Viscous coalescence of unequally sized spherical and cylindrical doublets

Polychronopoulos, Nickolas D.; Benos, Lefteris; Stergiou, Constantinos; Sarris, Ioannis E.; Vlachopoulos, J.

doi:10.1039/d2sm00129b

Cited by 6 publications

(11 citation statements)

References 72 publications

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“…Hopper's analytic model [ 24 ] gives W ( t ) but not L ( t ). Both Equation () and Hopper's model fail to predict W ( t ) as discussed by Polychronopoulos et al [ 26 ] However, Equation () gives a good prediction for L ( t ), especially when the presumed capillary velocity γ / η is reduced to 0.024, as shown in Figure 8B.…”

Section: Comparisons To Experimentsmentioning

confidence: 87%

“…Details of the associated algebraic manipulations are available elsewhere. [ 26 ] The results are expressed as follows for a doublet of unequal spheres:

\frac{d θ_{1}}{dt} goodbreak= \frac{1}{τ} (2^{- 5 / 3} b^{2}) \frac{\sin^{3} θ_{1} {(2 - \cos θ_{1})}^{1 / 3}}{{(1 goodbreak+ \cos θ_{1})}^{4 / 3}} \frac{(\cos θ_{1} + \cos θ_{2})}{b^{3} {(\cos θ_{1} - 1)}^{2} + {(\cos θ_{2} - 1)}^{2}}

\frac{d θ_{2}}{dt} goodbreak= b \frac{d θ_{1}}{dt} {(\frac{1 + \cos θ_{2}}{1 + \cos θ_{1}})}^{2 / 3} {(\frac{2 - \cos θ_{2}}{2 - \cos θ_{1}})}^{4 / 3}

…”

Section: Generalization Of Frenkel's Approach For Unequal Doubletsmentioning

confidence: 99%

“…Other measures have also been used, such as normalized surface area, circularity, and normalized anisotropy. [ 26 ] These measures are less sensitive, and it is difficult to determine how good the model predictions are. Measurements of neck growth involving cylindrical particles are very difficult.…”

Section: Comparisons To Experimentsmentioning

confidence: 99%

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Mathematical modelling of coalescence of viscous particles: An overview

2023

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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.

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Section: Comparisons To Experimentsmentioning

confidence: 87%

“…Details of the associated algebraic manipulations are available elsewhere. [ 26 ] The results are expressed as follows for a doublet of unequal spheres:

\frac{d θ_{1}}{dt} goodbreak= \frac{1}{τ} (2^{- 5 / 3} b^{2}) \frac{\sin^{3} θ_{1} {(2 - \cos θ_{1})}^{1 / 3}}{{(1 goodbreak+ \cos θ_{1})}^{4 / 3}} \frac{(\cos θ_{1} + \cos θ_{2})}{b^{3} {(\cos θ_{1} - 1)}^{2} + {(\cos θ_{2} - 1)}^{2}}

\frac{d θ_{2}}{dt} goodbreak= b \frac{d θ_{1}}{dt} {(\frac{1 + \cos θ_{2}}{1 + \cos θ_{1}})}^{2 / 3} {(\frac{2 - \cos θ_{2}}{2 - \cos θ_{1}})}^{4 / 3}

…”

Section: Generalization Of Frenkel's Approach For Unequal Doubletsmentioning

confidence: 99%

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Mathematical modelling of coalescence of viscous particles: An overview

2023

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“…As the coalescence phenomenon is predominately extensional, 24 both the upper and lower convected derivative can be used to model the physics. 25 In the present analysis, we have used the lower convected derivative s…”

Section: Theorymentioning

confidence: 99%

“…As the upper convective derivative is the predominant term, the present theory unifies these continuum based constitutive equations to eqn (5). However, for the coalescence of two sessile polymeric drops, 13 a theoretical model which is independent of characteristic stresses has been proposed for viscoelastic and elasticity dominated regimes using thin film lubrication approximation.As the coalescence phenomenon is predominately extensional, 24 both the upper and lower convected derivative can be used to model the physics. 25 In the present analysis, we have used the lower convected derivative .…”

Section: Theorymentioning

confidence: 99%

Sub-Newtonian coalescence in polymeric fluids

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2023

Can J Chem Eng

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A unified polymer reaction engineering methodology for catalytic olefin polymerization: From reaction conditions and catalyst reaction performance to molecular and rheological properties for forward, reverse engineering and deconvolution applications Vasileios TouloupidisThis work presents a unified polymer reaction engineering methodology for catalytic olefin polymerization process (singe-and multi-site catalysts). The proposed modelling approach offers a modelling pathway from polymerization recipe, to production rate and polymer microstructure, and finally to rheological properties. For the first time, the constraint of the actual reaction performance of the polymerization catalyst in the inverse rheology and microstructural deconvolution problem is introduced, limiting the solution to the most realistic molecular weight distributions (MWDs) that a specific catalyst can produce. The potential of the proposed methodology is highlighted within a series of indicative examples, including both forward and reverse engineering, as well as deconvolution applications. [1]

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Viscous coalescence of unequally sized spherical and cylindrical doublets

Abstract: A coalescence model is developed for pairs of unequally sized particles, assuming surface tension driven flow opposed by viscosity. The flow field is extensional, biaxial for spheres and planar for...

Cited by 6 publications

References 72 publications

Mathematical modelling of coalescence of viscous particles: An overview

Mathematical modelling of coalescence of viscous particles: An overview

Sub-Newtonian coalescence in polymeric fluids

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