Diffusion in water

For a solute diffusing in water, the diffusion coefficient depends primarily on temperature and solute size. Consider a particle moving through a simple Newtonian fluid, such as water. The velocity of the particle in the x-direction, Vx, is related to the force required to move it through the fluid, F  

While the Stokes-Einstein equation is strictly applicable only in cases where the diffusing particle is large when compared to the surrounding solvent molecules (so that the fluid can be considered a continuum), it has proven to be useful for solute-solvent pairs in which the radius, a, is only two to three times the solvent radius. For a solute with radius comparable to the solvent radius, the 6 in Equations 4-3 and 4-4 should be replaced by a 4, since the assumption of no slip at the solute surface is no longer valid [48]. 

Diffusion coefficients for globular proteins in water. Collection of diffusion coefficients published in the literature, similar figures have appeared previously [5] 

Protein diffusion coefficients depend on the pH and ionic composition of the medium. For example, in a 1% bovine serum albumin (BSA) solution, the diffusion coefficient of BSA increased by a factor of 4 when KCl concentration in the solution was decreased below 0.01 M[54]. 

Unlike globular proteins, fibrous proteins and nucleic acids do not behave as spheres. In some cases, the approach described above can be extended to particles of other shapes, provided that the frictional drag coefficient can be determined. For example, the drag coefficient for prolate ellipsoids with a major axis length, a, much larger than the minor axis length, b a has been determined  

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A = 4.05 X lO " cm/(s-kPa)(4.1 X 10 cm/(s-atm)) and = 1.3 x 10 cm/s (4)//= 1 mPa-s(=cP), NaCl diffusivity in water = 1.6 x 10 cm /s, and solution density = 1 g/cm . Figure 4 shows typical results of this type of simulation of salt water permeation through an RO membrane. Increasing the Reynolds number in Figure 4a decreases the effect of concentration polarization. The effect of feed flow rate on NaCl rejection is shown in Figure 4b. Because the intrinsic rejection, R = 1 — Cp / defined in terms of the wall concentration, theoretically R should be independent of the Reynolds... 

Early ultrafiltration membranes had thin surface retentive layers with an open structure underneath, as shown in Fig. 20-62. These membranes were prone to defects and showed poor retention and consistency. In part, retention by these membranes would rely on large retained components in the feed that polarize or form a cake layer that plugs defects. Composite membranes have a thin retentive layer cast on top of a microfiltration membrane in one piece. These composites demonstrate consistently high retention and can be integrity-tested by using air diffusion in water. 

Similarly, for diffusion in water a molecular diffusivity of 2 x 10-6 m2/h is reduced by a factor of 20 to an effective diffusivity of 10 7 m2/h, which is combined with a path length of 0.05 m to give an effective soil-to-water mass transfer coefficient of ksw 2 x 10 6 m/h. 

The mess caused by dropping sugar reflects the way nature always seeks to maximize disorder. Both examples so far, of dye diffusing in water and sugar causing a mess, demonstrate the achievement of greater disorder. But if we are specific, we should note how it is the energetic disorder that is maximized spontaneously. 

Diffusivity in water Molecular diffusion is defined as the transport of molecules (e.g., organic compounds) in either liquid or gaseous states. Typically, molecular diffusion is not a major factor under the majority of enviromnental conditions. However, in saturated aquifers with low pore water velocities (i.e., <0.002 cm/sec), diffusion can be a contributing factor in the transport of organic compounds. 

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