6 Where solute A is diffusing and solvent B is stagnant or nondiffusing. Example: Dilute solution of propionic Acid (A) in water (B) being contact with toluene.
7 EXAMPLE 6.3-1 An ethanol (A)-water (B) solution in the form of a stagnant film 2.0 mm thick at 293 K is inconstant at one surface with an organic solventin which ethanol is soluble and water is insoluble.Hence, NB = 0. At point 1 the concentration ofethanol is 16.8 wt % and the solution density isρ1 = kg/m3. At point 2 the concentrationof ethanol is 6.8 wt % and ρ2 = kg/m3.The diffusivity of ethanol is x 10-9 m2/s.Calculate the steady-state flux NA.
8 Solution The diffusivity of ethanol is 0.740 x 10-9 m2/s. The molecular weights of A and B are MA= andMB= for a wt % of 6.8, the mole fraction ofethanol (A) is as follows when using 10 kg solution:Then XB2 = = Calculating XA1 =and XB1 = = To calculate themolecular weight M2 at point 2,
9 Similarly, M1 = 20.07. From Eq. (6.3-2), To calculate XBM from Eq. (6.3-4), we can use the linearmean since XB1 and XB2 are close to each other:Substituting into Eq. (6.303) and solving,
19 EXAMPLE 6.5-1 The gas hydrogen at 17 °C and 0.010 atm partial pressure is diffusing through a membrane ofvulcanized neoprene rubber 0.5 mm thick. Thepressure of H2 on the other side of the neopreneis zero. Calculate the steady-state flux, assumingthat the only resistance to diffusion is in themembrane. The solubility S of H2 gas inneoprene at 17 °C is m3 (at STP of 0 °Cand 1 atm)/m3 solid.atm and the diffusivity DABis 1.03 x m2/s at 17 °C.
20 Solution A sketch showing the concentration is shown in Fig. The equilibrium concentration cA1 at the insidesurface of the rubber is, from Eq. (6.5-5),Since pA2 at the other side is 0, cA2 = 0. Substitutinginto Eq. (6.5-2) and solving,FIGURE concentrations for Example 6.5-1
21 EXAMPLE 6.5-2 A polyethylene film 0.00015 m (0.15 mm) thick is being considered for use in packaging a pharmaceutical productat 30 °C. If the partial pressure of O2 outside the packageis 0.21 atm and inside it is 0.01 atm, calculate thediffusion flux of O2 at steady state. Use permeability datafrom Table Assume that the resistances to diffusionoutside the film and inside are negligible compared to theresistance of the film.
22 Solution From Table 6.5-1, PM = 4.17 (10-12) m3 solute (STP)/(s.m2.atm/m). Substituting into Eq. (6.5-8)
24 EXAMPLE 6.5-3 A sintered solid of silica 2.0 mm thick is porous, with a void friction ε of 0.30 and a tortuosity τ of4.0. The pores are filled with water at 298 K. Atone face the concentration of KCl held at 0.10 gmol/liter, and fresh water flow rapidly past theother face. Neglecting any other resistance butthat in the porous solid, calculate the diffusion ofKCl at steady state.
25 Solution The diffusivity of KCL in water from Table 6.3-1 is DAB = 1.87 x 10-9 m2/s. Also, cA1 = 0.10/1000 = 1.0 x 10-4 gmol/m3, and cA2 = 0. Substituting into Eq. (6.5-13),
26 Molecular Diffusion in Biological Solutions and Gels
27 Diffusion of Biological Solutes in Liquids Important: The diffusion of solute molecules (macromolecules)Food processing: drying of fruit juice, coffee, tea, water, volatile flavorFermentation process: diffuse through microorganisms like nutrient, sugar, oxygenTable shows Diffusion Coefficient for Dilute Biological Solutes in Aqueous Solution.
28 Prediction of Diffusivities for Biological Solutes Small solutes in aqueous solution with molecular weight less than 1000 or solute molar less than about m3/kgmolFor larger solutes, an approximation the Stokes-Einsteinequation can be used
29 Prediction of Diffusivities for Biological Solutes For a molecular weight above 1000
30 EXAMPLE 6.4-1 Predict the diffusivity of bovine serum albumin at 298 K in water as a dilute solution using themodified Polson equation and compare with theexperimental value in Table
31 Solution The molecular weight of bovine serum albumin (A) from Table is MA= kg/kg mol. The viscosity ofwater at 25 °C is x 10-3 Pa.s at T = 298 K.Substituting into Eq. (6.4-1),This value is 11% higher than the experimental value of6.81 x m2/s
32 Diffusion in Biological Gels Gel can be looked as semisolid materials which are porous.Example: agarose, agar, gelatin.The pores or open spaces in the gel structure are filled with water.The rates of diffusion of small solutes in the gels are somewhat less than in aqueous solution.A few typical values of diffusivities of some solutes in various gel are given in Table
33 EXAMPLE 6.4-2 A tube or bridge of a gel solution of 1.05 wt % agar in water at 278 K is 0.04 m long andconnects two agitated solutions of urea in water.The urea concentration in the first solution is0.2 g mol urea per liter solution and is 0 in theother. Calculate the flux of urea in kg mol/s.m2at steady state.
34 Solution From Table 6.4-2 for the solute urea at 278 K, DAB = 0.727 x 10-9 m2/s. For urea diffusing through stagnantwater in the gel, Eq. (6.3-3) can be used. However,since the value of xA1 is less than about 0.01, thesolution is quite dilute and xBM Hence Eq. (6.3-5) can be used. The concentrations are cA1= 0.20/1000= g mol/cm3 = 0.20 kg mol/m3 and cA2= 0.Substituting into Eq. (6.3-5),