Concentration gradients diffusive fluxes

Laminar flow reactors have concentration and temperature gradients in both the radial and axial directions. The radial gradient normally has a much greater effect on reactor performance. The diffusive flux is a vector that depends on concentration gradients. The flux in the axial direction is... 

For the case of a binary electrolyte (i.e., a single salt that dissociates in solution into one cation and one anion species), we can rewrite the molar flux equations for positive and negative ions in terms of a salt concentration gradient diffusion term, a migration term explicit in the current density (as opposed to the VO driving force term in Equation (26.54)), and a bulk convection term ... 

In the presence of a nonuniformity in concentration a diffusive flux occurs, resulting in the creation of entropy. The rate of irreversible entropy production is, in general, a homogeneous quadratic function of the gradients of... 

Diffusion is the net flux of matter resulting from the random motion of a species in a concentration gradient. The flux of a dissolved species i due to diffusion, Tdjff,... 

A halfway bounce-back boundary condition was imposed at the spheres/fluid interface. Gas particles (molecules) which are propagated into a solid point bounce back immediately and stay where they were. The flux through the membrane depended on the local pressure (advective contribution) and local concentration gradient (diffusive contribution) across the membrane. 

The second mode of transport of ions is diffusion, a process caused by a concentration gradient [6]. A difftisional flux appears near the electrode surface where the charge-transfer reaction causes a depletion of ions and the development of the concentration gradient. The flux is determined by Ficks s first law ... 

Molecules in solution undergo random motions, giving rise to the process of diffusion. Under a concentration gradient, diffusion results in flux (J) of molecules that tends to homogenize the concentration (c) of that molecular species. 

Concentration gradient Mass flux Jy Diffusion coefficient Fick s Law... 

The driving force for ion transport in a polymer phase can be either a concentration gradient (diffusive transport), an electric field (migration), or both. The resulting flux of the ionic species i, Ji, is usually described by the Nernst-Planck equation ... 

Diffusion, migration, and convection are the three possible mass transport processes accompanying an electrode reaction. In the first case, the particles move due to the formed concentration gradient. The flux in the case of planar (onedimensional or linear) diffusion can be described by Pick s first law ... 

Electrorefining and concentration polarization (a) sample electrode pair and electrolytic bath (b) concentration gradients (c) flux due to diffusion and electrostatic potential. 

Gas permeation through the porous membranes may be driven by pressure or concentration gradient. Under a pressure or concentration gradient, gas will permeate through the membrane in a convective or a diffusive flow, respectively. In general, the pressure-driven convective fluxes are much higher than the concentration-driven diffusion fluxes. 

The constant of proportionality D is called the diffusion coefficient, which is expressed in m s , c is the concentration in m and hence / is expressed in m s . The negative sign in this expression indicates that the direction of diffusion is opposite to the concentration gradient. This means that diffusion happens from a high- to a low-concentration region. This relationship between concentration gradient and flux is called Pick s first law and is formally identical to the Fourier law that relates thermal flux to temperature gradient. 

Diffusivity measures the tendency for a concentration gradient to dissipate to form a molar flux. The proportionality constant between the flux and the potential is called the diffusivity and is expressed in m /s. If a binary mixture of components A and B is considered, the molar flux of component A with respect to a reference plane through which the exchange is equimolar, is expressed as a function of the diffusivity and of the concentration gradient with respect to aji axis Ox perpendicular to the reference plane by the fpllqvving relatipn 6 /... 

Diffusion may be defined as the movement of a species due to a concentration gradient, which seeks to maximize entropy by overcoming inhomogeneities within a system. The rate of diffusion of a species, the flux, at a given point in solution is dependent upon the concentration gradient at that particular point and was first described by Pick in 1855, who considered the simple case of linear difflision to a planar surface ... 

If a sedimentation experiment is carried out long enough, a state of equilibrium is eventually reached between sedimentation and diffusion. Under these conditions material will pass through a cross section perpendicular to the radius in both directions at equal rates downward owing to the centrifugal field, and upward owing to the concentration gradient. It is easy to write expressions for the two fluxes which describe this situation ... 

The tme driving force for any diffusive transport process is the gradient of chemical potential rather than the gradient of concentration. This distinction is not important in dilute systems where thermodynamically ideal behavior is approached. However, it becomes important at higher concentration levels and in micropore and surface diffusion. To a first approximation the expression for the diffusive flux may be written... 

The concentration boundary layer forms because of the convective transport of solutes toward the membrane due to the viscous drag exerted by the flux. A diffusive back-transport is produced by the concentration gradient between the membranes surface and the bulk. At equiUbrium the two transport mechanisms are equal to each other. Solving the equations leads to an expression of the flux ... 

Mutual Diffusivity, Mass Diffusivity, Interdiffusion Coefficient Diffusivity is denoted by D g and is defined by Tick s first law as the ratio of the flux to the concentration gradient, as in Eq. (5-181). It is analogous to the thermal diffusivity in Fourier s law and to the kinematic viscosity in Newton s law. These analogies are flawed because both heat and momentum are conveniently defined with respec t to fixed coordinates, irrespective of the direction of transfer or its magnitude, while mass diffusivity most commonly requires information about bulk motion of the medium in which diffusion occurs. For hquids, it is common to refer to the hmit of infinite dilution of A in B using the symbol, D°g. 

Here / is the number of ink molecules diffusing down the concentration gradient per second per unit area it is called the flux of molecules (Fig. 18.3). The quantity c is the concentration of ink molecules in the water, defined as the number of ink molecules per unit volume of the ink-water solution and D is the diffusion coefficient for ink in water - it has units of m s . ... 

Physically, diffusion occurs because atoms, even in a solid, are able to move - to jump from one atomic site to another. Figure 18.4 shows a solid in which there is a concentration gradient of black atoms there are more to the left of the broken line than there are to the right. If atoms jump across the broken line at random, then there will be a net flux of black atoms to the right (simply because there are more on the left to jump), and, of course, a net flux of white atoms to the left. Pick s Law describes this. It is derived in the following way. 

Either the and the two e s diffuse outward through the film to meet the 0 at the outer surface, or the oxygen diffuses inwards (with two electron holes) to meet the at the inner surface. The concentration gradient of oxygen is simply the concentration in the gas, c, divided by the film thickness, x and the rate of growth of the film dx/dt is obviously proportional to the flux of atoms diffusing through the film. So, from Pick s Law (eqn. (18.1)) ... 

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