In a special case of mass transfer, as in the evaporation of a pure liquid in a diffusion cell or the absorption of a pure gas in an agitated vessel, transfer of material is onedimensional and we can neglect the convective terms in the diffusion equation.
Equation 1
Integration of Equation 1 gives:
Equation 2:
Equation 1 indicates that the concentration distribution is linear, as shown in Figure 1 If we assume unidirectional diffusion and that the surface concentration is very low (ws ≈ 0), the mass flux of component A, NA [kg.m–2.s–1], can be expressed by the following equation:
Equation 3:
Here, D is the diffusivity [m2.s–1], δc is the thickness of the concentration film in which the concentration profile exists [m], ρ is the density of the fluid [kg.m–3], and ws and w∞ are the mass fractions at the interface and in the bulk fluid, respectively. Equation 3 indicates that the rate of mass transfer in this special case is proportional to the diffusion coefficient and inversely proportional to the thickness of the film, δc. 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 Equation 3.
Figure 1. Film model
Referring to,
Asano, K. 2006. Mass Transfer From Fundamentals to Modern Industrial Applications. WILEY-VCH Verlag GmbH & Co. KGaA: Weinheim, Germany.
Was completed in Malang, on 11 January 2017
by Supriyono, S.T., M.T.