Leas equation
for two-phase flow. Numerical solutions are also presented and compared to the analytical ones. 相似文献
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We present a numerical analysis of the stochastic population balance (SPB) theory for foam motion in porous media. The theory
condenses into a set of non-linear partial differential equations in the saturation, pressure, and bubble density. We solve
the equations using the IMPES method and perform sensitivity and parametric analysis. Finally, we compare the saturation profiles
obtained numerically with those obtained from CT scan foam experiments. The agreement between the theory and experiments confirms
that the stochastic population balance model describes adequately foam dynamics in porous media. 相似文献
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W. K. van Wijngaarden F. J. Vermolen G. A. M. van Meurs C. Vuik 《Transport in Porous Media》2011,87(2):397-420
Biogrout is a new soil reinforcement method based on microbial-induced carbonate precipitation. Bacteria are placed and reactants are flushed through the soil, resulting in calcium carbonate precipitation, causing an increase in strength and stiffness of the soil. Due to this precipitation, the porosity of the soil decreases. The decreasing porosity influences the permeability and therefore the flow. To analyse the Biogrout process, a model was created that describes the process. The model contains the concentrations of the dissolved species that are present in the biochemical reaction. These concentrations can be solved from a advection?Cdispersion?Creaction equation with a variable porosity. Other model equations involve the bacteria, the solid calcium carbonate concentration, the (decreasing) porosity, the flow and the density of the fluid. The density of the fluid changes due to the biochemical reactions, which results in density driven flow. The partial differential equations are solved by the Standard Galerkin finite-element method. Simulations are done for some 1D and 2D configurations. A 1D configuration can be used to model a column experiment and a 2D configuration may correspond to a sheet or a cross section of a 3D configuration. 相似文献
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Filion L Hermes M Ni R Vermolen EC Kuijk A Christova CG Stiefelhagen JC Vissers T van Blaaderen A Dijkstra M 《Physical review letters》2011,107(16):168302
We determine the phase diagram of a binary mixture of small and large hard spheres with a size ratio of 0.3 using free-energy calculations in Monte Carlo simulations. We find a stable binary fluid phase, a pure face-centered-cubic (fcc) crystal phase of the small spheres, and binary crystal structures with LS and LS(6) stoichiometries. Surprisingly, we demonstrate theoretically and experimentally the stability of a novel interstitial solid solution in binary hard-sphere mixtures, which is constructed by filling the octahedral holes of an fcc crystal of large spheres with small spheres. We find that the fraction of octahedral holes filled with a small sphere can be completely tuned from 0 to 1. Additionally, we study the hopping of the small spheres between neighboring octahedral holes, and interestingly, we find that the diffusion increases upon increasing the density of small spheres. 相似文献
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