Concentration gradient, for diffusion

FA Long, D Richman. Concentration gradients for diffusion of vapors in glassy polymers and their relation to time dependent diffusion phenomena. J Am Chem Soc 82 513-522, 1960. 

Richman, D. Long, F.A. (1960). Measurement of Concentration Gradients for Diffusion of Vapors in Polymers. Journal of the American Chemical Society, Vol. 82, pp. 509-513. 

Figure 1.3 Concentration gradient for diffusive mass transfer. 

The ohmic drop within the electrolyte is a consequence of large currents. It depends on the conductivity of the electrolyte and the geometry of the electrode and its environment, similar to the concentration gradient for diffusion. For a large planar electrode, the ohmic resistance / q increases for a given conductivity k of the electrolyte with the distance d from its surface according to the relation (in Q cm )... 

Long FA, Richman D (1960) Concentration gradients for diffusion of vapors in glassy polymers and their relation to time dependent diffusion phenomena. J Am Chem Soc 82(3) 513-519 Lundgren J, Gudmundson P (1999) Moisture absorption in glass-fibre/epoxy laminates with transvCTse matrix cracks. Cranpos Sci Technol 59(13) 1983-1991 Macedo PB, Litovitz TA (1965) On the relative roles of free volume and activation energy in the viscosity of liquids. J Chem Phys 42(1) 245... 

Note 3.8.- If diffusion is far from equilibrium (which leads to a very high concentration gradient for diffusion), the concentration at the end of the diffusion path is insignificant compared to that at the starting point. The reactivity can then be written as ... 

Concentration gradients for the analyte in the absence of convection, showing the time-dependent change in diffusion as a method of mass transport. 

Concentration gradient for the analyte showing the effects of diffusion and convection as methods of mass transport. 

For an ion to move through the lattice, there must be an empty equivalent vacancy or interstitial site available, and it must possess sufficient energy to overcome the potential barrier between the two sites. Ionic conductivity, or the transport of charge by mobile ions, is a diffusion and activated process. From Fick s Law, J = —D dn/dx), for diffusion of a species in a concentration gradient, the diffusion coefficient D is given by... 

An analogy exists between mass transfer by diffusion and heat transfer by conduction. Each involves coHisions between molecules and a gradient as the driving force which causes flow. Eor diffusion, this is a concentration gradient for conduction, the driving force is an energy gradient. Eourier s... 

Diffusion is the molecular transport of mass without flow. The diffu-sivity (D) or diffusion coefficient is the proportionality constant between the diffusion and the concentration gradient causing diffusion. It is usually defined by Fick s first law for one-dimensional, binary component diffusion for molecular transport without turbulence shown by Eq. (2-149)... 

Both pH and the availability of nutrient ions in soil play important roles in rhizo-sphere dynamics and are often dependent on one another. Nutrient ions move in soil toward plant roots either by mass flow with the soil water or by diffusion. Mass flow is the result of bulk convective movements of the soil solution toward roots, whereas diffusion occurs in response to a concentration gradient for a particular ion, which results from its absorption by the root and depletion from the... 

Possible driving forces for solute flux can be enumerated as a linear combination of gradient contributions [Eq. (20)] to solute potential across the membrane barrier (see Part I of this volume). These transbarrier gradients include chemical potential (concentration gradient-driven diffusion), hydrostatic potential (pressure gradient-driven convection), electrical potential (ion gradient-driven cotransport), osmotic potential (osmotic pressure-driven convection), and chemical potential modified by chemical or biochemical reaction. 

Glucose and galactose enter the absorptive cells by way of secondary active transport. Cotransport carrier molecules associated with the disaccharidases in the brush border transport the monosaccharide and a Na+ ion from the lumen of the small intestine into the absorptive cell. This process is referred to as "secondary" because the cotransport carriers operate passively and do not require energy. However, they do require a concentration gradient for the transport of Na+ ions into the cell. This gradient is established by the active transport of Na+ ions out of the absorptive cell at the basolateral surface. Fructose enters the absorptive cells by way of facilitated diffusion. All monosaccharide molecules exit the absorptive cells by way of facilitated diffusion and enter the blood capillaries. 

An essential requirement for diffusion of Na+ ions is the creation of a concentration gradient for sodium between the filtrate and intracellular fluid of the epithelial cells. This is accomplished by the active transport ofNa+ ions through the basolateral membrane of the epithelial cells (see Figure 19.4). Sodium is moved across this basolateral membrane and into the interstitial fluid surrounding the tubule by the Na+, K+-ATPase pump. As a result, the concentration of Na+ ions within the epithelial cells is reduced, facilitating the diffusion of Na+ ions into the cells across the luminal membrane. Potassium ions transported into the epithelial cells as a result of this pump diffuse back into the interstitial fluid (proximal tubule and Loop of Henle) or into the tubular lumen for excretion in the urine (distal tubule and collecting duct). 

Formation of Na+, K+-ATPase carrier molecules in the basolateral membrane of the tubular epithelial cells (promotes extrusion of Na+ ions from the cells and their movement into plasma by way of peritubular capillaries enhances the concentration gradient for passive diffusion through Na+ channels in the luminal membrane)... 

When the action potential reaches the synaptic bouton, depolarisation triggers the opening of voltage-operated calcium channels in the membrane (Figure 2.5). The concentration gradient for Ca2+ favours the passive movement of this ion into the neuron. The subsequent rise in cytoplasmic Ca2+ ion concentration stimulates the release of neurotransmitter into the synaptic cleft, which diffuses across this narrow gap and binds to receptors located on the postsynaptic neuronal membrane (Figure 2.5). 

Equation 9.1-17 is the continuity equation for unsteady-state diffusion of A through the ash layer it is unsteady-state because cA = cA(r, a To simplify its treatment further, we assume that the (changing) concentration gradient for A through the ash layer is established rapidly relative to movement of the reaction surface (of the core). This means that for an instantaneous snapshot, as depicted in Figure 9.3, we may treat the diffusion as steady-state diffusion for a fixed value of rc i.e., cA = cA(r). The partial differential emiatm. 

In contrast, a fast reaction rate will result in steep concentration gradients for the reactants and a higher reaction rate near the solvent interface. This concept is represented diagrammatically in Figure 2.13b, where the concentration of reactant A is almost as high as that in phase 1 at the solvent interface, but plummets as it is rapidly consumed by the reaction. Thus, for a fast reaction, the majority of reactant is converted to product near the phase boundary layer and the rate of the reaction is limited by the rate of phase transfer and diffusion. 

Reactions carried in aqueous multiphase catalysis are accompanied by mass transport steps at the L/L- as well as at the G/L-interface followed by chemical reaction, presumably within the bulk of the catalyst phase. Therefore an evaluation of mass transport rates in relation to the reaction rate is an essential task in order to gain a realistic mathematic expression for the overall reaction rate. Since the volume hold-ups of the liquid phases are the same and water exhibits a higher surface tension, it is obvious that the organic and gas phases are dispersed in the aqueous phase. In terms of the film model there are laminar boundary layers on both sides of an interphase where transport of the substrates takes place due to concentration gradients by diffusion. The overall transport coefficient /cl can then be calculated based on the resistances on both sides of the interphase (Eq. 1) ... 

The diffusion theory states that interpenetration and entanglement of polymer chains are additionally responsible for bioadhesion. The intimate contact of the two substrates is essential for diffusion to occur, that is, the driving force for the interdiffusion is the concentration gradient across the interface. The penetration of polymer chains into the mucus network, and vice versa, is dependent on concentration gradients and diffusion coefficients. It is believed that for an effective adhesion bond the interpenetration of the polymer chain should be in the range of 0.2-0.5 pm. It is possible to estimate the penetration depth (/) by Eq. (5),... 

The cell potential is simply the work that can be accomplished by the electrons produced in the SOFC, and this potential decreases from the equilibrium value due to losses in the electrodes and the electrolyte. For YSZ electrolytes, the losses are purely ohmic and are equal to the product of the current and the electrolyte resistance. Within the electrodes, the losses are more complex. While there can be an ohmic component, most of the losses are associated with diffusion (both of gas-phase molecules to the TPB and of ions within the electrode) and slow surface kinetics. For example, concentration gradients for either O2 (in the cathode) or H2 (in the anode) can change the concentrations at the electrolyte interface,which in turn establish the cell potential. Similarly, slow surface kinetics could result in the surface at the electrolyte interface not being in equilibrium with the gas phase. 

A parameter (usually symbolized by P, and often containing a subscript to indicate the specific ion) that is a measure of the ease with which an ion can cross a unit area of membrane by simple (or passive) diffusion through a membrane experiencing a 1.0 M concentration gradient. For a particular biological membrane, the permeabilities are dependent on the concentration and activity of various channel or transporter proteins. In an electrically active cell (e.g., a neuron), increasing the permeability of K+ or CF will usually result in hyperpolarization of the membrane. Increasing will cause depolarization. 

Interdiffusion, effective binary diffusion, and multicomponent diffusion may be referred to as chemical diffusion, meaning there are major chemical concentration gradients. Chemical diffusion is defined relative to self diffusion and tracer diffusion, for which there are no major chemical concentration gradients. 

Pick s Second Law of Diffusion relates the change in concentration of a diffusing species with time to the diffusion coefficient and the concentration gradient for non-steady-state diffusion ... 

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