Net transport of ions

Consider a microchannel filled with an aqueous solution. There is an eleetrieal doubly layer field near the interface of the channel wall and the liquid. If an electric field is applied along the length of the channel, an electrical body force is exerted on the ions in the diffuse layer. In the diffuse layer of the double layer field, the net charge density, pe is not zero. The net transport of ions is the excess counterions. If the solid surface is negatively eharged, the counterions are the positive ions. These excess counterions will move under the influenee of the... 

FIGURE 10.16 The H+,lO-ATPase of gastric mucosal cells mediates proton transport into the stomach. Potassimn ions are recycled by means of an associated K /Cl cotransport system. The action of these two pnmps results in net transport of and Cl into the stomach. 

If there is a net transport of charge across the membrane, the membrane potential will influence the solute transfer and also be affected by it, complicating the data treatment. The starting point for most descriptions of the internalisation flux of permeant ions, i, is the one-dimensional Nernst-Planck equation (cf. equation (10)) that combines a concentration gradient with the corresponding electric potential gradient [270] ... 

The behavior of an ion type is described quantitatively by the Nernst equation (3). A /g is the membrane potential (in volts, V) at which there is no net transport of the ion concerned across the membrane (equilibrium potential). The factor RT/Fn has a value of 0.026 V for monovalent ions at 25 °C. Thus, for K, the table (2) gives an equilibrium potential of ca. -0.09 V—i. e., a value more or less the same as that of the resting potential. By contrast, for Na ions, A /g is much higher than the resting potential, at +0.07 V. Na" ions therefore immediately flow into the cell when Na channels open (see p. 350). The disequilibrium between Na" and IC ions is... 

As the estimations above display, the net flows of chloride and bicarbonate ions are negligible, and the transport of ions is passive. 

This search for the atomistic basis of the diffusion coefficient will commence from the picture ofrandom-walking ions (see Sections 4.2.4 to 4.2.6). It will be recalled that a net diffusive transport of ions occurs in spite of the completely random zigzag dance of individual ions, because of unequal numbers of ions in different regions. 

In the absence of an electric field, ions are in ceaseless random motion. This random walk of ions has been shown to have an important characteristic The mean distance traversed by the ions as a whole is zero because while some are displaced in one direction, an equal number are displaced in the opposite direction. From a phenomenological view, therefore, the random walk of ions can be ignored because it does not lead to any net transport of matter (as long as there is no difference in... 

Under these balanced conditions, the situation may be regarded as tantamount to equilibrium because there is no net flux or transport of ions. Hence, the Boltzmann law can be used. The argument is that since the potential varies along the x direction, the concentration of ions at any distance x is given by... 

The phenomena observed in living cells have much in common with those in artificial polymer membrane ISEs. In membrane electrodes, ionophores allow the net movement of ions in a membrane only down their electrochemical gradients. The equilibrium state is reached when the electrochemical gradient becomes zero and the cell potential reaches its final equilibrium value net transport no longer occurs. 

An ion channel must transport ions in either direction at the same rate. The net flow of ions is determined only by the composition of the solutions on either side of the membrane. 

This is accompanied by the transport of ions into L and transport of N03 ions out of L. The net change in number of moles of Cu ion in compartment L is... 

Invert emulsion drilling fluids are commonly selected for their temperature stability and their ability to prevent the wellbore stability problems associated with the hydration of clays in shale formations. The thermodynamic activity aw of the water in the aqueous (dispersed) phase is controlled by the addition of a salt (usually calcium chloride) to ensure that it is equal to or less than the activity of the water in the drilled shale formations. The emulsified layer around the water droplets is claimed to act as a semipermeable membrane that allows the transport of water into and out of the shale but not the transport of ions (61). When the activities (or, more strictly, the chemical potentials) of the water in the shale and invert emulsion are equal, then no net transport of water into or out of the shale occurs (i.e., the drilling fluid does not hydrate or dehydrate the shale). This equality of water activity has lead to the development of so-called balanced activity oil-based drilling fluids. 

Since three Na" ions are transported out for every two ions that are transported in, there is a net efflux of one positively charged ion. The net movement of ions sets up an electric current. 

Membranes represent formidable barriers to the movement of ions (and electrons). Thus, transport of ions as net charges across the insulator offered by the membrane will establish an electrical potential difference (a voltage = V) across the membrane (Vm or Aij/). This phenomenon is well known and can be described by Equation. (5.1) ... 

Since neutral ionophores essentially render the membrane differentially permeable to a positive charge (the charge carried by M ) and since electrical potentials are actively maintained across the membranes of virtually all cells, two factors determine the thermodynamic gradient governing net transport of M by neutral ionophores (1) the magnitude of the membrane potential, i.e. AEmAB, and (2) the concentration gradient of the permeable ion M across the membrane. In terms of experimentally measurable parameters, a Nernstian relationship is established ... 

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