Transport theory, continuum

A combination of continuum transport theory and the Poisson distribution of solution charges has been popular in interpreting transport of ions or conductivity of electrolytes. Assuming zero gradient in pressure and concentration of other species, the flux of an ion depends on the concentration gradient, the electrical potential gradient, and a convection... 

In this chapter we develop formulas describing local vapor concentration and temperature fields for two juxtaposed drops in a gas-vapor mixture of infinite extent. Instantaneous growth or evaporation rates can be calculated straightforwardly from knowledge of the vapor concentration fields in the vicinity of the drop. Our primary and fundamental assumptions are that continuum transport theory is a valid approxima-... 

Thus, the particle charge distribution is approximated by the Boltzmann equation. This expression holds best for particles larger than about 1 /.tm. For smaller particles, the flux terms (2,49) based on continuum transport theory must be modified semiempirically. The results of calculations of the fraction of charged particles are given in Table 2.2. The fraction refers to particles of charge of a given sign. 

Computation of shear viscosity of hard spheres has been attempted using NEMD [11], Modified non-equilibrium molecular dynamics methods have also been developed for study of fluid flows with energy conservation [12], NEMD simulations have also been recently performed to compare and contrast the Poiseuille and Electro-osmotic flow situations. Viscosity profiles obtained from the two types of flows are found to be in good mutual agreement at all locations. The simulation results show that both type of flows conform to continuum transport theories except in the first monolayer of the fluid at the pore wall. The simulations further confirm the existence of enhanced transport rates in the first layer of the fluid in both the cases [13, 14]. 

Lustig, SR Camthers, JM Peppas, NA, Continuum Thermodynamics and Transport Theory for Polymer-Fluid Mixtures, Chemical Engineering Science 12, 3037, 1992. 

Experimental studies have demonstrated that many microchannel huid how and heat transfer phenomena cannot be explained by the conventional theories of transport theory, which are based on the continuum hypotheses. Eor friction factors and Nusselt numbers. 

Lustig SR, Camthers JM, and Peppas NA. Continuum thermodynamics and transport theory for polymer-fluid mixtures. Chem. Eng. Sci. 1992 47(12) 3037-3057. 

For particles of a size similar to that of the bath molecules, the Knudsen number is insufficient to characterize the transport processes, but nonetheless it is found exp>erimentally in many cases that the transport properties of single particles and pairs of particles are surprisingly well modeled by continuum (hydrodynamic) theories at high densities and molecular theories at low densities. 

In a staged multi-scale approach, the energetics and reaction rates obtained from these calculations can be used to develop coarse-grained models for simulating kinetics and thermodynamics of complex multi-step reactions on electrodes (for example see [25, 26, 27, 28, 29, 30]). Varying levels of complexity can be simulated on electrodes to introduce defects on electrode surfaces, composition of alloy electrodes, distribution of alloy electrode surfaces, particulate electrodes, etc. Monte Carlo methods can also be coupled with continuum transport/reaction models to correctly describe surfaces effects and provide accurate boundary conditions (for e.g. see Ref. [31]). In what follows, we briefly describe density functional theory calculations and kinetic Monte Carlo simulations to understand CO electro oxidation on Pt-based electrodes. 

Continuous models. The extension from the finite models of 2 to multigroup diffusion and transport theory models involving a continuum of possible positions and velocities, involves some very careful technical analysis. 

S. R. Lustig, A Continuum Thermodynamics Theory for Transport in Polymer Fluid Systems, Ph.D. Dissertation, School of Chemical Engineering, Purdue University,... 

Since lijima identified carbon nanotubes (CNTs) in 1991, CNTs have been investigated in various fields and become extremely desirable for a wide range of applications. CNTs, with diameters in nanometer scale and a smooth surface may offer a very unique molecular transport through their pores. In fact, several studies in recent years suggest that the water transport through single-walled carbon nanotubes (SWNT) would become much faster than the transport rate that the continuum hydrodynamic theory would predict. This was attributed by Molecular Dynamic (MD) simulation to the smoothness of the nano-tube wall [1,2]. 

Baumgartner, L. P. Rumble III, D. (1988). Transport of stable isotopes I Development of a kinetic continuum theory for stable isotope transport. Contrib. Mineral. Petrol., 98, 417-30. 

Historically, one of the central research areas in physical chemistry has been the study of transport phenomena in electrolyte solutions. A triumph of nonequilibrium statistical mechanics has been the Debye—Hiickel—Onsager—Falkenhagen theory, where ions are treated as Brownian particles in a continuum dielectric solvent interacting through Cou-lombic forces. Because the ions are under continuous motion, the frictional force on a given ion is proportional to its velocity. The proportionality constant is the friction coefficient and has been intensely studied, both experimentally and theoretically, for almost 100... 

The first step in applying volume averaging is to consider a representative volume for every point A in the porous medium. This volume must be large enough to contain sufficient amount of each phase such that continuum theory for transport of mass, energy, and... 

Soft biological structures exhibit finite strains and nonlinear anisotropic material response. The hydrated tissue can be viewed as a fluid-saturated porous medium or a continuum mixture of incompressible solid (s), mobile incompressible fluid (f), and three (or an arbitrary number) mobile charged species a, (3 = p,m, b). A mixed Electro-Mechano-Chemical-Porous-Media-Transport or EMCPMT theory (previously denoted as the LMPHETS theory) is presented with (a) primary fields (continuous at material interfaces) displacements, Ui and generalized potentials, ifi ( , r/ = /, e, to, b) and (b) secondary fields (discontinuous) pore fluid pressure, pf electrical potential, /7e and species concentration (molarity), ca = dna/dVf or apparent concentration, ca = nca and c = Jnca = dna/dVo. The porosity, n = 1 — J-1(l — no) and no = no(Xi) = dVj/dVo for a fluid-saturated solid. Fixed charge density (FCD) in the solid is defined as cF = dnF/dV , cF = ncF, and cF = cF (Xf = JncF = dnF/d o. 

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