Chemical gradient diffusion

Major differences are the following (1) Facihtated diffusion can operate bidirectionally, whereas active transport is usually unidirectional. (2) Active transport always occurs against an electrical or chemical gradient, and so it requires energy. 

Let us assume that the molecular transport is governed only by the differences in the chemical potential (diffusion) and neglect a possible order parameter transport by the hydrodynamic flow [1,144,157]. Then, one can postulate a linear relationship between the local current and the gradient of the local chemical potential difference p(r) [146,147] as... 

Gradient diffusion was assumed in the species-mass-conservation model of Shir and Shieh. Integration was carried out in the space between the ground and the mixing height with zero fluxes assumed at each boundary. A first-order decay of sulfur dioxide was the only chemical reaction, and it was suggested that this reaction is important only under low wind speed. Finite-difference numerical solutions for sulfur dioxide in the St. Louis, Missouri, area were obtained with a second-order central finite-difference scheme for horizontal terms and the Crank-Nicolson technique for the vertical-diffusion terms. The three-dimensional grid had 16,800 points on a 30 x 40 x 14 mesh. 

When it comes to the equilibration of water concentration gradients, the relevant transport coefficient is the chemical diffusion coefficient, Dwp. This parameter is related to the self-diffusion coefficient by the thermodynamic factor (see above) if the elementary transport mechanism is assumed to be the same. The hydration isotherm (see Figure 8) directly provides the driving force for chemical water diffusion. Under fuel-cell conditions, i.e., high degrees of hydration, the concentration of water in the membrane may change with only a small variation of the chemical potential of water. In the two-phase region (i.e., water contents of >14 water molecules... 

Figure 3. Concentration dependence of the diffusion coefficient of polystyrene in THF at 23 C. (a) collective modes, (b) cumulant values and classical gradient diffusion, (c) cooperative mode. (Reproduced from Ref. 19. Copyright 1985 American Chemical Society. ...

The release location influences the vertical distribution of the time-averaged concentration and fluctuations. For a bed-level release, vertical profiles of the time-averaged concentration are self-similar and agreed well with gradient diffusion theory [26], In contrast, the vertical profiles for an elevated release have a peak value above the bed and are not self-similar because the distance from the source to the bed introduces a finite length scale [3, 25, 37], Additionally, it is clear that the size and relative velocity of the chemical release affects both the mean and fluctuating concentration [4], The orientation of the release also appears to influence the plume structure. The shape of the profiles of the standard deviation of the concentration fluctuations is different in the study of Crimaldi et al. [29] compared with those of Fackrell and Robins [25] and Bara et al. [26], Crimaldi et al. [29] attributed the difference to the release orientation, which was vertically upward from a flush-mounted orifice at the bed in their study. 

Matano developed a graphical method which, for certain classes of boundary value problems, relates the form of the diffusion profile with the concentration dependence of the interdiffusivity, D(c), introduced in Section 3.1.3 [5]. This method can determine D(c) from the diffusion profile in chemical concentration-gradient diffusion experiments where atomic volumes are sufficiently constant so that changes in overall specimen volume are insignificant and diffusion can be formulated in a F-frame. The method uses scaling, as discussed in Section 4.2.2. 

We will see that in the steady state of the blocking cells, we can extract partial conductivities, and from the transients chemical diffusion coefficients (and/or interfacial rate constants). Cell 7 combines electronic with ionic electrodes here a steady state does not occur but the cell can be used to titrate the sample, i.e., to precisely tune stoichiometry. Cell 1 is an equilibrium cell which allows the determination of total conductivity, dielectric constant or boundary parameters as a function of state parameters. In contrast to cell 1, cell 2 exhibits a chemical gradient, and can be used to e.g., derive partial conductivities. If these oxygen potentials are made of phase mixtures212 (e.g., AO, A or AB03, B203, A) and if MO is a solid electrolyte, thermodynamic formation data can be extracted for the electrode phases. 

Ion channels are transmembrane proteins that span the cell membrane and are formed from one or more protein subunits. The channels are shaped like tunnels, which form pores through the plasma membrane. The pores have gates that open and close to allow ions to diffuse down their chemical gradient and move in or out of a cell. Ion channels are specific for certain types (and combinations of types) of ions, such as chloride, sodium, potassium, and calcium. 

If the bulk process is dominating, in the electrical experiment the total conductivity (ionic and electronic) is measured, the second gives information on the tracer diffusion coefficient (D ) which is directly related to the ionic conductivity (or DQ). In the third experiment one measures the chemical diffusion coefficient (D5), which is a measure of the propagation rate of stoichiometric changes (at given chemical gradient) it is evidently a combination of ionic and electronic conductivities and concentrations.3,4,173 175... 

IONIC DRIFT UNDER A CHEMICAL-POTENTIAL GRADIENT DIFFUSION... 

In the case of nonequilibrium spatial distribution of a certain species, characterized by a nonuniform distribution of chemical potential, diffusion of this species will occur in accordance with the gradient of its chemical potential. If a gradient exists in the chemical potential for one of the species, then a statistical force will be exerted on the particle distribution. The average velocity of a particle will be given by the product of its mobility and the sum of the forces acting on it (4). During the transport of a substance across a membrane, it must move through phase boundaries, such as aqueous phase/membrane/aqueous phase. As mentioned before, the substance has different affinities to each phase encountered. In most cases, the diffusion within the membrane is much slower than in the liquid phase. 

The membrane is essentially a barrier, that separates two phases and restricts transport of various chemicals in a selective maimer. A membrane can be homogeneous or heterogeneous, symmetric or asymmetric, sofid or liquid it can carry positive or negative charges or can be neutral. Transport through a membrane can be affected by convection or by diffusion of individual molecules, and induced by the chemical gradient or electrical gradient. 

In general, the diffusive mass flux is composed of diffusion due to concentration gradients (chemical potential gradients), diffusion due to thermal effects (Soret diffusion) and diffusion due to pressure and external forces. It is possible to include the full multicomponent model for concentration gradient driven diffusion (Taylor and Krishna, 1993 Bird, 1998). In most cases, in the absence of external forces, it is... 

There seem to be several ways for substances to enter the cell across the membrane. The simplest method, that works for the smaller molecules and ions, is one of passive diffusion, and occurs whenever their relative concentrations inside and outside the cell are different. Thus a chemical gradient in the case of non-electro-ly tes or an electrochemical gradient in the case of charged particles... 

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