Formation of membranes by means of immersion precipitation: Part I. A model to describe mass transfer during immersion precipitation

Equations and boundary conditions are derived for the isothermal diffusion processes in the coagulation bath and in the polymer solution after immersion of a cast (ternary) polymer solution into a (binary) coagulation bath. The mass transfer is expressed in terms of thermodynamic driving forces and frictional coefficients. The frictional coefficients in the ternary system are assumed to be interrelated through the Onsager reciprocal relations and to be related to the measurable frictional coefficients defined in the three limiting binary composition ranges. In combination with knowledge about the demixing processes which can take place in the polymer solution (liquid-liquid phase separation or solid-like aggregate formation), this model makes it possible to calculate the polymer concentration profile in the immersed film at the moment of demixing of the polymer solution as a function of several process parameters. The calculated concentration profile and its relation to the asymmetric structure of the ultimate membrane are presented in Part II1.