Modification of Frenkel's model for sintering

Pokluda, Ondřej; Bellehumeur, C. T.; Vlachopoulos, J.

doi:10.1002/aic.690431213

Cited by 234 publications

(271 citation statements)

References 16 publications

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“…The results are given in Figure 6, in which we see that all lines overlap. This indicates that the shape evolution of the contact radius y is independent of the flow history, if the round off parameter R n = R × (y n /R) 3 [20] is used. Next, we keep the initial contact radius constant y n = 0.4, and we change the round off parameter R n = [R × (y n /R) 3 , (R/2) × (y n /R) 3 , (R/4) × (y n /R) 3 ].…”

Section: Effect Of the Initial Geometrymentioning

confidence: 99%

“…From Figure 8, it follows that the curvature κ at point (0, y) increases with respect to the initial geometry until it reaches a maximum value and subsequently decreases. This holds for all different values of the round off parameter R n = [R × (y n /R) 3 , (R/2) × (y n /R) 3 , (R/4) × (y n /R) 3 ]. This behavior is depicted in Figure 9, where the contour line r = g(z) of the two particles is shown at times t = [0, 0.08, 0.2], using R n = R × (y n /R) 3 .…”

Section: Effect Of the Initial Geometrymentioning

confidence: 99%

“…This holds for all different values of the round off parameter R n = [R × (y n /R) 3 , (R/2) × (y n /R) 3 , (R/4) × (y n /R) 3 ]. This behavior is depicted in Figure 9, where the contour line r = g(z) of the two particles is shown at times t = [0, 0.08, 0.2], using R n = R × (y n /R) 3 . Herein, t = 0.08 is the time at which the curvature κ reaches its maximum value.…”

Section: Effect Of the Initial Geometrymentioning

confidence: 99%

“…The radii of the particles R, together with the initial contact radius y n , define the initial geometry. To avoid discontinuities in the slope of the interface, the parameter R n = R × (y n /R) 3 [20] rounds off the neck region. Due to the round off by R n , the real initial contact radius becomes y t=0 = y n + w. These two liquid particles will merge into one larger sphere with radius R final , determined by the initial volume of the geometry, under the influence of the surface tension prescribed on surface Γ.…”

Section: Problem Descriptionmentioning

confidence: 99%

“…Eshelby [2] corrected this model for continuity, assuming biaxial extensional flow. Pokluda et al [3] improved the corrected model by taking the change in particle radius into account. To describe the sintering of viscoelastic particles, Bellehumeur et al [4] extended Frenkel's approach with the steady-state upper-convected Maxwell (UCM) constitutive model, and Scribben et al [5] continued this work by describing the transient viscoelastic coalescence of two particles using UCM.…”

Section: Introductionmentioning

confidence: 99%

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Sintering of Two Viscoelastic Particles: A Computational Approach

2017

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Selective laser sintering (SLS) is a high-resolution additive manufacturing fabrication technique. To fully understand the process, we developed a computational model, using the finite element method, to solve the flow problem of sintering two viscoelastic particles. The flow is assumed to be isothermal and the particles to be in a liquid state, where their rheology is described using the Giesekus and XPP constitutive models. In this work, we assess the parameters that define this problem, such as the initial geometry, the Deborah number and other dimensionless parameters present in the rheological models. In particular, the conformation tensor is considered, which is a measure for the polymeric strain and plays an important role in the crystallization kinetics of semicrystalline polymers like polyamide 12, usually used in SLS.

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Section: Effect Of the Initial Geometrymentioning

confidence: 99%

Section: Effect Of the Initial Geometrymentioning

confidence: 99%

Section: Effect Of the Initial Geometrymentioning

confidence: 99%

Section: Problem Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Sintering of Two Viscoelastic Particles: A Computational Approach

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Paste Development for an Optimized Filament Stretching Effect during Parallel Dispensing on Transparent Conductive Oxide Layers for Solar Cell Metallization

Gensowski,

Palme,

Langhof

et al. 2023

Adv Eng Mater

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The availability of silver as an electrically conductive filler material in printing pastes for solar cell metallization is becoming a more crucial issue for multiterawatt‐scale production due to its global constraints. Therefore, the silver consumption for solar cell production needs to be reduced drastically by substituting silver with alternative conductive filler materials or utilizing process‐specific phenomena. The phenomenon of filament stretching during microextrusion allows significantly lower paste laydowns. The magnitude of filament stretching is paste‐dependent and therefore further knowledge of the pastes’ impact to the filament stretching is required. This study presents nine low‐temperature curing pastes differing in the particle system and binder resin. The rheological and thermal behavior of these suspensions are investigated and printing tests onto silicon heterojunction (SHJ) precursors are carried out. Additionally, scanning electron microscopy (SEM)‐based microstructure analyses of printed electrodes are performed. Based on these experimental results, the impact of paste compositions regarding the paste behavior during microextrusion and the SHJ solar cell performances are analyzed. The developed paste formulations exhibit a strong filament stretching, leading to a reduced silver laydown of down to ΔmAg = −60%rel. and an absolute efficiency gain of up to Δη = +0.75%abs. due to less shading losses.

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Restructuring of aggregates and their primary particle size distribution during sintering

Eggersdorfer

Pratsinis

2013

AIChE Journal

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During sintering (coalescence) of aggregates of polydisperse primary particles (PPs), restructuring takes place, the average PP size increases and the PP size distribution (PPSD) narrows affecting particle performance in a number of applications. Here, aggregate sintering by viscous flow, lattice, and grain boundary diffusion is simulated by multiparticle discrete element methods focusing on PP growth dynamics and elucidating the detailed restructuring of aggregates during their coalescence. The effect of initial PPSD and sintering mechanisms on the evolution of PP polydispersity (geometric standard deviation) and surface area mean diameter are presented. Each sintering mechanism results in a distinct evolution of PPSD but quite similar growth in average PP diameter. Grain boundary diffusion has the strongest impact among all sintering mechanisms and rapidly results in the narrowest PPSD, as it has the strongest dependence on PP size. During sintering of aggregates with initially monodisperse PPs, the PPSD goes through a maximum width before narrowing again as PPs coalesce. A power law holds between projected aggregate surface area and number of PPs regardless of sintering mechanism and initial PP polydispersity. This law can be readily used in aerosol reactor design and for characterization of aggregates independent of material composition, initial PP polydispersity, and sintering mechanism.Theory Geometric models frequently describe sintering of agglomerates of PPs by viscous flow, 16,17 grain boundary, 18 and lattice diffusion. Such agglomerates are generated here by Correspondence concerning this article should be addressed to S. E. Pratsinis at pratsinis@ptl.mavt.ethz.ch.A grain boundary forms at the neck of nanoparticles in contact with two misaligned crystals. The high particle curvature in the neck induces a stress gradient resulting in a diffusive flux of atoms J from the neck center (source) to its surface (sink) 40 J5Dwhere dC v /dR is the vacancy concentration gradient, R the neck radius, C v the fraction of sites occupied by vacancies and X the volume of an atom or vacancy. During sintering by grain boundary diffusion, the atoms diffuse along the grain boundary ( Figure A1). 36

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Modification of Frenkel's model for sintering

Cited by 234 publications

References 16 publications

Sintering of Two Viscoelastic Particles: A Computational Approach

Sintering of Two Viscoelastic Particles: A Computational Approach

Paste Development for an Optimized Filament Stretching Effect during Parallel Dispensing on Transparent Conductive Oxide Layers for Solar Cell Metallization

Restructuring of aggregates and their primary particle size distribution during sintering

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