PRACTICAL APPLICATION OF A HIGHER-ORDER PERTURBATION-THEORY FOR SLENDER VISCOELASTIC JETS AND FIBERS

All thin-filament models to date yield leading-order approximations in a slender asymptotic sense. This paper illustrates practical applications of a higher-order, comprehensive theory for slender viscoelastic jets and fibers. From this comprehensive framework we list the leading three orders of asymptotic equations for four physical examples. We proceed to solve the steady equations through three orders for all four examples and illustrate several points: (1) many leading-order steady solutions are asymptotically valid and robust to neglected higher-order physical effects (we compute the higher-order corrections and find they are small); (2) other leading-order solutions are invalid in the presence of higher-order effects; specifically, we show corrections due to weak elastic relaxation can be as large as the Newtonian leading-order approximation; (3) it is straightforward using this higher-order theory to determine if a particular leading-order solution is a valid approximation of physical behavior.