Fick s law of diffusion first

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. 

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 ... 

Diffusion is the movement of mass due to a spatial gradient in chemical potential and as a result of the random thermal motion of molecules. While the thermodynamic basis for diffusion is best apprehended in terms of chemical potential, the theories describing the rate of diffusion are based instead on a simpler and more experimentally accessible variable, concentration. The most fundamental of these theories of diffusion are Fick s laws. Fick s first law of diffusion states that in the presence of a concentration gradient, the observed rate of mass transfer is proportional to the spatial gradient in concentration. In one dimension (x), the mathematical form of Fick s first law is... 

We can obtain an additional expression for the diffusion current by considering Fick s first law of diffusion, first introduced in chapter 1, equation (1.34). If J is the flux of species to the electrode, it will be related to the observed current, /, by ... 

The original and simplest form of the diffusion layer theory was developed by Nemst [105] and Brunner [106], who assumed that the mass flux is given by Fick s first law of diffusion. In that case,... 

Transport across the direction of flow can be determined using Fick s first law of diffusion for the flux of material in particles/cm2 sec-1 in a steady, time-independent state... 

Diffusion is quantified by measuring the concentration of the diffusing species at different distances from the release point after a given time has elapsed at a precise temperature. Raw experimental data thus consists of concentration and distance values. The degree of diffusion is represented by a diffusion coefficient, which is extracted from the concentration-distance results by solution of one of two diffusion equations. For one-dimensional diffusion, along x, they are Fick s first law of diffusion ... 

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... 

The ideas of Overton are reflected in the classical solubility-diffusion model for transmembrane transport. In this model [125,126], the cell membrane and other membranes within the cell are considered as homogeneous phases with sharp boundaries. Transport phenomena are described by Fick s first law of diffusion, or, in the case of ion transport and a finite membrane potential, by the Nernst-Planck equation (see Chapter 3 of this volume). The driving force of the flux is the gradient of the (electro)chemical potential across the membrane. In the absence of electric fields, the chemical potential gradient is reduced to a concentration gradient. Since the membrane is assumed to be homogeneous, the... 

The rate at which they diffuse depends on the concentration gradient, dN dx the larger the gradient, the faster the rate of diffusion. This is the basis of the well-known Fick s first law of diffusion ... 

This is the correct expression for use in the analysis of closed diffusion-cell experiments for the measurement of diffusion coefficients. Equation (48) is known as Fick s First Law of Diffusion. Note that Na = — NB corresponds to saying that w = 0. 

We saw above, from Fick s first law of diffusion, that the flux at a distance r from the central particle is given by... 

In Chap. 2 and 3, the motion of two reactants was considered and a diffusion equation was derived based upon the equation of continuity and Fick s first law of diffusion (see, for instance, Chap. 2 and Chap. 3, Sect. 1.1). When one reactant (say D) can transfer energy or an electron to the other reactant (say A) over distances greater than the encounter separation, an additional term must be considered in the equation of continuity. The two-body density n (rj, r2, t) decays with a rate coefficient l(r, — r2) due to long-range transfer. Furthermore, if energy is being transferred from an excited donor to an acceptor, the donor molecular excited state will decay, even in the absence of acceptor molecules with a natural lifetime r0. Hence, the equation of continuity (42) becomes extended to include two such terms and is... 

Fick s first law of diffusion relates the diffusive flux of species k to its mass fraction or mole fraction gradient. For a binary mixture of species j and k, the mass flux of species k relative to the mass average velocity is, related to the mass fraction gradient of k as... 

Here Dt is a positive proportionality constant ( diffusion constant for Et), Jfz is z-ward flow induced by the gradient, and superscript e denotes eigenmodt character of the associated force or flow. The proportionality (13.25) corresponds to Fick s first law of diffusion when Et is dominated by mass transport or to Fourier s heat theorem when Et is dominated by heat transport, but it applies here more deeply to the metric eigenvalues that control all transport phenomena. In the near-equilibrium limit (13.25), the local entropy production rate (13.24) is evaluated as... 

Both the current and the concentration profiles of O and R are determined by diffusion to and from the electrode. These quantities are obtained from calculations using Fick s laws of diffusion. Fick s first law of diffusion... 

Diffusion processes occur in all systems where concentration differences exist. Diffusion is the main mechanism which aids Ln the elimination of concentration gradients. Fick s first law of diffusion defines this phenomenon by correlating mass flow and concentration gradient. This law may be shown as... 

The rate of diffusion is proportional to the concentration gradient, and the proportionality constant is defined as the diffusion coefficient (D) in Fick s first law of diffusion. Experimental determination of D is commonly performed ex vivo due to the difficulty of measuring concentration gradients in the interstitium. In vivo measurement can be performed in specific tissues, using transparent chamber preparations in combination with the FRAP technique (Berk et al., 1997 Jain et al., 1997 Pluen et al, 2001). However, the in vivo approach is limited only to fluorescent molecules or solutes whose D is not affected by labeling with fluorescent markers. 

The steady state mass flux (J ) of component i through a homogeneous film of uniform thickness separating two gaseous phases is given by Fick s "First Law of diffusion ... 

The intercellular pathway is now accepted as the major pathway for absorption. Recall that the rate of penetration is often correlated with the partition coefficient. In fact this is a very tortuous pathway, and the h (skin thickness) in Fick s first law of diffusion is really 10 x the measured distance. By placing a solvent (e.g., ether, acetone) on the surface or tape stripping the surface, the stratum comeum (SC) is removed, and absorption can be significantly increased by removing this outer barrier. This may not be the case for very lipophilic chemical. This is because the viable epidermis and dermis are regarded as aqueous layers compared to the SC. Note that the more lipophilic the drug, the more likely it will form a depot in the SC and be slowly absorbed over time and thus have a prolonged half-life. 

In the ideal case the resistance to mass transfer of a diffusive sampler is confined to the stagnant air gap between the sampling face of the device and the surface of the collecting sorbent material (Van den Hoed and Van Asselen, 1991). Then the mass flow through the sampler can be described by Fick s first law of diffusion... 

The rate at which a substance enters a cell via passive diffusion is represented by Fick s First Law of Diffusion (Equation (1)) ... 

Fick s first law of diffusion (analogous with the equation of heat conduction) states that the mass of substance dm diffusing in the x direction in a time df across an area A is proportional to the concentration gradient dc/dx at the plane in question ... 

The rate of permeation for the case shown schematically in Fig. 2.57 is defined as the mass of penetrating gas or liquid that passes through a polymer membrane per unit time. The rate of permeation, m, can be defined using Fick s first law of diffusion as... 

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