Mathematical modelling of coalescence of viscous particles: An overview

Abstract

Viscous particles of polymer melts and glasses coalesce under the action of surface tension. Resistance is due to viscosity, while inertia is not a contributing factor, with the Ohnesorge number being very high. Russian physicist Yakov Frenkel developed a model for neck growth during the initial stage of the merging process of two spherical particles, assuming uniform biaxial extensional flow. Frenkel's model was extended for prediction of neck size as a function of time to the completion of coalescence, expressed by an ordinary differential equation. The time t is expressed in dimensionless form as (tγ/ηR), where η, γ, and R denote the viscosity, surface tension, and particle radius, respectively. Models were also developed for viscoelastic effects, non‐isothermal conditions, and unequal diameter particles. For the coalescence of infinitely long cylinders, planar extensional flow is assumed. Other investigators presented numerical solutions of the Navier–Stokes equations, which include shear flow components, but the predictions of neck growth are not much different from those of the Frenkel‐based models. Comparisons to experiments are also discussed, involving polymers, glasses, animal tissue cells, and biomacromolecules. The models are also used in additive manufacturing applications for the determination of bonding and pore shrinkage.

Direct Ink Writing for Electrochemical Device Fabrication: A Review of 3D-Printed Electrodes and Ink Rheology

“…Simpler analytical models of predictive power, developed for flows of shear-thinning liquids with yield stress in a large reservoir (syringe barrel in DIW) and a straight cylindrical or conical channel (nozzle in DIW) [70-73], have not yet been used for modeling ink flow in DIW for the fabrication of energy devices. Also, numerical flow simulation-based models using the above rheological parameters to evaluate the degree of joining (referred to as sintering or coalescence) regarding the adjacent filaments of the fabricated structures [74,75] or relevant analytical sintering models [76][77][78][79][80] must be taken in consideration for the effective design of energy devices via DIW.…”

Archie E. Hamielec memorial issue

“…The authors of the articles in this issue join us from many countries and institutions across the globe (Figure 1 and Table 1) to thank Archie for his enduring legacy in polymerization reaction engineering, a field of academic and industrial interest that he established practically single‐handedly. [ 1–45 ]…”