Kinematics of the fountain flow during pipe filling with a power‐law fluid

Abstract

The fountain flow of a non‐Newtonian fluid during a circular pipe filling is investigated. Mathematical description of the process is based on the equations of motion and continuity. The system of equations is completed by the Ostwald‐de Waele rheological equation. The slip condition is used at the contact line. The numerical solution of the formulated problem is obtained using a computational technology based on the finite volume method, SIMPLE procedure, and invariant method, which is used for numerical realization of the boundary conditions on the free surface. The results of parametric studies of the flow kinematic characteristics are presented depending on the governing dimensionless criteria and power‐law index. © 2018 American Institute of Chemical Engineers AIChE J, 65: 850–858, 2019

Simulation of Fountain Flow based on Molecular Dynamics Method

“…As well as the equation for the center of mass of a single dumbbell molecule: 2 + = 12 c rr r (9) By subtracting the position evolution equation for the rigid bead, we derive the configurational control equation for the dumbbell:…”

“…Liu et al [6], leveraging the Rolie-Poly model, explored the effects of inlet velocity, polymer molecular weight, and temperature on the evolution of the leadingedge fountain effect of polystyrene melts, effectively simulating the viscoelastic behavior of polystyrene. Borzenko et al [7][8][9], through the Ostwald-de Waele rheological equation, examined the impact of pseudo-plastic and dilatational characteristics of the liquid medium on the fountain flow motion of non-Newtonian fluids during the tube filling process, thereby explaining the elimination of contact line singularity in traditional methods. Smit et al [10] predicted the instability of fountain flow using the PTT-XPP model, compared the elastic effects in the flow, and validated the impact of reduced critical Weissenberg numbers on fountain flow characteristics.…”