By Linus Pauling
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Extra info for College Chemistry : An Introductory Textbook of General Chemistry
39) Molar Sherwood Number, Sh*, by Eq. 40) Sh or Sh* kL D kH L Hs À HI os À oI rD ky L cD kG RTL D kY L Ys À YI ys À yI cD kL L D kx L cD kX L Xs À XI xs À xI cD Mass Transfer Coefficient Symbol Definition k NA rk os À oI kH NA kH Hs À HI ky NAÃ ky ys À yI kG NAÃ kG ps À pI kY NAÃ ky Ys À YI kL NAÃ kL cs À cI kx NAÃ kx xs À xI kX NAÃ kX Xs À XI a) c = molar density [kmol m–3], D = diffusivity [m2 s–1], H = absolute humidity [–], L = characteristic length [m], MA = molecular weight [kg kmol–1], NA = mass flux [kg m–2 s–1], NA* = NA/MA = molar flux [kmol m–2 s–1], p = partial pressure [Pa], R = gas constant [J mol–1 K–1], T = temperature [K], x = mole fraction of liquid [–], y = mole fraction of gas [–], X = x/(1 – x),Y = y/(1 – y), r = density [kg m–3], o = mass fraction [–] The fact that the values of the two Sherwood numbers, Sh and Sh*, are unequal even for the same mass transfer data may seem quite strange.
Let us investigate, for instance, the dimensions of each term of the equation of motion for a one-dimensional steady flow in a horizontal circular pipe. 47 48 3 Governing Equations of Mass Transfer ru @u @p @2 u m 2 @z @z @r 3:42 The dimensions of each term of Eq. 42) are as follows: Left-hand side: M L3 L L 1 M 2 2 T T L L T First term on the right-hand side: F L2 1 M 1 M L LT2 L L2 T2 The second term on the right-hand side: M LT L 1 M T L2 L2 T2 This clearly indicates that the above theoretical equation automatically satisfies the condition of the principle of dimensional homogeneity and we say that the equation is dimensionally perfect.
17) indicates that the rate of mass transfer in this special case is proportional to the diffusion coefficient and inversely proportional to the Fig. 3 Film model. 4 Some Approximate Solutions of the Diffusion Equation thickness of the film, dc . This model is commonly known as the film model. Although the film model offers some explanation of the mechanism of mass transfer in fluid media, it does not provide us with any means of estimating the thickness of the concentration film. Due to this disadvantage, application of the model is restricted to mass transfer in a diffusion cell, in which case the diffusion coefficients can be determined by the use of Eq.