Viscous Effects on Inertial Drop Formation

Deblais, Antoine; Herrada, Miguel A.; Hauner, Ines; Velikov, Krassimir P.; Roon, T. van; Kellay, Hamid; Eggers, Jens; Bonn, Daniel

doi:10.1103/physrevlett.121.254501

Cited by 49 publications

(41 citation statements)

References 25 publications

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“…Here t ic represents the time scale of an inertia-dominated pinchoff process, while t R represents Rayleigh time t R = ðρR 3 0 =σÞ 1=2 associated with the oscillation frequency of a droplet. Recent computational and experimental studies (19,20) show that the value of prefactor X is close to 0.4, although the early theoretical and experimental studies (15,(74)(75)(76)85) reported or utilized values in the range of 0.6 to 0.8. The radius evolution data for a higher-concentration c = 1.5 wt % polymer solution shows a delayed onset of the EC regime.…”

Section: Resultsmentioning

confidence: 99%

“…polymer physics | rheology | processing | extensional rheology | interfacial flows Q uantitative understanding of the role played by material properties in determining capillary-driven thinning and breakup is critically important for jetting (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13), dripping (14)(15)(16)(17)(18)(19)(20) and dispensing (21)(22)(23)(24)(25)(26), liquid-bridge breakup in printing (27)(28)(29), atomization and spraying (30)(31)(32), drop fission under strong extensional flows (33,34), and drop and emulsion formation in microfluidics or from membranes (35)(36)(37)(38)(39). Longer-lived viscoelastic filaments are also accredited with the stickiness of saliva (40,41) and deadly fluids produced by carnivorous plants (42,43), as well as increasing fiber spinnability (44)(45)…”

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confidence: 99%

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Macromolecular relaxation, strain, and extensibility determine elastocapillary thinning and extensional viscosity of polymer solutions

Dinic

Sharma

2019

Proc. Natl. Acad. Sci. U.S.A.

164

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Delayed capillary break-up of viscoelastic filaments presents scientific and technical challenges relevant for drop formation, dispensing, and adhesion in industrial and biological applications. The flow kinematics are primarily dictated by the viscoelastic stresses contributed by the polymers that are stretched and oriented in a strong extensional flow field resulting from the streamwise gradients created by the capillarity-driven squeeze flow. After an initial inertiocapillary (IC) or viscocapillary (VC) regime, where elastic effects seem to play no role, the interplay of capillarity and viscoelasticity can lead to an elastocapillary (EC) response characterized by exponentially-slow thinning of neck radius (extensional relaxation time is determined from the delay constant). Less frequently, a terminal visco-elastocapillary (TVEC) response with linear decay in radius can be observed and used for measuring terminal, steady extensional viscosity. However, both IC/VC–EC and EC–TVEC transitions are inaccessible in devices that create stretched necks by applying a step strain to a liquid bridge (e.g., capillary breakup extensional rheometer). In this study, we use dripping-onto-substrate rheometry to obtain radius evolution data for unentangled polymer solutions. We deduce that the plots of transient extensional viscosity vs. Hencky strain (scaled by the respective values at the EC–TVEC transition) emulate the functional form of the birefringence–macromolecular strain relationship based on Peterlin’s theory. We quantify the duration and strain between the IC/VC–EC and the EC–TVEC transitions using measures we term elastocapillary span and elastocapillary strain increment and find both measures show values directly correlated with the corresponding variation in extensional relaxation time.

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Section: Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

Macromolecular relaxation, strain, and extensibility determine elastocapillary thinning and extensional viscosity of polymer solutions

Dinic

Sharma

2019

Proc. Natl. Acad. Sci. U.S.A.

164

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“…For nearly inviscid liquid, however, the experiments and simulations showed that the thinning liquid filament followed the I regime when it finally approached singularity [25,26]. This scenario remained valid even when Oh was up to ∼0.02 [27]. In fact, depending on the Oh and also the initial conditions, the observed dynamics can alternate between the different regimes (I, V, and IV) [18,28].…”

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confidence: 81%

“…1(b), the same scenario is observed, ending in the formation of a satellite droplet. Before breakup, the two asymmetrical necks pinch to microthreads (3.92 ms), which can be seen as well in the pinch-off of a dripping drop made of slightly and highly viscous liquids [18,27,33]. The transition from the dumbbell-like drop with a center neck to that with double necks at opposite locations always occurred at the relaxation stage of the separation process.…”

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confidence: 88%

Pinching Dynamics and Satellite Droplet Formation in Symmetrical Droplet Collisions

2019

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In head-on collisions between two droplets, reflexive separation is frequently formed, showing tentative coalescence followed by disintegration into two primary drops. With higher impact inertia relative to surface tension, characterized by a Weber number (We), more satellite droplets are created between the primary drops. In the symmetric configuration, the existing phenomenological models indicate the absence of satellite droplets at the onset We when the coalesced drops start to break. Supported by experimental and simulation evidence, here we demonstrate the exclusive formation of at least one droplet after pinch of the thread connecting the colliding drops. In accordance with the universal features of a thinning liquid filament approaching singularity as predicted by scaling theories of pinch-off, the mechanism of satellite droplet formation in the symmetrical impact of droplets is clarified. Via slight breaking of the symmetry, no satellite droplet can be observed, thus providing a possible interpretation for the discrepancy in the literature and implications for controlling undesirable drop formation.

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“…A few recent examples of relevance include the inclusion of interface effects in a continuum-based study of transport phenomena in a microfluidic channel by Vo and Kim [57], a classical unsteady Stokes flow analysis of oscillating sphere near a wall by Fouxon and Leshansky [58], which would differ at close range where the confinement effect may be operative, and the study of droplet breakup by Deblais et al [59]. In this latter combined experimental and numerical study, the authors show inclusion of a small amount of viscosity is sufficient to induce breakdown of the universality of the breakup dynamics predicted by inviscid theory.…”

Section: A Generalizations and Implicationsmentioning

confidence: 99%

Confinement-Induced Control of Similarity Solutions in Premelting Dynamics and Other Thin Film Problems

Pramanik¹,

Wettlaufer²

2019

SIAM J. Appl. Math.

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We study the combined effects of nonlocal elasticity and confinement induced ordering on the dynamics of thermomolecular pressure gradient driven premelted films bound by an elastic membrane. The confinement induced ordering is modeled using a film thickness dependent viscosity. When there is no confinement induced ordering, we recover the similarity solution for the evolution of the elastic membrane, which exhibits an infinite sequence of oscillations. However, when the confinement induced viscosity is comparable to the bulk viscosity, the numerical solutions of the full system reveal the conditions under which the oscillations and similarity solutions vanish. Implications of our results for general thermomechanical dynamics, frost heave observations and cryogenic cell preservation are discussed. Finally, through its influence on the viscosity, the confinement effect implicitly introduces a new universal length scale into the volume flux. Thus, there are a host of thin film problems, from droplet breakup to wetting/dewetting dynamics, whose properties (similarity solutions, regularization, and compact support) will change under the action of the confinement effect. Therefore, our study suggests revisiting the mathematical structure and experimental implications of a wide range of problems within the framework of the confinement effect.

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Viscous Effects on Inertial Drop Formation

Cited by 49 publications

References 25 publications

Macromolecular relaxation, strain, and extensibility determine elastocapillary thinning and extensional viscosity of polymer solutions

Macromolecular relaxation, strain, and extensibility determine elastocapillary thinning and extensional viscosity of polymer solutions

Pinching Dynamics and Satellite Droplet Formation in Symmetrical Droplet Collisions

Confinement-Induced Control of Similarity Solutions in Premelting Dynamics and Other Thin Film Problems

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