With an adequate mathematical model, it is possible to study the effect of the most important technological parameters on the fibre formation process and to optimize it with consideration of the equipment, spinning conditions, and linear density of the fibre. The promise of regulating the spinning process by addition of a precipitator to the spinning solution was demonstrated.Spinning of polyacrylonitrile (PAN) fibre has been relatively widely described in the international literature [1][2][3], but as always in the study of complex, multiparameter technological processes, there are still a number of important factors which it is difficult for the human mind to grasp without using computers and mathematical models. Regulation of the technical and economic parameters of the technology and the properties of the fibre by varying the conditions of fibre formation is such a factor in the technology of production of PAN fibre by the water-dimethylformamide method. We will assign the parameters which have the greatest effect on the spinning process to such conditions: the temperature of the spinning solution and spinning bath, the concentration of precipitator in the spinning bath and spinning solution, and the duration of the process. The latest mathematical model of this process accounts for all of these parameters. The model, its substantiation, and verification of the adequacy were published previously [4][5][6][7].In contrast to the previously developed models of this process, the model accounts for heat exchange and phase transition processes. The equilibrium and heat exchange conditions will naturally undergo some changes during fibre formation under the effect of rheological factors. Unfortunately, this model does not yet take into consideration the rheological factor, but based on previous experimental testing of the model, it is poss~le to perform calculations of the fibre-formation process with sufficient certainty (from the technological point of view).Obtaining a gel-like (totally coagulated) fibre with a def'med structure of the gel at the outlet of the spinning bath is the basic problem of fibre formation. If gelation is not terminated in the spinning bath, spinning becomes unstable and the quality of the fibre becomes inhomogeneous, which is usually undesirable. For this reason, the time of total gelation (solidification) of the spinning solution in the spinning bath is one of the basic parameters in fibre fabrication technology.Let us consider the effect of the above parameters -temperature of the spinning solution tsp and spinning bath tsb, concentration of water in the spinning bath Csb and spinning solution Css on the gelation time ~-g.The research described here was conducted by the classic method. The total gelation time was determined by setting the fibre formation parameters, except for one, at a constant level, only varying one parameter, with a computer, model, and appropriate software.One of the simplest methods of changing the gelation time of the spinning solution in the spinning bath is to ...

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More than one-third of the chemical fibres manufactured in the world --cellulose, polyacrylonitrile, aramid, polyvinyl chloride, etc. --are now manufactured by wet spinning fi'om polymer solutions. All of these technologies have a common mechanism of fibre formation. Beginning with S. E Papkov's studies [ 1 ], the gelation process in spinning has been considered with respect to the phase state of the polymer solutions. The kinetics of fibre formation (gelation) was investigated experimentally in [2], and there are also studies on modeling this process [2-6] based on its diffusion nature.The growth rate of the gel coating in time and the duration of total gelation in a small jet of spinning solution are very important features in wet spinning technology. Our previously proposed [7] model for describing gelation in "'wet" spinning of chemical fibres from polymer solutions differs from the existing models [2-6] due to the possibility of calculating the gelation kinetics using the phase diagram.The phase transition in polymer systems can be caused by not only a change in the composition of the solvent (addition of a precipitator) but also by a change in the temperature or application of a mechanical field. The kinetics of attaining the condition of phase equilibrium to a significant degree determines the structure and physicomechanical properties of the gel. The gel phase, in turn, is the primary structure of the fibre which greatly determines its properties. The further investigation of gelation from polymer solution is pressing. The formation of a gel in thermotropic conditions [8], where fibre formation takes place due to heat exchange alone without diffusion, is described in recent publications on gelation.Thermotropic gelation is examined in the present study. The current gel layer thickness can be determined from the transcendental equation in [7] C[R(r),t] = Cc,[r(r,t)],where C[~;t] is the concentration of precipitator in the polymer solution jet (r is a coordinate along the radius of the jet; t is the time); C is the concentration of precipitator at the time of the phase transition at temperature T; the value of Cis found from the Cr phase diagram of the polymer--solvent--precipitator system. Equation (1) is solved relative to R -R(t) --the coordinates of the gelation front. The current gel layer thickness R(t) is determined as the difference between the radius of the fibreR 0 and the coordinate of the gelation front Rg(t) =R 0 -R(t). "(his relation and Eq. (1) can be used to find the gel layer thickness as a function of time R(t).The calculation ofR(t) for a nonlinear model ofgelation is reported in [7]. An approximate linear model of the process, expressed in algebraic equa'tions, will be examined tbr the analysis of the change in the size of the gelation zone in time R(t) and for the estimations. It is hypothesized that the qualitative shape of Rg(t) will be preserved when the nonlinear model is

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