Two-dimensional cell model

An analysis of radial flow, fixed bed reactor (RFBR) is carried out to determine the effects of radial flow maldistribution and flow direction. Analytical criteria for optimum operation is established via a singular perturbation approach. It is shown that at high conversion an ideal flow profile always results in a higher yield irrespective of the reaction mechanism while dependence of conversion on flow direction is second order. The analysis then concentrates on the improvement of radial profile. Asymptotic solutions are obtained for the flow equations. They offer an optimum design method well suited for industrial application. Finally, all asymptotic results are verified by a numerical experience in a more sophisticated heterogeneous, two-dimensional cell model. 

For concentrated emulsions and foams, Prin-cen [1983, 1985] proposed a stress-strain theory based on a two-dimensional cell model. Consider a steady state shearing of such a system. Initially, at small values of strain, the stress increases linearly as in elastic body. As the strain value increases, the stress reaches its yield value, then at stiU higher deformation, it catastrophically drops to the negative values. The reason for the latter behavior is the creation of unstable cell structure that provides the recoil mechanism. The predicted dependencies for modulus and the yield stress were expressed as ... 

Two-dimensional cell modeled as a liquid and a compound drop [N Dri etal, 2003] Cell deforms with nucleus inside Bonds are elastic springs Macro/micro model for cell deformation Kinetics model based on Dembo [ 1988]. Nano scale model for hgand-receptor Uniform flow at the inlet as in parallel-flow chamber assay Results compare well with numerical and experimental results found in the literature for simple liquid drop Cell viscosity and surface tension affect Leukocyte rolling velocity Nucleus increases the bond hfetime and decreases leukocyte rolling velocity Cell with larger diameter rolls faster Uniform flow at the inlet as in parallel flow chamber assay... 

Most microscopic theories of adsorption and desorption are based on the lattice gas model. One assumes that the surface of a sohd can be divided into two-dimensional cells, labelled i, for which one introduces microscopic variables Hi = 1 or 0, depending on whether cell i is occupied by an adsorbed gas particle or not. (The connection with magnetic systems is made by a transformation to spin variables cr, = 2n, — 1.) In its simplest form a lattice gas model is restricted to the submonolayer regime and to gas-solid systems in which the surface structure and the adsorption sites do not change as a function of coverage. To introduce the dynamics of the system one writes down a model Hamiltonian which, for the simplest system of a one-component adsorbate with one adsorption site per unit cell, is... 

Thermal stress calculations in the five cell stack for the temperature distribution presented above were performed by Vallum (2005) using the solid modeling software ANSYS . The stack is modeled to be consisting of five cells with one air channel and gas channel in each cell. Two dimensional stress modeling was performed at six different cross-sections of the cell. The temperature in each layer obtained from the above model of Burt et al. (2005) is used as the nodal value at a single point in the corresponding layer of the model developed in ANSYS and steady state thermal analysis is done in ANSYS to re-construct a two-dimensional temperature distribution in each of the cross-sections. The reconstructed two dimensional temperature is then used for thermal stress analysis. The boundary conditions applied for calculations presented here are the bottom of the cell is fixed in v-dircction (stack direction), the node on the bottom left is fixed in x-direction (cross flow direction) and y-direction and the top part is left free to... 

When the site spinor vj/V - p is a symmetric fourth-rank spinor QA u/p (corresponding to the two-dimensional AKLT model[13]), only the quintet component out of the six multiplets on each spin quartet is present in the wave function (60). The sixth-rank spinors (62) are symmetric with respect to two triplets of indices and, hence, contain four multiplets with S = 0, 1, 2, 3 formed from two quintets. Consequently, the cell Hamiltonian (Hi and H coincide in this case) has the form... 

In the above Equations x the total area created by the intersection of a plane perpendicular to the cylinder axis and passing through the origin. denotes the interfacial length of the two dimensional cells in this plane. Crazes may be modeled by a system of parallel cylinders. For a realistic description of the craze microstructure, a distribution in fibril diameter, D, must be taken into account. This yields... 

We summarize a number of simulations aimed at deciphering some of the basic effects which arise from the interaction of chemical kinetics and fluid dynamics in the ignition and propagation of detonations in gas phase materials. The studies presented have used one- and two-dimensional numerical models which couple a description of the fluid dynamics to descriptions of the detailed chemical kinetics and physical diffusion processes. We briefly describe, in order of complexity, a) chemical-acoustic coupling, b) hot spot formation, ignition and the shock-to-detonation transition, c) kinetic factors in detonation cell sizes, and d) flame acceleration and the transition to turbulence. 

An intrinsic time-dependent one-dimensional (ID) model and a macro two-dimensional (2D) model for the anode of the DMFC are presented in [178]. The two models are based on the dual-site mechanism, which includes the coverage of intermediate species of methanol, OH, and CO on the surface of Pt and Ru. The intrinsic ID model focused on the analysis of the effects of operating temperature, methanol concentration, and overpotential on the transient response. The macro 2D model emphasizes the dimensionless distributions of methanol concentration, overpotential and current density in the CL which were affected by physical parameters such as thickness, specific area, and operating conditions such as temperature, bulk methanol concentration, and overpotential. The models were developed and solved in the PDEs module of COMSOL Multiphysics, giving good agreement with experimental data. The dimensionless distributions of methanol concentration, overpotential, and current density and the efficiency factor were calculated quantitatively. The models can be used to give accurate simulations for the polarizations of methanol fuel cell. 

Kulikovsky AA (2000) Two-dimensional numerical modeling of a direct methanol fuel cell. J Appl Electrochem 30 1005-1014... 

Chick, L.A., Korolev, V., and Khaleel, M. (2011) A quasi-two-dimensional electrochemistry modeling tool for planar solid oxide fuel cell stacks. J. Power Sources, 196, 3204-3222. 

Sengers, B.G., Please, C.P., Oreffo, R.O.C., 2007. Experimental characterization and computational modeling of two-dimensional cell spreading for skeletal regeneration. J. R. Soc. Interface 4, 1107-1117. 

Dimpault-Darcy, E. C., Nguyen, T. V., and White, R. E. (1988). A two-dimensional mathematical model of a porous lead dioxide electrode in a lead-acid cell, Electrochemical Society 135, 278-285. 

The model of two-dimensional cells (cellular model) leads to the following expressions for D, (Reed and Ehrlich 1981, Zubcus and Tornau 1989) ... 

Nagayama et al. [57] carried out nonequilibrium molecular dynamic simulations to study the effect of interface wettability on the pressure driven flow of a Lennard-Jones fluid in a nanochannel. The velocity profile changed significantly depending on the wettability of the wall. The no-slip boundary condition breaks down for a hydrophobic wall. Siegel et al. [58] developed a two-dimensional computational model for fuel cells. 

---