Fluxes of ions

A number of metals, such as copper, cobalt and h on, form a number of oxide layers during oxidation in air. Providing that interfacial thermodynamic equilibrium exists at the boundaries between the various oxide layers, the relative thicknesses of the oxides will depend on die relative diffusion coefficients of the mobile species as well as the oxygen potential gradients across each oxide layer. The flux of ions and electrons is given by Einstein s mobility equation for each diffusing species in each layer... 

Maintenance of electrical potential between the cell membrane exterior and interior is a necessity for the proper functioning of excitable neuronal and muscle cells. Chemical compounds can disturb ion fluxes that are essential for the maintenance of the membrane potentials. Fluxes of ions into the cells or out of the cells can be blocked by ion channel blockers (for example, some marine tox-... 

The maximum kinetic energy flux of ions. (eTlmax (W m ), can be defined as... 

The general Planck s solution of the liquid-junction potential is based on the assumption that the fluxes of ions in the liquid junction are in a steady state. As the mathematical treatment is rather space-consuming the reader is recommended to inspect a more recent treatment of this by W. E. Morf... 

Receptor-effector mechanisms include (1) enzymes with catalytic activities, (2) ion channels that gate the transmembrane flux of ions (ionotropic receptors), (3) G protein-coupled receptors that activate intracellular messengers (metabotropic receptors), and (4) cytosolic receptors that regulate gene transcription. Cytosolic receptors are a specific mechanism of many steroid and thyroid hormones. The ionotropic and metabotropic receptors are discussed in relevance to specific neurotransmitters in chapter 2. 

The flux of ions across the interface at equilibrium is generally given by an exchange current (jq) expressed in A cm If a potential difference between the bulk phases, different from A(f>, is imposed on the interface, a net current of Ag will flow (Fig. 10.2). 

The fluxes of charged solutes depend on the diffusion potential arising from differences in the mobihties of individual ions, as well as on an ion s own concentration gradient (Equation 2.21). The effect of diffusion potentials will be important if the carbonate species are a large part of the total ion concentration, as they often will be. Therefore we have for the net flux of ion B... 

The flux of ions across a membrane barrier, usually in the downward direction with respect to ion concentra-... 

For thick membranes and sufficiently fast reaction kinetics at the membrane boundaries ( equilibrium domain ), diffusion through the membrane interior is rate limiting and we obtain for the mass flux of ions ... 

Although attractive isotope effects may be expected especially in the Ca2H selective solvent polymeric membranes mentioned [see B. E. Jepson and R. DeWitt, J. Inorg. Nucl. Chem., 38, 1175 (1976)], we have not so far studied such effects. As compared to the flux of ions in the elec-trodialytic transport experiments we carried out on solvent polymeric membranes, the flux of ions is negligible in the absence of an electric field (other parameters kept constant). 

The transmembrane potential of cardiac cells is determined by the concentrations of several ions—chiefly sodium (Na+), potassium (K+), calcium (Ca2+), and chloride (Cl-)—on either side of the membrane and the permeability of the membrane to each ion. These water-soluble ions are unable to freely diffuse across the lipid cell membrane in response to their electrical and concentration gradients they require aqueous channels (specific pore-forming proteins) for such diffusion. Thus, ions move across cell membranes in response to their gradients only at specific times during the cardiac cycle when these ion channels are open. The movements of the ions produce currents that form the basis of the cardiac action potential. Individual channels are relatively ion-specific, and the flux of ions through them is... 

At the copper electrode, reduction of Cu2+ is favoured and oxidation of Cu atoms is restricted, so that net cathodic flow occurs. Finally, to prevent a build up of Zn2+ ions near the zinc/electrolyte interface and of SO42-counter ions near the copper, a flux of ions must take place in the electrolytic phase to balance the charge transfer processes at the interfaces. To maintain the flux continuity condition, the applied voltage difference becomes distributed in such a way that ... 

A variation of in-situ volumetry (or manometry) is its combination with high temperature coulometry as shown in Figure 16-4. The A n( ) change in the gas volume due to the reaction is compensated for by a corresponding flux of ions across an appropriate solid electrolyte. This coulometric transport is potentiostatically controlled with a reference electrode (Fig. 16-4). Since 10 p A times 1 s = 10 pC corresponds to ca. 10-11 mol, the sensitivity of the combined volumetry-coulometry matches that of tensiometry. Limitations of this method are leaks and the small electronic transference in the electrolyte. 

Helffekich calculated the fluxes of ions and the concentration-profiles. Steady-state conditions are assumed. 

Here, m Tw is the water transport number, Jw is the water flux, and J is the flux of ions through a given membrane. 

Figure 5.4 Schematic drawing illustrating the concentration profiles of a salt in the laminar boundary layer on both sides of a cation-exchange membrane and the flux of ions in the solutions and the membrane.

It has been shown that the impact of any electric potential gradient on the flux of ions may be disregarded under flue gas desulfurization conditions, as long as the mass flux equations are combined with a flux charge equation [99]. Therefore, the mass balances must be combined with a flux of charge balance as the potential gradient is neglected [70]. 

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