Fick first law

The rate of mass transfer depends on the inlerfacial contact area and on the rate uf mass transfer per unit inlerfacial area, i.e.. the mass flux. Lie mass flux very close to ihe liquid-liquid interface is determined by molecular diffusion in accordance with Ficks First law ... 

The Fick first law of binary diffusion [29], expressing the mass flux as a function of the driving force, can be defined by ... 

The resistance to oxygen diffusion at the blood-tissue interface is negligible (21, 22). The oxygen partial pressure profile is continuous at the blood-tissue interface, and transport across the blood-tissue interface can be described by Ficks first law (22). 

This is the familiar Ficks first law of diffusion. The phenomenological coefficient, D, is the molecular diffusivity of the gas species in the membrane. The gradient of the flux is equal to the negative time rate of change of the concentration. Thus, nonsteady diffusion is described by the following ... 

A = maximal respiration volume, K = kinetic rate constant). Only steady-state conditions are analyzed (dc/dt = 0). Furthermore, the validity of Ficks first law is assumed. 

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 Ficks first law for one-dimensional, binary component diffusion for molecular transport without turbulence shown by Eq. (2-149)... 

Diffusion is described by Ficks first law of diffusion (Equation 7), which states that the number of particles diffusing through a cross-sectional area per... 

A few simple equations describe most appHcations of barrier polymers. Equation 1 is an adaptation for films of Fick s First Law. 

Fick s First Law This law relates flux of a component to its composition gradient, employing a constant of proportionahty called a... 

In most cases, activity coefficients are close to one, and Fick s first law is written as ... 

According to Fick s first law, the rate of diffusion (i.e., the flux) is directly proportional to the slope of the concentration gradient ... 

Derive the Cottrell equation by combining Fick s first law of diffusion with the tune-dependent change of the concentration gradient during a potential-step experiment. 

If the rate of a reaction is governed by the encounter frequency, it is said to be diffusion-controlled. This frequency imposes an upper limit on the rate of reaction that can be evaluated by the use of Fick s laws of diffusion. The mathematical expression of this phenomenon was first presented by von Smoluchowski.2 We shall adopt a simple approach,3,4 although more rigorous derivations have been given.5... 

The quantity of solute B crossing a plane of area A in unit time defines the flux. It is symbolized by J, and is a vector with units of molecules per second. Fick s first law of diffusion states that the flux is directly proportional to the distance gradient of the concentration. The flux is negative because the flow occurs in a direction so as to offset the gradient ... 

A pure gas is absorbed into a liquid with which it reacts. The concentration in the liquid is sufficiently low for the mass transfer to be covered by Fick s Law and the reaction is first-order with respect to the solute gas. It may be assumed that the film theory may be applied to the liquid and that the concentration of solute gas falls from the saturation value to zero across the film. The reaction is initially carried out at 293 K. By what factor will the mass transfer rate across the interface change, if the temperature is raised to 313 K ... 

A solute diffuses from a liquid surface at which its molar concentration is C, into a liquid with which it reads. The mass transfer rate is given by Fick s law and the reaction is first order with respect to the solute, fn a steady-state process the diffusion rate falls at a depth L to one half the value at the interface. Obtain an expression for the concentration C of solute at a depth z from the surface in terms of the molecular diffusivity D and the reaction rate constant k. What is the molar flux at the surface ... 

To inject a general note it may be pointed out that two very important laws, called Fick s laws, form the basis of diffusion theory. The first law can be expressed in the following form ... 

If the flux Jo) and the concentration profile [C(x)] are measured, the diffusivity can be obtained through Fick s first law ... 

If we consider the limiting current ( ,) to be confined to a merely diffusion-limited current (id), we can consider its value as follows. As an example we take the cathodic reduction of a Zn2+ solution with a considerable amount of KC1. We chose an Eapp value greater than Eiecomp of Zn2+ and less than decomp of K +, so that only Zn2+ is reduced. The transport of electricity is completely provided for by the excess of K+ and Cl ions and hence Zn2+ ions can reach the cathode only by diffusion. Suppose [Zn2+ ] in the bulk of the solution is equal to C and at the cathode surface is equal to c the latter therefore determines the electrode potential. For diffusion perpendicular to the electrode surface we have Fick s first law ... 

Fick s first law applied to homogeneous membranes at steady state is a transport equation... 

It is practical to make the approximation that CM(oo) m Cm (t). This is justified if the membrane is saturated with the sample in a short period of time. This lag (steady-state) time may be approximated from Fick s second law as tlag = h2 / (n2Dm), where h is the membrane thickness in centimeters and Dm is the sample diffusivity inside the membrane, in cm2/s [40,41]. Mathematically, xLAG is the time at which Fick s second law has transformed into the limiting situation of Fick s first law. In the PAMPA approximation, the lag time is taken as the time when solute molecules first appear in the acceptor compartment. This is a tradeoff approximation to achieve high-throughput speed in PAMPA. With h = 125 pm and Dm 10 7 cm2/s, it should take 3 min to saturate the lipid membrane with sample. The observed times are of the order of 20 min (see below), short enough for our purposes. Cools... 

We will first consider the simple case of diffusion of a non-electrolyte. The course of the diffusion (i.e. the dependence of the concentration of the diffusing substance on time and spatial coordinates) cannot be derived directly from Eq. (2.3.18) or Eq. (2.3.19) it is necessary to obtain a differential equation where the dependent variable is the concentration c while the time and the spatial coordinates are independent variables. The derivation is thus based on Eq. (2.2.10) or Eq. (2.2.5), where we set xj> = c and substitute from Eq. (2.3.18) or Eq. (2.3.19) for the fluxes. This yields Fick s second law (in fact, this is only a consequence of Fick s first law respecting the material balance—Eq. 2.2.10), which has the form of a partial differential equation... 

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