Diffusion transport system

Though drugs appear to cross the blood-brain barrier by passive diffusion, transporter systems in the blood-brain barrier pump drugs back out into the systemic circulation. As in the gut, the Pgp transporter system is the primary active transporter in the blood-brain barrier identified to date. This ATP-dependent transporter system picks up substrates that have crossed the capillary endothelial cells and transports them back to the systemic circulation, limiting their penetration into the CNS. Thus, not only are the physicochemical properties of the drug a determinant for penetration into the CNS but penetration also depends on whether the drug is a substrate for the Pgp transporter system. 

Glucose cannot diffuse directly into cells, but enters by one of two transport mechanisms a Na+-independent, facilitated diffusion transport system or a Na+-monosaccharide co-transporter system. 

Sedimentary denitrification rates have been estimated from measured pore-water solute profiles using diagenetic models, determined direcdy via sediment incubation both on deck and in situ, and determined from N-incubation techniques. Sedimentary diagenetic process can be thought of as a simple reaction—diffusion-transport system (Berner, 1980 Boudreau, 1997). In a simple fine-grained sediment system, transport is via molecular diffusion and the diagenetic equation describing this system can be expressed as ... 

The tme driving force for any diffusive transport process is the gradient of chemical potential rather than the gradient of concentration. This distinction is not important in dilute systems where thermodynamically ideal behavior is approached. However, it becomes important at higher concentration levels and in micropore and surface diffusion. To a first approximation the expression for the diffusive flux may be written... 

Sorption Rates in Batch Systems. Direct measurement of the uptake rate by gravimetric, volumetric, or pie2ometric methods is widely used as a means of measuring intraparticle diffusivities. Diffusive transport within a particle may be represented by the Fickian diffusion equation, which, in spherical coordinates, takes the form... 

Calcium is absorbed from the intestine by facilitated diffusion and active transport. In the former, Ca " moves from the mucosal to the serosal compartments along a concentration gradient. The active transport system requires a cation pump. In both processes, a calcium-binding protein (CaBP) is thought to be required for the transport. Synthesis of CaBP is activated by 1,25-DHCC. In the active transport, release of Ca " from the mucosal cell into... 

Mass Transport. An expression for the diffusive transport of the light component of a binary gas mixture in the radial direction in the gas centrifuge can be obtained directly from the general diffusion equation and an expression for the radial pressure gradient in the centrifuge. For diffusion in a binary system in the absence of temperature gradients and external forces, the general diffusion equation retains only the pressure diffusion and ordinary diffusion effects and takes the form... 

Passive diffusion is the simplest transport process. In passive diffusion, the transported species moves across the membrane in the thermodynamically favored direction without the help of any specific transport system/molecule. For an uncharged molecule, passive diffusion is an entropic process, in which movement of molecules across the membrane proceeds until the concentration of the substance on both sides of the membrane is the same. For an uncharged molecule, the free energy difference between side 1 and side 2 of a membrane (Figure 10.1) is given by... 

All of the transport systems examined thus far are relatively large proteins. Several small molecule toxins produced by microorganisms facilitate ion transport across membranes. Due to their relative simplicity, these molecules, the lonophore antibiotics, represent paradigms of the mobile carrier and pore or charmel models for membrane transport. Mobile carriers are molecules that form complexes with particular ions and diffuse freely across a lipid membrane (Figure 10.38). Pores or channels, on the other hand, adopt a fixed orientation in a membrane, creating a hole that permits the transmembrane movement of ions. These pores or channels may be formed from monomeric or (more often) multimeric structures in the membrane. 

In the case of systems containing ionic liquids, components and chemical species have to be differentiated. The methanol/[BMIM][PF6] system, for example, consists of two components (methanol and [BMIM][PFg]) but - on the assumption that [BMIM][PFg] is completely dissociated - three chemical species (methanol, [BMIM] and [PFg] ). If [BMIM][PFg] is not completely dissociated, one has a fourth species, the undissociated [BMIM][PFg]. From this it follows that the diffusive transport can be described with three and four flux equations, respectively. The fluxes of [BMIM] ... 

Excretion via the kidney can be a straightforward question of glomerular filtration, followed by passage down the kidney tubules into the bladder. However, there can also be excretion and reabsorption across the tubular wall. This may happen if an ionized form within the tubule is converted into its nonpolar nonionized form because of a change in pH. The nonionized form can then diffuse across the tubular wall into plasma. Additionally, there are active transport systems for the excretion of lipophilic acids and bases across the wall of the proximal tubule. The antibiotic penicillin can be excreted in this way. 

Pollard and Newman" have also studied CVD near an infinite rotating disk, and the equations we solve are essentially the ones stated in their paper. Since predicting details of the chemical kinetic behavior is a main objective here, the system now includes a species conservation equation for each species that occurs in the gas phase. These equations account for convective and diffusive transport of species as well as their production and consumption by chemical reaction. The equations stated below are given in dimensional form since there is little generalization that can be achieved once large chemical reaction mechanisms are incorporated. 

Many investigators have studied diffusion in systems composed of a stationary porous solid phase and a continuous fluid phase in which the solute diffuses. The effective transport coefficients in porous media have often been estimated using the following expression ... 

In order to illustrate the effects of media structure on diffusive transport, several simple cases will be given here. These cases are also of interest for comparison to the more complex theories developed more recently and will help in illustrating the effects of media on electrophoresis. Consider the media shown in Figure 18, where a two-phase system contains uniform pores imbedded in a matrix of nonporous material. Solution of the one-dimensional point species continuity equation for transport in the pore, i.e., a phase, for the case where the external boundaries are at fixed concentration, Ci and Cn, gives an expression for total average flux... 

The form of the effective mobility tensor remains unchanged as in Eq. (125), which imphes that the fluid flow does not affect the mobility terms. This is reasonable for an uncharged medium, where there is no interaction between the electric field and the convective flow field. However, the hydrodynamic term, Eq. (128), is affected by the electric field, since electroconvective flux at the boundary between the two phases causes solute to transport from one phase to the other, which can change the mean effective velocity through the system. One can also note that even if no electric field is applied, the mean velocity is affected by the diffusive transport into the stationary phase. Paine et al. [285] developed expressions to show that reversible adsorption and heterogeneous reaction affected the effective dispersion terms for flow in a capillary tube the present problem shows how partitioning, driven both by electrophoresis and diffusion, into the second phase will affect the overall dispersion and mean velocity terms. 

Ochoa-Tapia, JA Stroeve, P Whitaker, S, Diffusive Transport in Two-Phase Media Spatially Periodic Modles and Maxwell s Theory for Isotropic and Anisotropic Systems, Chemical Engineering Science 49, 709, 1994. 

Solute flux within a pore can be modeled as the sum of hindered convection and hindered diffusion [Deen, AIChE33,1409 (1987)]. Diffusive transport is seen in dialysis and system start-up but is negligible for commercially practical operation. The steady-state solute convective flux in the pore is J, = KJc = where c is the radially... 

Diffusion—transport of matter as a result of differing values of the chemical potential of a given component at various sites within the system, or in the system and its surroundings. Obviously, the particles... 

Experimental methods which yield precise and accurate data are essential in studying diffusion-based systems of pharmaceutical interest. Typically the investigator identifies a mechanism and associated mass transport model to be studied and then constructs an experiment which is consistent with the hypothesis being tested. When mass transport models are explicitly involved, experimental conditions must be physically consistent with the initial and boundary conditions specified for the model. Model testing also involves recognition of the assumptions and constraints and their effect on experimental conditions. Experimental conditions in turn affect the maintenance of sink conditions, constant surface area for mass transport, and constant and known hydrodynamic conditions. 

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