Diffusion coefficient of solute

D( = diffusion coefficient of solute in liquid g = gravity-acceleration constant h = length of wetted wall kf = mass-transfer coefficient, liquid phase r = mass rate of flow of hqnid. f = viscosity of liquid = density of hqnid... 

Parameters a and b are related to the diffusion coefficient of solutes in the mobile phase, bed porosity, and mass transfer coefficients. They can be determined from the knowledge of two chromatograms obtained at different velocities. If H is unknown, b can be estimated as 3 to 5 times of the mean particle size, where a is highly dependent on the packing and solutes. Then, the parameters can be derived from a single analytical chromatogram. 

Diffusion Coefficients of Solutes in Enhanced-Fluidity Liquid Mixtures... 

Die next parameter we need is the diffusion coefficient Df of hydrogen peroxide in water. Here, we can assume the approximate value of 10 9 m2/s. However, this coefficient will be needed further in this example for the determination of the effective solid-phase diffusion coefficient, in a calculation that is extremely sensitive to the value of the liquid-phase diffusion coefficient. For this reason, coefficient should be evaluated with as much accuracy as possible. The diffusion coefficient of solutes in dilute aqueous solutions can be evaluated using the Hayduk and Laudie equation (see eq. (1.26) in Appendix I) ... 

For the determination of diffusion coefficient of solutes (except from salts and ions) in water and dilute solutions (<10%) the Hayduk and Laudie equation is used (Lyman et al., 1990 Perry and Green, 1999) ... 

Supercritical fluid chromatography provides increased speed and resolution, relative to liquid chromatography, because of increased diffusion coefficients of solutes in supercritical fluids. (However, speed and resolution are slower than those of gas chromatography.) Unlike gases, supercritical fluids can dissolve nonvolatile solutes. When the pressure on the supercritical solution is released, the solvent turns to gas. leaving the solute in the gas phase for easy detection. Carbon dioxide is the supercritical fluid of choice for chromatography because it is compatible with flame ionization and ultraviolet detectors, it has a low critical temperature. and it is nontoxic. 

The physical factors include mechanical stresses and temperature. As discussed above, IFP is uniformly elevated in solid tumors. It is likely that solid stresses are also increased due to rapid proliferation of tumor cells (Griffon-Etienne et al., 1999 Helmlinger et al., 1997 Yuan, 1997). The increase in IFP reduces convective transport, which is critical for delivery of macromolecules. The temperature effects on the interstitial transport of therapeutic agents are mediated by the viscosity of interstitial fluid, which directly affects the diffusion coefficient of solutes and the hydraulic conductivity of tumor tissues. The temperature in tumor tissues is stable and close to the body temperature under normal conditions, but it can be manipulated through either hypo- or hyper-thermia treatments, which are routine procedures in the clinic for cancer treatment. 

An important conclusion to be drawn from the Stokes-Einstein equation is that the diffusion coefficient of solutes in a liquid only changes slowly with molecular weight, because the diffusion coefficient is proportional to the reciprocal of the radius, which in turn is approximately proportional to the cube root of the molecular weight. 

Application of the Stokes-Einstein equation requires a value for the solute radius. A simple approach is to assume the molecule to be spherical and to calculate the solute radius from the molar volume of the chemical groups making up the molecule. Using values for the solute radius calculated this way along with measured and known diffusion coefficients of solutes in water, Edward [26]... 

Figure 2.20 Permeant diffusion coefficient as a function of permeant molecular weight in water, natural rubber, silicone rubber and polystyrene. Diffusion coefficients of solutes in polymers usually lie between the value in natural rubber, an extremely permeable polymer, and the value in polystyrene, an extremely impermeable material [28]...

It is to be hoped that future calculations will attempt to predict the diffusion coefficients of solutes in narrow pores. Measurements in such systems are extremely difficult to carry out and recent experiments in an admittedly broad pore (a 2 mm diameter capillary) are therefore of particular interest. Liukkonen and co-workers [61] found that the diffusion coefficient of NaCl in a dilute aqueous solution was 75% greater at the walls of this capillary than in the bulk solution, a result in line with the phenomenon of "surface conductivity [62]. Yet this finding clearly runs counter to the trend in the self-diffusion calculations in much narrower pores. It rather looks at this stage as if electrolytes near polar walls behave quite differently from non-electrolytes. 

We will next use Fick s first law (Jj = —Djdcj/dx Eq. 1.1) to obtain an expression for describing the movement of a substance across a membrane. The negative concentration gradient will be replaced by (c° — cj)/Ax (Eq. 1.7). Because D is the diffusion coefficient of solute species j within the membrane, we must use the actual concentration drop within the membrane, Kj(Cj — Cj). These various considerations lead us to the following expression describing the diffusion of species / across a membrane or other barrier ... 

From Wilke-Chang correlation, D°AB=7.4xlO 8(tMB) TAlBVA - , where D°AB/cm l is mutual diffusion coefficient of solute A in solvent B, Mb /g-mok is molecular weight of solvent B, tib /cp is viscosity of solvent B, Va /cm3-mol is molar volume of solute A at its nomial boiling temperature, and is association factor of solvent B. 

Dm diffusion coefficient of solute on mobile phase <4 column diameter... 

The influence of temperature on diffusion coefficients of solutes in liquids has been studied in less detail. Diffusion coefficients often can be estimated from viscosity measurements. Hydrodynamic theory relates self-diffusion coefficients to the viscosity by... 

Mass Changes Related to Chemical Weathering The diffusion coefficients of solutes are commonly... 

The diffusion coefficients of solutes in supercritical fluids are in between those they possess in liquids and gases. Because diffusion coefficients in SFs are higher than those in liquids, mass transfer is usually more favourable in the former. The diffusion coefficient can also be altered to advantage as diffusivity in a supercritical fluid decreases with increasing pressure and increases with increasing temperature, especially in the vicinity of the critical point. 

The incorrectness of the steady-state approach was noted by the authors of Ref. 3 and can be explained as follows. There are two characteristic diffusion times in an FFF channel = wV4D and 1 2 = b l4D, where D is the diffusion coefficient of solute molecules. As the ratio b/w > 40, then > 1600. Experimental values of retention time are usually equal to several but are never as large as IbOOt i- Thus, the steady-state values of and K2 corresponding to t tj)2 are never reached during the experiment. (For the channel with w = 200 /zm, b = l cm, and solute with D = 10 cm /s,... 

Diffusion coefficient of solute in the membrane, m /s Diffusion coefficient of solvent in the membrane, m /s Quanhty difference Surface porosity... 

Diffusivity data are available only for a limited number of polymer-solvent systems. This paper describes research that has led to the development of the use of capillary column inverse gas chromatography (IGC) for the measurement of diffusion coefficients of solute molecules in polymers at infinite dilution. The work has resulted in a precise, rapid technique for the diffusion measurements that circumvents the many problems attendant to classical sorption methods and packed column IGC methods. Initial results of the program appeared in two recent publications (1,2)- Some of the material introduced in those papers is discussed here to present background for... 

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