Uniaxial extension of an isothermal fluid cylinder in the presence of inertia,surface tension and gravity

Effects of inertia, surface tension and gravity in the constant force stretching of isothermal cylindrical filaments of Newtonian, power-law and Maxwell-type fluids were analysed in Lagrangian coordinates. Solution for the purely gravitational extension of Newtonian fluid cylinder was found to be as simple as = 1 – C₃(1 – ) where designates the cross sectional area, the Lagrangian distance and the time. Analytical solutions were also available for the case of inertialess Newtonian and power-law fluids.A first-order backward differencing scheme and minimal computer time were sufficient to numerically analyse the constant force extension of Maxwell-type fluids in the presence of inertia, gravity and surface tension. Effects of inertia, surface tension and gravity on the severity of neck down occurring at either end of the filament are summarized in diagrams. The present approach is valid on any other constitutive model as far as there is a numerical scheme to analyse thehomogeneous extension of a cylinder of that particular fluid.