Concentration gradients, S

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 /... 

Diflfiisive processes nonnally operate in chemical systems so as to disperse concentration gradients. In a paper in 1952, the mathematician Alan Turing produced a remarkable prediction [37] that if selective diffiision were coupled with chemical feedback, the opposite situation may arise, with a spontaneous development of sustained spatial distributions of species concentrations from initially unifonn systems. Turmg s paper was set in the context of the development of fonn (morphogenesis) in embryos, and has been adopted in some studies of animal coat markings. With the subsequent theoretical work at Brussels [1], it became clear that oscillatory chemical systems should provide a fertile ground for the search for experimental examples of these Turing patterns. 

When a sample is injected into the carrier stream it has the rectangular flow profile (of width w) shown in Figure 13.17a. As the sample is carried through the mixing and reaction zone, the width of the flow profile increases as the sample disperses into the carrier stream. Dispersion results from two processes convection due to the flow of the carrier stream and diffusion due to a concentration gradient between the sample and the carrier stream. Convection of the sample occurs by laminar flow, in which the linear velocity of the sample at the tube s walls is zero, while the sample at the center of the tube moves with a linear velocity twice that of the carrier stream. The result is the parabolic flow profile shown in Figure 13.7b. Convection is the primary means of dispersion in the first 100 ms following the sample s injection. 

The electron current density J has units of A/cm and in a semiconductor results from drift and diffusion. In the absence of concentration gradients, equation 7 reduces to Ohm s law, = nqp E = [Pg.346]

Molecular transport concerns the mass motion of molecules in condensed and gaseous phases. The mass motions are driven primarily by temperature. As time progresses, the initial mass motion results in concentration gradients. In the condensed phase, dow along concentration gradients is described by Fick s law. 

When a relatively slow catalytic reaction takes place in a stirred solution, the reactants are suppHed to the catalyst from the immediately neighboring solution so readily that virtually no concentration gradients exist. The intrinsic chemical kinetics determines the rate of the reaction. However, when the intrinsic rate of the reaction is very high and/or the transport of the reactant slow, as in a viscous polymer solution, the concentration gradients become significant, and the transport of reactants to the catalyst cannot keep the catalyst suppHed sufficientiy for the rate of the reaction to be that corresponding to the intrinsic chemical kinetics. Assume that the transport of the reactant in solution is described by Fick s law of diffusion with a diffusion coefficient D, and the intrinsic chemical kinetics is of the foUowing form... 

For an ion to move through the lattice, there must be an empty equivalent vacancy or interstitial site available, and it must possess sufficient energy to overcome the potential barrier between the two sites. Ionic conductivity, or the transport of charge by mobile ions, is a diffusion and activated process. From Fick s Law, J = —D dn/dx), for diffusion of a species in a concentration gradient, the diffusion coefficient D is given by... 

Membra.ne Diffusiona.1 Systems. Membrane diffusional systems are not as simple to formulate as matrix systems, but they offer much more precisely controlled and uniform dmg release. In membrane-controlled dmg deUvery, the dmg reservoir is intimately surrounded by a polymeric membrane that controls the dmg release rate. Dmg release is governed by the thermodynamic energy derived from the concentration gradient between the saturated dmg solution in the system s reservoir and the lower concentration in the receptor. The dmg moves toward the lower concentration at a nearly constant rate determined by the concentration gradient and diffusivity in the membrane (33). 

An analogy exists between mass transfer by diffusion and heat transfer by conduction. Each involves coHisions between molecules and a gradient as the driving force which causes flow. Eor diffusion, this is a concentration gradient for conduction, the driving force is an energy gradient. Eourier s... 

When concentration gradients in the solution can be ignored, equations 25 through 29 show that the electric potential is governed by Laplace s equation... 

Back-diffusion is the transport of co-ions, and an equivalent number of counterions, under the influence of the concentration gradients developed between enriched and depleted compartments during ED. Such back-diffusion counteracts the electrical transport of ions and hence causes a decrease in process efficiency. Back-diffusion depends on the concentration difference across the membrane and the selectivity of the membrane the greater the concentration difference and the lower the selectivity, the greater the back-diffusion. Designers of ED apparatus, therefore, try to minimize concentration differences across membranes and utilize highly selective membranes. Back-diffusion between sodium chloride solutions of zero and one normal is generally [Pg.173]

Diffusion is the molecular transport of mass without flow. The diffu-sivity (D) or diffusion coefficient is the proportionality constant between the diffusion and the concentration gradient causing diffusion. It is usually defined by Fick s first law for one-dimensional, binary component diffusion for molecular transport without turbulence shown by Eq. (2-149)... 

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. 

HONO the mean flux was an emission of 1 ng Nm s but this includes periods both of emission and deposition. On several occasions, no concentration gradients were detected. The direction of the flux was dependent on NOj concentration, with emission observed only when NOj concentration was less than 10 ppb. The process of HONO exchange appears to be regulated by the net result of small deposition flux to the surface and a surface chemistry production of HONO from NOj. Fluxes of PAN deposition were measured using a chamber technique " and were small (less than 0.5ng Nm s ). 

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)) ... 

Concentration gradient inside the catalyst particle. The continuity statement, at the catalyst surface, is similar to Pick s first law for diffiasion. The reaction rate is equal to the diffusion rate at the outside layer of the catalyst... 

Of particular interest in the usage of polymers is the permeability of a gas, vapour or liquid through a film. Permeation is a three-part process and involves solution of small molecules in polymer, migration or diffusion through the polymer according to the concentration gradient, and emergence of the small particle at the outer surface. Hence permeability is the product of solubility and diffusion and it is possible to write, where the solubility obeys Henry s law,... 

Next, the German Adolph Eick (1829-1901), stimulated by Graham s researches, sought to turn diffusion into a properly quantitative concept and formulated the law named after him, relating the rate of diflfusion to the steepness of the concentration gradient (Eick 1855), and confirmed his law by measurements of diflfusion in liquids. In a critical examination of the influence of this celebrated piece of theory, Tyrrell... 

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