Water diffusion coefficient

Here A//adS is the enthalpy of adsorption, T is the temperature, and AAads is the entropy change associated with the adsorption of the protein onto the surface. Protein adsorption will take place if AGads < 0. Considering a complex system, where proteins are dissolved in an aqueous environment, and are brought into contact with an artificial interface, there are a vast number of parameters that impact AGads due to their small size (i.e., large diffusion coefficient), water molecules are the first to reach the surface when a solid substrate is placed in an aqueous biological environment. Hence, a hydrate layer is formed. With some delay, proteins diffuse to the interface and competition for a suitable spot for adsorption starts. This competition... 

Kuroiwa T, Nagaoka T, Ueki M, Yamada I, Miyasaka N, Akimoto H (1998) Different apparent diffusion coefficient water content correlations of gray and white matter during early ischemia. Stroke 29 859-865... 

The experimental coefficients fci and k2 depend on material properties and bed characteristics such as particle diameter, diffusion coefficient, water concenttation gradient, etc. For example, for the bed of silica gel with equivalent diameter de = 0.22 mm, ki = 5.72 10 , and kz = 0.23 g/(cm s), while... 

The oil droplets in a certain benzene-water emulsion are nearly uniform in size and show a diffusion coefficient of 3.75 x 10 cm /sec at 25°C. Estimate the number of benzene molecules in each droplet. 

The state of an adsorbate is often described as mobile or localized, usually in connection with adsorption models and analyses of adsorption entropies (see Section XVII-3C). A more direct criterion is, in analogy to that of the fluidity of a bulk phase, the degree of mobility as reflected by the surface diffusion coefficient. This may be estimated from the dielectric relaxation time Resing [115] gives values of the diffusion coefficient for adsorbed water ranging from near bulk liquids values (lO cm /sec) to as low as 10 cm /sec. 

Figure C2.3.8. Self-diffusion coefficients at 45°C for AOT ( ), water ( ) and decane ( ) in ternary AOT, brine (0.6% aqueous NaCl) and decane microemulsion system as a function of composition, a. This compositional parameter, a, is tire weight fraction of decane relative to decane and brine. Reproduced by pennission from figure 3 of [46].

Diffusion of the molecular gases can be compHcated by reactions with the glass network, especially at the sites of stmctural defects. The diffusion coefficient of water, for example, shows a distinct break around 550°C (110). Above 550°C, the activation energy is approximately 80 kj /mol (19 kcal/mol), but below 550°C, it is only 40 kJ/mol (9.5 kcal/mol). Proposed explanations for the difference cite the fact that the reaction between water and the sihca network to form hydroxyls is not in equiUbrium at the lower temperatures. 

Water Transport. Two methods of measuring water-vapor transmission rates (WVTR) ate commonly used. The newer method uses a Permatran-W (Modem Controls, Inc.). In this method a film sample is clamped over a saturated salt solution, which generates the desired humidity. Dry air sweeps past the other side of the film and past an infrared detector, which measures the water concentration in the gas. For a caUbrated flow rate of air, the rate of water addition can be calculated from the observed concentration in the sweep gas. From the steady-state rate, the WVTR can be calculated. In principle, the diffusion coefficient could be deterrnined by the method outlined in the previous section. However, only the steady-state region of the response is serviceable. Many different salt solutions can be used to make measurements at selected humidity differences however, in practice,... 

Carbon Dioxide Transport. Measuring the permeation of carbon dioxide occurs far less often than measuring the permeation of oxygen or water. A variety of methods ate used however, the simplest method uses the Permatran-C instmment (Modem Controls, Inc.). In this method, air is circulated past a test film in a loop that includes an infrared detector. Carbon dioxide is appHed to the other side of the film. AH the carbon dioxide that permeates through the film is captured in the loop. As the experiment progresses, the carbon dioxide concentration increases. First, there is a transient period before the steady-state rate is achieved. The steady-state rate is achieved when the concentration of carbon dioxide increases at a constant rate. This rate is used to calculate the permeabiUty. Figure 18 shows how the diffusion coefficient can be deterrnined in this type of experiment. The time lag is substituted into equation 21. The solubiUty coefficient can be calculated with equation 2. 

An overview of some basic mathematical techniques for data correlation is to be found herein together with background on several types of physical property correlating techniques and a road map for the use of selected methods. Methods are presented for the correlation of observed experimental data to physical properties such as critical properties, normal boiling point, molar volume, vapor pressure, heats of vaporization and fusion, heat capacity, surface tension, viscosity, thermal conductivity, acentric factor, flammability limits, enthalpy of formation, Gibbs energy, entropy, activity coefficients, Henry s constant, octanol—water partition coefficients, diffusion coefficients, virial coefficients, chemical reactivity, and toxicological parameters. 

Hayduk-Laudie They presented a simple correlation for the infinite dilution diffusion coefficients of nonelectrolytes in water. It has about the same accuracy as the Wilke-Chang equation (about 5.9 percent). There is no explicit temperature dependence, but the 1.14 exponent on I compensates for the absence of T in the numerator. That exponent was misprinted (as 1.4) in the original article and has been reproduced elsewhere erroneously. 

Example 8 Estimation of Rate Coejficient Estimate the rate coefficient for flow of a 0.01-M water solution of NaCl through a bed of cation exchange particles in hydrogen form with e = 0.4. The superficial velocity is 0.2 cm/s and the temperature is 25 C. The particles are 600 im in diameter, and the diffusion coefficient of sodium ion is 1.2 X 10 cmVs in solution and 9.4 X 10 cmVs inside the particles (of. Table 16-8). The bulk density is 0.7 g dry resin/cnd of bed, and the capacity of the resin is 4.9 mequiv/g dry resin. The mass action eqiiihbrium constant is 1.5. 

In this derivation, the diffusion coefficient which is used is really a parameter, since it is not certain which gas diffusion rate is controlling, that of hydrogen into a pore, or that of water vapour out of die pore. The latter seems to be the most probable, but the path of diffusion will be vety tormous drrough each pore and drerefore the length of the diffusion path is ill-defined. 

Here / is the number of ink molecules diffusing down the concentration gradient per second per unit area it is called the flux of molecules (Fig. 18.3). The quantity c is the concentration of ink molecules in the water, defined as the number of ink molecules per unit volume of the ink-water solution and D is the diffusion coefficient for ink in water - it has units of m s . ... 

Chemical Boiling Point C Desnity gm/cm Viscosity cP is-c Water Solubi- lity rag/L Vapor Pressure nun Hg Diffusion Coefficient, cnP/day ... 

Among the dynamical properties the ones most frequently studied are the lateral diffusion coefficient for water motion parallel to the interface, re-orientational motion near the interface, and the residence time of water molecules near the interface. Occasionally the single particle dynamics is further analyzed on the basis of the spectral densities of motion. Benjamin studied the dynamics of ion transfer across liquid/liquid interfaces and calculated the parameters of a kinetic model for these processes [10]. Reaction rate constants for electron transfer reactions were also derived for electron transfer reactions [11-19]. More recently, systematic studies were performed concerning water and ion transport through cylindrical pores [20-24] and water mobility in disordered polymers [25,26]. 

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