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Journal ArticleDOI

Thin-sheet creation and threshold pressures in drop splashing

25 Jan 2017-Soft Matter (The Royal Society of Chemistry)-Vol. 13, Iss: 4, pp 740-747

AbstractA liquid drop impacting a smooth solid substrate splashes by emitting a thin liquid sheet from near the contact line of the spreading liquid. This sheet is lifted from the substrate and ultimately breaks apart. Surprisingly, the splash is caused by the ambient gas, whose properties dictate when and if the sheet is created. Here, I focus on two aspects of this process. Using high-speed imaging I find that the time of thin-sheet creation displays a different quantitative dependence on air pressure if the sheet is created during the early stages of spreading, rather than when the liquid has already spread to a large radius. This result sheds light on previously observed impact velocity regimes. Additionally, by measuring impacts of drops on surfaces comprised of both rough and smooth regions, I identify a new threshold velocity that limits the times at which the thin sheet can be created. This velocity determines the threshold pressure below which splashing is suppressed.

Topics: Drop (liquid) (54%), Splash (53%)

Summary (2 min read)

INTRODUCTION

  • Experiments have found that drops splash only above a certain gas pressure in a variety of systems [1, 2, 3, 4, 5], and have provided insight into the liquid and air dynamics during splashing [6, 7, 8, 9].
  • When the liquid finally makes contact with the substrate [7], the air directly beneath the drop is trapped in a small bubble [15] and does not further influence the splashing process [16].
  • Next, the liquid spreads radially outward in the form of a liquid sheet that remains in direct contact with the substrate, as shown in Fig. 1.1a [6, 16, 17].
  • The majority of present theories of splashing do not take this mechanism into account.
  • Together, the air-dependent time of thin-sheet creation and the air-independent threshold velocity, below which thin-sheet creation is suppressed, form a pair of necessary and sufficient conditions for thin-sheet creation.

EXPERIMENTAL DETAILS

  • The experiments were conducted with a variety of liquids.
  • Ethanol and silicone oils (PDMS, Clearco Products) were used to vary the drop viscosity from µ = 1.2 to 48mPa s, while keeping the surface tension approximately constant between σ = 18.7 and 21.6mN m−1.
  • The time of etching was chosen to produce a root-mean-square roughness Rrms = 1.9µm, sufficient to prevent thin-sheet creation for the liquids used [5].
  • This accuracy was provided by ultra-fast interference imaging, which measures the interference between the light reflected from the bottom surface of the spreading liquid and the top surface of the substrate [16].
  • The thinnest air gap the authors can reliably detect, approximately 30nm, is set by the wavelength of the light source (ThorLabs LED, λ = 625nm), the sensitivity of the camera, and the exposure time.

TIME OF THIN-SHEET CREATION

  • The thin-sheet creation time depends on a number of parameters, in particular on the ambient gas pressure [6].
  • The phase diagram can be understood by considering distinct thresholds for small-r∗ and large-r∗ sheets.
  • In the low velocity regime, the small-r∗ sheet persists to lower pressures and Psheet = Psmall-r∗ and the dependence of sheet threshold pressure on impact velocity follows from the properties of small-r∗ sheet creation.
  • There, a thin sheet begins to be created, despite the fact that t > tsheet, while the part of the drop that remains in the rough region continues to spread smoothly on the surface.
  • The ustop pressure independence has an important practical consequence, as it allows one to measure ustop by simply measuring usheet on a smooth surface.

DISCUSSION AND CONCLUSIONS

  • The cause of the sharp transition between small-r∗ and large-r∗ sheets can potentially be understood by considering the geometry of the drop.
  • Notably, ucritical and ustop differ with respect to surface tension.
  • Further research in both forced wetting and splashing is necessary before the role of surface tension in both processes can be understood.
  • Existing experiments [7] and a recent simulation [10] confirm that early during drop impact the contact line does in fact behave differently in the early and late stages of spreading.
  • Here, I showed that the threshold pressure is set by two distinct conditions: the air-dependent time of thin-sheet creation, and the air-independent threshold velocity ustop that is related to contact line stability.

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THE UNIVERSITY OF CHICAGO
THIN-SHEET CREATION AND THRESHOLD PRESSURES IN DROP SPLASHING
A DISSERTATION SUBMITTED TO
THE FACULTY OF THE DIVISION OF THE PHYSICAL SCIENCES
IN CANDIDACY FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
DEPARTMENT OF PHYSICS
BY
ANDRZEJ LATKA
CHICAGO, ILLINOIS
DECEMBER 2016

Copyright
c
2016 by Andrzej Latka
All Rights Reserved

To my mother, Maria Latka: I owe nobody more.
To my father, Miroslaw Latka: my role model for physics and life.
To my sister, Agnieszka Latka: my first and closest friend.
To my grandmother, Maria Latka: the strongest person I have ever known.
To my grandfather, Henryk Latka: for showing me how to be a man.
To my grandmother, Anna Lorenz: for the memories carried by the smell of the best apple
pie in the world.
To my grandfather, Roman Lorenz: for teaching me the importance of history.
To Nicholas Minutillo and his family: for becoming my American family.
To Michal Niewiara, a brother.
To Ryszard Chytrowski: for everything.
With all my love to Agnieszka Wergieluk: for making me a better physicist than I would
have been and for making me a happier person than I ever thought I could be.

TABLE OF CONTENTS
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 EXPERIMENTAL DETAILS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3 TIME OF THIN-SHEET CREATION . . . . . . . . . . . . . . . . . . . . . . . . 6
4 THRESHOLD VELOCITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
5 DISCUSSION AND CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . 22
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
iv

LIST OF FIGURES
1.1 Images of a splashing drop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3.1 Time of thin-sheet creation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.2 Interference imaging of sheet creation . . . . . . . . . . . . . . . . . . . . . . . . 8
3.3 Drop shape at time of thin-sheet creation . . . . . . . . . . . . . . . . . . . . . . 9
3.4 Diagram of drop impact outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.5 Threshold pressures of small-r
and large-r
sheets . . . . . . . . . . . . . . . . 12
4.1 Plot of u
sheet
and u
stop
vs. pressure . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.2 Effect of changing the ambient gas . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.3 Threshold velocity u
stop
vs. liquid viscosity . . . . . . . . . . . . . . . . . . . . 19
4.4 Threshold velocity u
stop
vs. impact velocity . . . . . . . . . . . . . . . . . . . . 20
v

Figures (10)
Citations
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Journal ArticleDOI
Abstract: In this letter we study the splashing behaviour of droplets upon impact onto a variety of substrates with different wetting properties, ranging from hydrophilic to super-hydrophobic surfaces. In particular, we study the effects of the dynamic contact angle on splashing. The experimental approach uses high-speed imaging and image analysis to recover the apparent contact angle as a function of the spreading speed. Our results show that neither the Capillary number nor the so-called splashing parameter are appropriate to characterise the splashing behaviour under these circumstances. However, we show that the maximum dynamic advancing contact angle and the splashing ratio β adequately characterise the splashing behaviour.

38 citations


Journal ArticleDOI
Abstract: It is well known that rough surfaces trigger prompt splashing and suppress corona splashing on droplet impact. Upon water droplet impact, we experimentally found that a slightly rough substrate triggers corona splashing which is suppressed to prompt splashing by both further increase and further decrease of surface roughness. The nonmonotonic effect of surface roughness on corona splashing weakens with decreasing droplet surface tension. The threshold velocities for prompt splashing and corona splashing are quantified under different conditions including surface roughness, droplet diameter, and droplet surface tension. It is determined that slight roughness significantly enhances both prompt splashing and corona splashing of a water droplet, whereas it weakly affects low-surface-tension droplet splashing. Consistent with previous studies, high roughness triggers prompt splashing and suppresses corona splashing. Further experiments on droplet spreading propose that the mechanism of slight roughness enhanci...

33 citations


Journal ArticleDOI
Abstract: A liquid drop impacting a dry solid surface with sufficient kinetic energy will splash, breaking apart into numerous secondary droplets. This phenomenon shows many similarities to forced wetting, including the entrainment of air at the contact line. Because of these similarities and the fact that forced wetting has been shown to depend on the wetting properties of the surface, existing theories predict splashing to depend on wetting properties as well. However, using high-speed interference imaging, we observe that at high capillary numbers wetting properties have no effect on splashing for various liquid-surface combinations. Additionally, by fully resolving the Navier-Stokes equations at length and time scales inaccessible to experiments, we find that the shape and motion of the air-liquid interface at the contact line/edge of the droplet are independent of wettability. We use these findings to evaluate existing theories and to compare splashing with forced wetting.

32 citations


Journal ArticleDOI
05 Apr 2018-Langmuir
TL;DR: The contact line instabilities at relatively low The authors numbers ( They ∼ O(10)) observed in this study provide insight into the conventional understanding of hydrodynamic instabilities under drop impact which usually require They ≫ 10.
Abstract: Drop impact is fundamental to various natural and industrial processes such as rain-induced soil erosion and spray-coating technologies. The recent discovery of the role of air entrainment between the droplet and the impacting surface has produced numerous works, uncovering the unique physics that correlates the air film dynamics with the drop impact outcomes. In this study, we focus on the post-failure air entrainment dynamics for We numbers well below the splash threshold under different ambient pressures and elucidate the interfacial instabilities formed by air entrainment at the wetting front of impacting droplets on perfectly smooth, viscous films of constant thickness. A high-speed total internal reflection microscopy technique accounting for the Fresnel reflection at the drop-air interface allows for in situ measurements of an entrained air rim at the wetting front. The presence of an air rim is found to be a prerequisite to the interfacial instability which is formed when the capillary pressure in...

12 citations


Journal ArticleDOI
Abstract: This report investigates how different splashing mechanisms affect the oblique splash threshold of drops impacting a dry solid surface The splashing behaviors of water, ethanol, and a water/ethylene glycol solution are observed over a wide range of drop diameters (07 mm < D < 22 mm) and Weber numbers (10 < We < 1040), and several published models are tested in order to predict the thresholds between deposition, one-sided splashing, and two-sided splashing We found that the splash threshold of liquids that exhibit the corona splashing mechanism can be readily predicted by existing models However, for liquids such as water that exhibit prompt splashing, the oblique splash threshold is not successfully predicted by any presently established correlation Hence, our findings identify a critical knowledge gap in the drop impact field, since the behavior of water is of fundamental importance to countless engineering problems Finally, combining our own results with others reported in the literature, we address some contradictory reports about the influence of liquid viscosity on the splash threshold and demonstrate that the presence or lack of thin-sheet in different experiments could explain the contradictions present in the literature

10 citations


References
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Book ChapterDOI

[...]

01 Jan 2012

123,310 citations


Journal ArticleDOI
TL;DR: Experimental scaling relations support a model in which compressible effects in the gas are responsible for splashing in liquid solid impacts.
Abstract: The corona splash due to the impact of a liquid drop on a smooth dry substrate is investigated with high-speed photography. A striking phenomenon is observed: splashing can be completely suppressed by decreasing the pressure of the surrounding gas. The threshold pressure where a splash first occurs is measured as a function of the impact velocity and found to scale with the molecular weight of the gas and the viscosity of the liquid. Both experimental scaling relations support a model in which compressible effects in the gas are responsible for splashing in liquid solid impacts.

560 citations


Journal ArticleDOI
TL;DR: It is demonstrated that, neglecting intermolecular forces between the liquid and the solid, the liquid does not contact theSolid, and instead spreads on a very thin air film, which develops a high curvature and emits capillary waves.
Abstract: A high velocity impact between a liquid droplet and a solid surface produces a splash. Classical work traced the origin of the splash to a thin sheet of fluid ejected near the impact point. Mechanisms of sheet formation have heretofore relied on initial contact of the droplet and the surface. We demonstrate that, neglecting intermolecular forces between the liquid and the solid, the liquid does not contact the solid, and instead spreads on a very thin air film. The interface of the droplet develops a high curvature and emits capillary waves.

203 citations


Journal ArticleDOI
TL;DR: The derived equation, which expresses the splash threshold velocity as a function of the material properties of the two fluids involved, the drop radius, and the mean free path of the molecules composing the surrounding gaseous atmosphere is thoroughly validated experimentally at normal atmospheric conditions.
Abstract: Making use of experimental and theoretical considerations, in this Letter we deduce a criterion to determine the critical velocity for which a drop impacting a smooth dry surface either spreads over the substrate or disintegrates into smaller droplets. The derived equation, which expresses the splash threshold velocity as a function of the material properties of the two fluids involved, the drop radius, and the mean free path of the molecules composing the surrounding gaseous atmosphere, has been thoroughly validated experimentally at normal atmospheric conditions using eight different liquids with viscosities ranging from μ=3×10(-4) to μ=10(-2) Pa s, and interfacial tension coefficients varying between σ=17 and σ=72 mN m(-1). Our predictions are also in fair agreement with the measured critical speed of drops impacting in different gases at reduced pressures given by Xu et al. [Phys. Rev. Lett. 94, 184505 (2005).

185 citations


Journal ArticleDOI
TL;DR: The results show that the dynamics of impacting drops are much more complex than previously thought, with a rich array of unexpected phenomena that require rethinking classic paradigms.
Abstract: The commonly accepted description of drops impacting on a surface typically ignores the essential role of the air that is trapped between the impacting drop and the surface. Here we describe a new imaging modality that is sensitive to the behavior right at the surface. We show that a very thin film of air, only a few tens of nanometers thick, remains trapped between the falling drop and the surface as the drop spreads. The thin film of air serves to lubricate the drop enabling the fluid to skate on the air film laterally outward at surprisingly high velocities, consistent with theoretical predictions. Eventually this thin film of air breaks down as the fluid wets the surface via a spinodal-like mechanism. Our results show that the dynamics of impacting drops are much more complex than previously thought, with a rich array of unexpected phenomena that require rethinking classic paradigms.

184 citations