Molecular diffusion coefficient in water

Equation [2-32] reduces to Eq. [2-29] when 8W/D is much greater than 8JDaH, and to Eq. [2-31] when it is much less. Note that the molecular diffusion coefficient for molecules in air (DJ is approximately 104 times greater than the corresponding molecular diffusion coefficient in water (Dw), whereas the air film thickness, 8a, is generally much less than 104 times the water film thickness, 8W. 

Molecular diffusion coefficients in water are usually determined in the laboratory by using a tracer in agar or gel to insure that the solution is totally free of turbulent motion. Values for gases and ions in pure water are presented in units of cm s in Table 9.1. The molecular diffusion coefficients and their temperature dependence for gases were calculated from the Eyring equation. 

Water is contained between two infinite parallel plates separated by a small distance h = m. The bottom plate is held stationary, and the top plate is moved at a constant velocity U = m s so that a simple shear flow is generated between the plates. A thin band of a dye of thickness A = 10 " m is injected between and perpendicular to the plates extending fully across the gap. The band depth is very deep and may be supposed to be infinite. The dye concentration is Cq = 10 mol m, and its molecular diffusion coefficient in water is D = 10 m s ... 

For diffusion dominated processes, D is the molecular diffusivity in water of the contaminant of interest multiplied by the porosity and divided by the tortuosity (or hindrance factor, ffp) of the sediment (D = Dv,s/Hp). The Millington and Quirk model (as referenced in Palermo [1]) suggests Hp which for a cap with 40% porosity is about 1.4. The molecular diffusion coefficient in water is a function of temperature and can be estimated by the methods defined by Lyman [4]. In the presence of advection D is increased due to mechanical dispersion in the medium (typically modeled as some dispersivity, a, multiphed by the interstitial velocity, v). The dispersiv-ity is an empirical parameter but is related to the mean particle size in nearly... 

Coefficients for both mechanical dispersion and molecular diffusion must be added to determine the total Fickian transport coefficient for a chemical in an aquifer. The molecular diffusion coefficient of a chemical in water (Section 1.4.2, Molecular Diffusion) must be adjusted for use in the groundwater regime, to accoimt for tortuosity and porosity. Commonly, the molecular diffusion coefficient in water is divided by tortuosity (sometimes approximated as the square root of two) and multiplied by porosity to obtain an effective molecular diffusion coefficient. Millington (1959) and Millington and Quirk (1961) provide a review of several approaches to the estimation of effective molecular diffusion coefficients in porous media. Note that mixing by molecular diffusion of chemicals dissolved in pore waters always occurs, even if there is no seepage velocity, and thus no mechanical dispersion. In the case of flow in porous media, the dimensionless Feclet number is defined as the ratio of the... 

These mixing processes are generally characterized by diffusion or dispersion coefficients, all with units such as m /h. Molecular diffusion coefficients in water are isotropic and typically 0.4m /h or 10 cm /s. They are usually negligible in comparison to eddy diffusion or dispersion. Eddy or turbulent diffusion coefficients are controlled by water flow, wind, biotic, and buoyancy effects and may be anisotropic. Dispersion coefficients are controlled by velocity gradients in the water and are anisotropic with vertical, lateral, and longitudinal components. These individual coefficients can be added to give a net coefficient that depends on flow conditions and the system geometry. 

Fig. 2.7.5 Two-dimensional D—T2 map for Berea sandstone saturated with a mixture of water and mineral oil. Figures on the top and the right-hand side show the projections of f(D, T2) along the diffusion and relaxation dimensions, respectively. In these projections, the contributions from oil and water are marked. The sum is shown as a black line. In the 2D map, the white dashed line indicates the molecular diffusion coefficient of water,...

The level of vapor movement in the unsaturated zone is much less important than transport in liquid form. However, this might not be true if the water content of the soil is very low or if there is a strong temperature gradient. The movement of vapor through the unsaturated zone is a function of temperature, humidity gradients, and molecular diffusion coefficients for water vapor in the soil. 

Table 24.5 Characteristic Data of Chemical Tracers Used for the Gas Exchange Experiment Nondimensional Henry s Law Constant, Ki3/vi, Molecular Diffusion Coefficient in Air, Dia, and Water, Diw, Octanol-Water Partition Coefficient, Kiow, All valid for 4°C (Data from Cirpka et al., 1993)...

Estimate the molecular weight (MW) of bushy stunt virus, density 1.35 g/cm3. Its diffusion coefficient in water at 20°C is 1.15 x 10"7 cm2/s. At this temperature the viscosity of water is 0.0100 poises. Assume that the virus is spherical in shape. 

Transport in the subsurface environment is slow compared with the other environmental media. Contaminants may move only tens of meters per year by advection, contrasting sharply with surface waters, which travel this far in minutes or hours, and air, which may travel this far in seconds (as discussed in the next chapter). Similarly, Fickian transport coefficients are rarely higher than thousandths of a square centimeter per second and are often no larger than a fraction of the molecular diffusion coefficient in free water. Many organic compounds that would rapidly volatilize into the atmosphere from surface waters may reside in groundwaters for decades or longer. 

The difference between diffusion coefficients in water of low molecular weight substances (M = 10—200, molecular diameter 3 A) and high molecular weight polyclectrolytes = 100,000, molecular diameter... 

Figure 4.17 Reduced diffusion coefficient as a function of molecular size. Hydrodynamic radii were determined from the diffusion coefficient in water according to Equation 4-4. (a) Diffusion of proteins and peptides in mid-cycle human cervical mucus [5], Measurements were performed by FPR (squares) or quantitative imaging of fluorescence profiles (circles), (b) Protein and dextran diffusion through granulation (squares) or tumor tissue (circles) in the rabbit ear [20, 21]. (c) Glucose diffusion through capsular tissue (squares) and cartilage (circles and triangles) [92]. Each symbol represents a separate measurement.

Diffusion coefficients in water depend on molecular size and shape, as well as concentration. 

Molecular weight (Da), number of amino acids (A aa)> number of polypeptide chains (A c), diffusion coefficients in water 25 °C (D ). Protein diffusion coefficients from [11], unless otherwise indicated. Half-life in the plasma following i.v. injection, f[/2. 

Estimate the volumetric mass transfer coefficient in a Taylor flow capillary with an internal diameter of 1 mm and a volumetric gas flow of Vq = 2.71 cm min and a volumetric liquid flow of = 2.0 cm min Use the simphfied model presented in Equation 7.27 and compare the values with those predicted with the empirical model Equation 7.14. Use the physical properties for air and water presented in Example 7.1. The molecular diffusion coefficient in the liquid phase is approximated with = 10 m s . ... 

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