Droplet formation and scaling in dense suspensions

Miskin, Marc Z.; Jaeger, Heinrich M.

doi:10.1073/pnas.1111060109

Cited by 57 publications

(38 citation statements)

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“…Letting the particles sediment inside a straight cylindrical syringe produces packing fractions of φ = 0.61 ± 0.02. As gravity pulls the suspension down, a pinch-off occurs below the cylinder opening [15,16]. In the dense suspension limit studied here, the plugs preserve the cylindrical shape of the syringe, resulting in a plug radius (R p ≈ 2.25 ± 0.05 mm), and have a height L ∼ 2R p .…”

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confidence: 99%

Dense Suspension Splat: Monolayer Spreading and Hole Formation after Impact

Lubbers

Wilken

et al. 2014

Phys. Rev. Lett.

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We use experiments and minimal numerical models to investigate the rapidly expanding monolayer formed by the impact of a dense suspension drop against a smooth solid surface. The expansion creates a lace-like pattern of particle clusters separated by particle-free regions. Both the expansion and the development of the spatial inhomogeneity are dominated by particle inertia, therefore robust and insensitive to details of the surface wetting, capillarity and viscous drag.PACS numbers: 82.70. Kj, 45.70.Qj, 82.70.Dd, 47.57.Qk, 47.57.Gc Since the pioneering work by Worthington [1] the spreading of liquids droplets upon impact has remained an active research area [2,3]. At meters-per-second impact speeds, the spreading divides into two stages [4]: an initial, rapid spreading dominated by liquid inertia and, consequently, insensitive to surface wetting, capillary or liquid viscosity, followed by a slower evolution where the intricate interplay of these effects is important.Here we examine an analogous inertia-dominated spreading dynamics in dense suspension impact. We use a suspension of rigid, non-Brownian particles at high volume fraction (60% or above). This impact regime has received little study [5]. Previous studies on particleladen drop impact have mainly analyzed slow evolution in dilute and semi-dilute suspensions [6][7][8][9]. We find that impact at several meters per second produces a novel outcome ( Fig. 1): the suspension drop deforms into a splat comprised of a single layer of densely packed particles immersed in a thin liquid layer. As the splat expands, void-like regions appear and grow, causing the final splat to display a lace-like pattern of particle clusters separated by particle-free regions. Because particle inertia dominates the expansion and the instability, the monolayer splat dynamics is robust and only weakly modified by surface wetting, capillary and viscous drag. This insensitivity to material and surface properties is often the desired outcome in coating processes. This makes our results useful in ongoing efforts to assess the cohesive strengths of colloidal semiconductor quantum dots by measuring their maximal splat size after impact [11], as well as applications such as thermal spray coating of sintered powders [12] and additive manufacturing using inkjet printing [13,14]. These processes often involve concentrated suspensions. Moreover the impact speeds are often very large. As a result, despite the smaller particles used in these processes, the post-impact spreading dynamics belongs in the same particle-inertia dominated regime as our experiments. straight cylindrical syringe produces packing fractions of φ = 0.61 ± 0.02. As gravity pulls the suspension down, a pinch-off occurs below the cylinder opening [15,16]. In the dense suspension limit studied here, the plugs preserve the cylindrical shape of the syringe, resulting in a plug radius (R p ≈ 2.25 ± 0.05 mm), and have a height L ∼ 2R p . The substrate was a smooth, horizontal glass plate 1.6 ± 0.03 m below the syringe.arXiv:1307....

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Dense Suspension Splat: Monolayer Spreading and Hole Formation after Impact

Lubbers

Wilken

et al. 2014

Phys. Rev. Lett.

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“…Dispersions that exhibit shear-thickening can show viscoelastic pinch-off or dilatancy effects depending on the strain rate 23,24 . However, other non-Brownian suspensions display a faster thinning rate close to pinch-off than that predicted by the viscous scaling law for the bulk viscosity [25][26][27][28][29][30] . This flow behaviour is not necessarily a strain-thinning effect and can rarely be captured by a power-law model 30 .…”

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confidence: 99%

“…However, other non-Brownian suspensions display a faster thinning rate close to pinch-off than that predicted by the viscous scaling law for the bulk viscosity [25][26][27][28][29][30] . This flow behaviour is not necessarily a strain-thinning effect and can rarely be captured by a power-law model 30 . The shear response of these systems is dominated by hydrodynamic interactions and can be described by a single viscosity up to moderate particle concentrations 31 .…”

Section: Introductionmentioning

confidence: 99%

Capillary breakup of suspensions near pinch-off

et al. 2015

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We present new findings on how the presence of particles alters the pinch-off dynamics of a liquid bridge. For moderate concentrations, suspensions initially behave as a viscous liquid with dynamics determined by the bulk viscosity of the suspension.Close to breakup, however, the filament loses its homogeneous shape and localised accelerated breakup is observed. This paper focuses on quantifying these final thinning dynamics for different sized particles with radii between 3 µm and 20 µm in a Newtonian matrix with volume fractions ranging from 0.02 to 0.40. The dynamics of these capillary breakup experiments are very well described by a one-dimensional model that correlates changes in thinning dynamics with the particle distribution in the filament. For all samples, the accelerated dynamics are initiated by increasing particle-density fluctuations that generate locally-diluted zones. The onset of these concentration fluctuations is described by a transition radius, which scales with the particle radius and volume fraction. The thinning rate continues to increase and reaches a maximum when the interstitial fluid is thinning between two particle clusters. Contrary to previous experimental studies, we observe that the final thinning dynamics are dominated by a deceleration, where the interstitial fluid appears not to be disturbed by the presence of the particles. By rescaling the experimental filament profiles, it is shown that the pinching dynamics return to the self-similar scaling of a viscous Newtonian liquid bridge in the final moments preceding breakup. a) christian.clasen@cit.kuleuven.be

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“…As gravity pulls the suspension down, a pinch-off will occur [38,39], resulting in highly reproducible suspension drops. We varied U by adjusting the release height, and r d by changing the nozzle size.…”

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Splashing Onset in Dense Suspension Droplets

Peters

Jaeger

2013

Phys. Rev. Lett.

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We investigate the impact of droplets of dense suspensions onto a solid substrate. We show that a global hydrodynamic balance is unable to predict the splash onset and propose to replace it by an energy balance at the level of the particles in the suspension. We experimentally verify that the resulting, particle-based Weber number gives a reliable, particle size and density dependent splash onset criterion. We further show that the same argument also explains why in bimodal systems smaller particles are more likely to escape than larger ones.Splashing of liquid droplets upon impact on a solid surface has been investigated for over a century [1][2][3][4][5][6][7][8][9][10][11]. More recently, there has also been a growing interest in what happens to the spreading and splashing if particles are added to the liquid [12][13][14]. On micron scales, ZrO 2 suspensions have been used in studies aiming to optimize ink-jet printing applications [15][16][17][18][19], and on truly macroscopic scales there has been the development of 3D printers that dispense cement slurry [20,21]. In all of these situations, an important concern is to prevent splashing, and particles from escaping, when droplets hit a surface. However, the question of when and why particles are ejected has remained unsettled, and existing experimental studies mostly focus on dilute suspensions.Current models for suspension drop impact associate the onset of splashing with the condition that K = Weexceeds a critical value K 0 , which has been the traditional criterion for pure liquid splashing on dry surfaces at atmospheric pressure in a regime independent of surface roughness [4,22,23]. Here the Weber and Reynolds numbers are defined as We d = ρ l r d U 2 /σ and Re d = ρ l r d U/µ, with r d the droplet radius, U the droplet impact velocity, and ρ l , σ and µ the liquid density, surface tension and dynamic viscosity, respectively.In these models, the addition of particles has been captured by replacing µ with an effective viscosity µ e that increases with packing fraction [12,[24][25][26][27][28]. This predicts that a droplet of a pure liquid that would splash under certain conditions should not splash after adding enough particles. To our knowledge, there exists no systematic study that confirms this prediction. In fact, Nicolas observed [12] that adding particles, instead, lowered the splashing threshold K 0 .To investigate the influence of added particles, we depart from the dilute limit described above, and instead focus here on the limit of dense granular suspensions with volume packing fractions φ = 0.62 ± 0.03, where the discrepancy with the above droplet-scale splash onset criterion is most pronounced.In pure liquid droplets, the size of the ejecta depends on either the destabilization of a thin liquid sheet [5,[29][30][31][32][33][34] or, in the case of prompt splashing, on an instability at the moving contact line [5,10,35]. At splash onset in a suspension, on the other hand, the ejecta are the solid particles (see Fig. 1), which implies a built-in...

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Droplet formation and scaling in dense suspensions

Cited by 57 publications

References 43 publications

Dense Suspension Splat: Monolayer Spreading and Hole Formation after Impact

Dense Suspension Splat: Monolayer Spreading and Hole Formation after Impact

Capillary breakup of suspensions near pinch-off

Splashing Onset in Dense Suspension Droplets

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