Unstirred layer effect

and Whitney and Nernst were the first to introduce and develop the concept of unstirred layer (quoted in [23]). According to the theoretical views of Nernst, there is a layer of static fluid present at a solid-liquid interface. The concentration of a given substance in this layer is not equal to that in the bulk solution and diffusion is the primary mode of transport within the unstirred layer. The thickness of the unstirred layer, though undetermined, is critically dependent on the rate of stirring in the bulk phase. 

One of the earliest theoretical objections to the calculation of the water permeability coefficients of biological membranes was advanced by Dainty [22] in his excellent review on water relations in plant cells. He argues—and correctly so—that all the equations used in calculating permeability coefficients are based on the implicit assumption that the aqueous solutions on both sides of the membrane are so well stirred that the concentrations at the membrane faces are the same as the bulk concentrations. It is well recognized that such a situation is impossible to achieve 

The presence of an unstirred layer which may adhere to a given cell membrane can be treated operationally as a barrier with its own permeability property in series with the actual membrane. Its importance in membrane transport processes depends essentially on the permeability of the membrane itself relative to that of the unstirred layer to the particular molecule being transported. Consequently, only molecules which permeate membranes at high rates are affected, since diffusion in the unstirred layer is quite rapid. Water transfer across human red cell membrane and those of most other cells and tissues studied falls within this category. Dainty [22] has given the following equation by which the apparent diffusion permeability coefficient may be corrected for the effect of an unstirred layer of thickness, 8  

Because a correct molecular interpretation of the permeability coefficients of a membrane to a given substance rests on determining the contribution of the unstirred layer, it is usually necessary to measure the thickness of the unstirred layer that may be present under a given experiment condition. Such measurements have been made [14,23]. 

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Log Pa. Apparent permeability. It is directly calculated from the concentration in the acceptor concentration LogP Effective permeability. This is logP corrected by membrane retention (if any). In absence of membrane retention, logP = logP LogP Membrane permeability. Th t is logP, corrected by the unstirred layer effect. 

Figure 15.3. Diclofenac effective permeability pH profile corrected for the unstirred layer effect. The solid line represents the effective membrane permeability, while the dotted line represents the membrane permeabiltiy, corrected by the unstirred layer effect.

Unstirred Water Layer Effect (Transport across Barriers in Series and in Parallel)... 

Permeability is a property closely tied to the environment of the epithelial cell surface. There is little point in measuring permeability at pH 1.7, if the microclimate barrier has pH >5 and <8, averaging 6. An in vitro permeability screen based on donor pH 5.0-7.4 and acceptor pH 7.4 seems about right. It will be useful to correct the data for the unstirred water layer effect, using computational methods. 

Gutknecht, J. Tosteson, D. C., Diffusion of weak acids across lipid membranes Effects of chemical reactions in the unstirred layers, Science 182, 1258-1261 (1973). 

Gutknecht, J. Bisson, M. A. Tosteson, F. C., Diffusion of carbon dioxide through lipid bilayer membranes. Effects of carbonic anhydrase, bicarbonate, and unstirred layers, J. Gen. Physiol. 69, 779-794 (1977). 

Cotton, C. U. Reuss, L., Measurement of the effective thickness of the mucosal unstirred layer in Necturus gallbladder epithelium, J. Gen. Physiol. 93, 631-647 (1989). 

However, some effects are less intuitively obvious, and have been neglected. Unstirred layer formation can have large effects on solute transport, and, on a minute-by-minute basis, animals are constantly readjusting physiological systems (e.g. gill ventilation rate, blood flow) which will affect unstirred layer formation. Ventilation and blood flow are influenced by many environmental factors, but the interrelationship between environmentally induced cardiovascular adjustment, unstirred layer formation, and the cost of solute transport remain to be explored. 

Wilson, F.A. and Dietschy, J.M. (1974). The intestinal unstirred layer—its surface area and effect on active transport kinetics. Biochem. Biophys. Acta. 363 112-126. 

Influence of unstirred layers near the membrane. Near the membrane there exist unstirred layers which under unfavourable conditions can exert a considerable influence on the fluxes and the membrane potential too. F. Helfferich (57) has drawn the attention to this effect. The thickness of these layers depends on the rate of stirring. Under good stirring conditions the film-thickness amounts to 20 to 1 10-3 cm. Under extreme conditions it can be reduced to 10-4 cm. It is not always possible to eliminate its influence (139). The transport in the films is diffusion-controlled. In some cases the effect of the films can be involved in the calculations. As an example the case of selfdiffusion is given here. A cation-exchange resin separates two solutions of identical chemical composition. The cations on either side are isotopes of the same element. 

Flourie, B., Vidon, N., Florent, C.H., and Bernier, J.J. 1984. Effect of pectin on jejunal glucose absorption and unstirred layer thickness in normal man. Gut 25, 936-941. 

Johnson, I.T. and Gee, J.M. 1981. Effect of gel-forming gums on the intestinal unstirred layer and sugar transport in vitro. Gut 22, 398-403. 

Fig. 4.9 (a) Logarithm of the apparent permeability coefficient, for perfusion experiments in rats (filled symbols) and Caco-2 (empty symbols) versus logarithm of the intrinsic permeability coefficients based on PAMPA. (b) The unstirred water layer effect in the Caco-2 data. 

Podesta, R. B. (1977). Hymenolepis diminuta unstirred layer thickness and effects on active and passive transport kinetics. Experimental Parasitology, 43 12-24. 

Figure 1-11. Hie effect of unstirred layers (see dashed lines) on the concentration of species j near a membrane across which the solute is diffusing.

Without correcting for the effect of an unstirred layer 20 pm thick outside a membrane 7.5 nm in thickness, the apparent (total) permeability coefficients were measured to be 1.0 x 10 4ms 1 for D20, 2.0 x 10-5 m s-1 for methanol, and 3.0 x 10-s m s-1 for L-leucine. For barriers in series, the overall permeability coefficient for species j (Pjotal) is related to those of the individual barriers (Pj) as follows l/ptotai T.l/pj. For purposes of calculation, we will assume that in the present case the unstirred layer on the inner side of the membrane is negligibly thin. 

The villi and microvilli of the small intestine are lined by a sulphated mucoprotein, glycocalyx. Fluid trapped within the glycocalyx is stationary, and a series of thin layers, each progressively more stirred, extends to the bulk phase of the intestinal lumen. This series of unstirred layers has an effective thickness of 0.01-1.0 mm. 

The bulk luminal pH is heavily affected by the fermentation of carbohydrates to short-chain fatty acids however, near the colonic mucosa, the pH rises and changes in the bulk pH have little effect on the epithelial microclimate. Bicarbonate/chloride exchange is partly responsible for raising the pH against the challenge posed by the high colonic pCOi and the acid production by fermentation. The mucus has been shown to contain a distinct carbonic anhydrase, produced by epithelial tissues that help to carefully regulate the thick unstirred layer of the colonic epithelium. 

The effects immobilization of the enzyme has on its activity have been neglected in EIA. Fortunately, a large body of information is now available based on studies on immobilized enzymes (Trevan, 1980 Sharma et al., 1982). The immediate vicinity of a solid-phase may profoundly affect the activity of the enzyme. The first noticeable effects are the partitioning of the substrate between the fluid phase and the charged-polymer solid-phase, due to the charges of ionic species, and the limitation of diffusion of the solute to the solid-phase due to an unstirred layer of about 1 pm (i.e., more than 100 times the diameter of an average protein). 

Winne, D. 1979. Rat jejunum perfused in situ Effect of perfusion rate and intraluminal radius on absorption rate and effective unstirred layer thickness. Naunyn-Schmiedeberg s Arch. Pharmacol. 307 265-274. 

Frank-Kamenetzkii, on the other hand, described the other limiting case of a totally unstirred exothermic reacting system. This is also of practical relevance, as this is a good model for particle beds as such exist in drying and storage operations. The main heat transfer resistance prevails within the reaction mass itself The wall is taken as an infinitely large isothermal reservoir in this case, neglecting all boundary layer effects. 

Earlier, the unstirred layer adjacent to the bilayer membrane was investigated by Le Blanc.58 The effect of the unstirred layer on the transport of ions was observed in the individual cells,59 thylakoids,60 and other objects.61-67... 

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