Rheology on the drawing zone in glass spinning

Summary Among investigations concerning the rheology of spinning materials from melt, or in other terms the problem of spinnability, glasses perform an example of fibre forming without crystallization along the spinning way and with surface tension playing an important role. Furthermore glasses show aNewtonian behaviour at least in the upper part of the drawing zone.As the absence of crystallization simplifies the formulation of the governing energy equation, on the other hand, the surface tension makes the applied motion equations quite complex to solve, above all in the two-dimensional analysis.The present paper shows that only a two-dimensional approach can give reliable results on the temperature, velocity and stress distribution in the drawing zone by a comparison of the theoretical and the experimental diameter profile of the forming fibre.The temperature profile has been obtained by a numerical solution of the energy equation, only after gaining experimentally the heat transfer coefficient. The results shown in the one-dimensional analysis cannot be applied in the opper part of the drawing zone.The velocity and stress distribution can be obtained by very complex numerical solutions in the very upper part of the drawing zone where the one-dimensional approach is shown unreliable. This can be thought an asymptotic solution of two-dimensional approach, reliable only after a certain distance of the spinning way from the exit of the nozzle.Furthermore, an analysis of the dimensionless numbers involved in the spinning phenomena brings up some information concerning the instability of the glass jet in comparison with that shown by materials as molten polymers or metals.As far as the rheological behaviour of glasses in the elongational shear rate is concerned, some conclusions can be drawn.F_r Froude numberU₀²/gR₀ withg acceleration gravity (cm/sec²) - N_u Nusselt number 2Rh/Ka withh heat transfer coefficient (cal/cm² sec °C) andK_a air thermal conductivity (cal/cm sec °C) around the forming fibre - Q Volume rate of flow (cm³/sec) - r Radial distance from the central axis of the fibre (cm) - R Cross section radius of the fibre (cm) - R₀ Inside diameter of the nozzle (cm) - t Quenching time (sec) - T_aT_s Temperature of fibre at the centre (°C) - T_i Initial temperature at the distancex = 0 (°C) - T₀ Mean value of temperature of air surrounding the forming fibre (°C) - U₀ Mean value of velocity of glass atx = 0 (cm/sec) - V Local velocity of fibre in the axial direction (cm/sec) - x Axial distance of the fibre from the nozzle exit (cm/sec) - W Weight rate of flow (g/minute) - W_e Weber numberU₀²R₀/ - Glass surface tension (dynes/cm) - Angle between the fibre axis and the tangent to the fibre surface in ther, x plane (radiant). - v Air kinematic viscosity (cm²/sec) - Glass density (g/cm³) - Glass viscosity (poises) - _i Glass viscosity atT_i. - Maxwell relaxation time/G (sec) withG (dynes/cm²) elastic shear modulus of glassWith 10 figures and 2 tables