Abstract
Diffusion of dye in the composite media with skin and core is investigated in non-steady state. The composite membrane considered here is symmetric with respect to x=h, where h is the half thickness of the membrane. The region 0_??_x_??_h1 is of substrate 1 (skin) and h1_??_x_??_h is of substrate 2 (core). C1 and D1 denote the concentration and diffusion coefficient in substrate 1, and C2, D2 are the corresponding quantities in substrate 2. Cs1, Cs2 are the surface concentrations in substrates 1 and 2. In the case that Di, and Csi are constant, the differential equations to be solved are
The initial and boundary conditions are assumed as follows:
The final results are where are the positive roots of and
The amounts of dye Mt1, Mt2 in the substrates 1, 2 are derived by integrating the equations (1) and (2) with respect to X.
The total amount Mct in the composite is where Mc∞ is the amount of dye in the composite at equilibrium.
The films of nylon 6 (N6) and cellulose diacetate (Ac) are used to make a composite film roll as a model with skin and core. One of the films is rolled 5 times around a glass rod (radius=1cm) and the other is also rolled same times on the film roll. The composite film rolls are represented by 5N6-5Ac and 5Ac-5N6 depending on the sequence of the films. These film rolls are dyed at 60°C in the aqueous solution of p-aminoazobenzene (PAAB).
The concentration distributions of PAAB in the composite film rolls agreed with the theoretical curves calculated by the equations (1) and (2). The dyeing rate of the composite 5N6-5Ac was larger than that of 5Ac-5N6, and those were in accordance with the theoretical values on the basis of the equations (3)_??_(5). Some of the properties for the dyeing curves of the composite membranes were described.
The analytical solutions of diffusion equations are also derived for a semi-infinite composite medium. Experimental results agreed with the solutions.
