DIFFUSION DURING THE COAGULATION PROCESS OF WET SPINNING OF ACRYLIC FIBERS (I) MATHEMATICAL APPROACH

The coagulation of viscous polymer solutions by diffusional interchange in a coagulation bath is an important step for fiber formation of wet-spun acrylic fibers. The analytical method to handle the coagulation process was investigated and it is pointed out that several equations derived so far for calculating the apparent diffusion coefficients of solvent and/or coagulant are not adequate, since the effect of contraction of the fiber during coagulation is not taken into account and under certain conditions, the equations become invalid.Therefore, the author has studied an adequate equation for calculating apparent diffusion coefficient of solvent, which is based on the amount of solvent transferred from the inside of fibers to the coagulation bath instead of the amount of solvent remaining in the fibers. The equation is expressed by: where t is the time, R the raduis of the fiber, λn the root of zero-th order Bessel function Jo (λn)=0, DLthe diffusion coefficient of the solvent.