Fick s law of diffusion second

In this context, the relative terms far, short, small, and large can be defined as follows. Fick s second law of diffusion dictates that the distance, 5, that a species having a diffusion coefficient, D, may diffuse within a period of time, t, is given by (12) ... 

A crystal is suspended in fresh solvent and 5% of the crystal dissolves in 300 s. How long will it take before 10% of the crystal has dissolved Assume that the solvent can be regarded as infinite in extent, that the mass transfer in the solvent is governed by Fick s second law of diffusion and may be represented as a unidirectional process, and that changes in the surface area of the crystal may be neglected. Start your... 

Hence by substitution of the convection term and from Fick s second law of diffusion (eqn. 3.2), we obtain... 

Many extensions have been derived for the Ilkovic equation from the consideration that the dme does not behave as a flat electrode but in fact shows a spherical growth. For instance, Fick s second law of diffusion (cf., eqn. 3.2) becomes12... 

Fick s second law of diffusion can be derived from Fick s first law by using a mass balance approach. Consider the differential fluid element shown in Figure 4. This differential fluid element is simply a small cube of liquid or gas, with volume Ax Ay Az, and will be defined as the system for the mass balance. Assume now that component A enters the cube at position x by diffusion and exits the cube at x + Ax by the same mechanism. For the moment, assume that no diffusion occurs in the y or z directions and that the faces of the cube that are perpendicular to the y and z axes thus are impermeable to the diffusion of A. Under these conditions, the component mass balance for A in this system is... 

This is Fick s second law of diffusion, the equation that forms the basis for most mathematical models of diffusion processes. The simple form of the equation shown above is applicable only to diffusion in one dimension (x) in systems of rectangular geometry. The mathematical form of the equation becomes more complex when diffusion is allowed to occur in more than one dimension or when the relationship is expressed in cylindrical or spherical coordinate geometries. Since the simple form shown above is itself a second-order partial differential equation, the threat of added complexity is an unpleasant proposition at best. 

Equation (9) is Fick s second law of diffusion, derived on the assumption that D is constant. Fick s second law essentially states that the rate of change in concentration in a volume within the diffusional field is proportional to the rate of change in the spatial concentration gradient at that point in the field, the proportionality constant being the diffusion coefficient. 

This is known as Fick s second law of diffusion or more commonly as the diffusion equation. In these equations, J is called the flux of the diffusing species, with units of [amount of substance (atoms or equivalent units) m2 s-1], c is the concentration of the diffusing species, with units of [amount of substance (atoms or equivalent units) m-3] at position x (m) after time t (s) D is the diffusion coefficient, units (m2 s 1). 

This is Fick s second law of diffusion, the diffusion equation. 

The simple kinetics for uptake of soluble substrate of the bacteria in a biofilm is traditionally described by a combination of mass transport across the water/biofilm interface, transport in the biofilm itself and the corresponding relevant biotransformations. Transport through the stagnant water layer at the biofilm surface is described by Fick s first law of diffusion. Fick s second law of diffusion and Michaelis-Menten (Monod) kinetics are used for describing the combined transport and transformations in the biofilm itself (Williamson... 

Guy et al. [5] derived an equation for the diffusion-controlled release of a drug from a sphere, radius r, by applying the three-dimensional form of Fick s second law of diffusion after transformation to spherical coordinates. This equation can be rearranged as ... 

The treatment of nonsteady-state diffusion is a question of solving Fick s second law of diffusion. In many cases, however, the equations can be taken from the treatments of the analogous problems in heat flow in solids. The point is that heat flow and diffusion are described by mathematically similar methods. 

We consider the diffusive motion of a B molecule relative to an A molecule. In order for a reaction to occur, the reactants must be brought close together by the diffusive motion, that is, a B molecule must approach an A molecule. For the sake of solving the differential equation used to describe this problem we need to specify some distance Rc between A and B at which reaction may take place. It is a necessary condition for a reaction to occur that the molecules must get close to each other, say at a distance Rc, but not a sufficient condition. Whether or not they will react is determined by the reaction rate constant ks in a simple second-order reaction scheme according to ksC-Q Rc,t) (it is second order because the concentration of A is one at Rc and therefore not seen explicitly in the expression). C-a Rc,t) is the concentration of B at a distance Rc from the A molecule. The diffusive motion of B is described by Fick s second law of diffusion ... 

On the assumption that the oxygen transfer can be represented by a surface renewal model, obtain the appropriate equation for mass transfer by starting with Fick s second law of diffusion and calculate ... 

State the assumptions made in the penetration theory for the absorption of a pure gas into a liquid. The surface of an initially solute-free liquid is suddenly exposed to a soluble gas and the liquid is sufficiently deep for no solute to have time to reach the far boundary of the liquid. Starting with Fick s second law of diffusion, obtain an expression for (i) the concentration, and (ii) the mass transfer rate at a time t and a depth y below the surface. 

When flow and mean displacement velocities are zero (U = 0 and v = 0), the above reduces to Fick s second law of diffusion... 

Equation (6.7) is referred to as Fick s second law of diffusion and relates the temporal and spatial distribution of concentration of the system. 

Higuchi s approximation of the pseudo-steady state is no longer valid when A < Cs. Instead of assuming a linear concentration gradient within the drug-depleted layer, Fick s second law of diffusion is used to calculate the concentration profiles of the dissolved drug as ... 

Equation (4.2) reveals that the fraction of drug released is linearly related to the square root of time. However, (4.2) cannot be applied throughout the release process since the assumptions used for its derivation are not obviously valid for the entire release course. Additional theoretical evidence for the time limitations in the applicability of (4.2) has been obtained [10] from an exact solution of Fick s second law of diffusion for thin films of thickness S under perfect sink conditions, uniform initial drug concentration with cq > cs, and assuming constant diffusion coefficient of drug T> in the polymeric film. In fact, the short-time approximation of the exact solution is... 

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