160 Liquid jet rebound upon impact on a soft gel

7/25/2019 160 Liquid jet rebound upon impact on a soft gel

1/5

Liquid jet rebound upon impact on a soft gel

Dan Daniel, Xi Yao, Michael Brenner, and Joanna Aizenberg

School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138(Dated: January 12, 2016)

A liquid jet can stably bounce off a sufficiently soft gel, by following the contour of the dimplecreated due to pressure upon impact. This phenomenon is relatively insensitive to the wettingproperties of the liquid and was observed for different liquids over a wide range of surface tensions,

= 24-72 mN/m. In contrast, other jet rebound phenomena are typically sensitive to : jet reboundoff a hard solid (e.g. superhydrophobic surface) or another liquid is possible only for high and low liquids respectively. This is because an air layer must exist between the two interfaces. For asoft gel, no air layer is necessary and jet rebound remains stable even when there is direct liquid-gelcontact.

The ability of surfaces to repel liquids, either in theform of droplets or jets, is of broad interests and hasnumerous applications [13]. The rebound of an imping-ing water droplet off a solid substrate, be it a superhy-drophic surface [46], a leidenfrost solid such as dry ice[7], or a soft substrate [8], is a well-known phenomenon;the equivalent rebound of liquid jet, on the other hand,

is relatively less-studied, despite the pervasiveness of liq-uid jets in various applications [9]. It was shown, onlyin recent years, that a water jet can stably bounce offa superhydrophobic surface with minimal energy loss ata low Weber number, We = RV2/ < 10, where ,R, V, are respectively the density, radius, velocityand viscosity of the jet [10]. In all the cases describedabove, the rebound of liquid droplet/jet is facilitatedby a cushion of air layer between liquid and solid, typi-cally with thickness in the range of 0.5 - 50 m. Whenthis air layer becomes unstable or disrupted, for exam-ple due to increased wettability of the solid or the pres-ence of dirt/defects along the interface, the rebound phe-nomenon is suppressed[1113].

The behavior of soft material in contact with a liquiddroplet has also been widely studied, but its interactionwith liquid jet is rarely so [1416]. In this letter, wedescribe the mechanism and stability of jet rebound asit impacts a soft gel. This stable rebound phenomenonis observed for liquid jets over a wide range of surfacetensions, = 24-72 mN/m, and intriguingly even whenthe gel contains the same liquid as the impinging jet,such as the case of a water jet (diameter D 1.0 mm,velocityV 1 m/s) bouncing off a gelatin gel that is 98.5wt% water (Fig. 1(a), see also Supplemental MaterialS1). The inset of Fig.1(a) shows a 10 L water dropletsitting on the gel with a contact angle of 16, i.e. the

gel is hydrophilic. The same rebound phenomenon wasobserved for other hydrogels, such as polyacrylamide, andalso for hydrophobic polydimethylsiloxane gels (PDMS,78-82 wt% silicone oil, contact angle of water = 905). Unlike superhydrophobic (SH) surface which losesits repellence for low liquid, the PDMS gel was able

[email protected]

to repel liquid jet with as low as 24 mN/m. Fig.1(b)illustrates this: soap-water jet (D = 0.3 mm, V 2m/s,= 30 mN/m) could bounce off the PDMS gel (78wt% silicone oil), but not the SH surface. The water

jet, in comparison, was repelled by both surfaces. Theinsets show 10 L droplets of either water or soap-watersitting on the corresponding surfaces. The SH surface

was a hexagonal array of micropores monolayer of size 1m, with static contact angle for water, = 150, andcontact angle hysteresis, = 10. Detailed methodsto fabricate the SH surface and PDMS gel are describedelsewhere [17, 18].

To avoid the complications of a hydrogel expand-ing/contracting due to absorption/evaporation of wa-ter, we chose to concentrate on jet rebound behavior onPDMS gels. Silicone oil is immiscible with water/ethanoland has a low vapour pressure 5 mm Hg. The Youngsmodulus, E, of a PDMS gel can also be varied easily byusing different wt% of silicone oil. In our experiment,we used 78, 80 and 82 wt% silicone oil gel to obtain E=

0.60.1, 1.50.3, 51 kPa respectively. The ratio (mass)of sylgard 184 PDMS base and curing agent was kept at1:1. For data presented below, the value of E for eachgel sample was measured individually using a rheome-ter. The PDMS gels used here behave mostly as elasticsolids; the viscous component can be safely ignored, sinceG/G 0.05, where G and G are the loss and elasticmoduli.

When a jet impacts a PDMS gel obliquely at an an-gle, i, and speed, V, a dimple of depth, h, and width,w, is formed on the gel (inset I, Fig. 2). The jet canthen follow the contour the dimple and bounce off atan angle r, while retaining its cylindrical shape. Aftertravelling a certain distance, the liquid jet then breaksup into droplets of size D, as well as satellite dropletsof size D, due to Plateau-Rayleigh instability (insetII, Fig.2, see also Supplemental Material S2). A similarmechanism - dimple formation, followed by rebound - hasbeen observed in the case of a liquid jet (Newtonian andnon-Newtonian) bouncing off a bath of the same liquid,but such rebound is only possible for low surface ten-sion liquids, where there is a stable air layer separatingthe liquid jet and bath [1922]. The existence of this airlayer is crucial for liquid-liquid rebound; without it, the

arXiv:1601.02065v

1

[physics.flu-dyn

]9Jan2016
mailto:[email protected]:[email protected]


2/5

2

liquid jet (e.g. water) simply merges with the liquid bath[2224].

In comparison, jet rebound off a soft gel does not re-quire an air layer; experimentally, no air layer was de-tected. For low liquids, such as ethanol solution (70wt%, = 24 mN/m), a three-phase contact line was al-ways observed where the jet exited the dimple, rulingout existance of a continuous air layer (See astericks, In-

set III, Fig. 2, see also Supplemental Material S3). Forwater jet, this three-phase contact line was not readilyobservable. However, we were able to confirm the ab-sence of the air layer by shining laser light into the thewater jet (See Supplemental Material S4 for more de-tails). If there were an air layer - as is the case for aliquid jet (e.g. silicone oil) bouncing off a liquid bath(Fig. 3(a)) - the liquid jet would act as an optical fiberand the laser light would remain inside the jet, followingits contour, due to total internal reflection. For water jetbouncing off a PDMS gel, however, the laser light passedthrough undeflected into the PDMS gel (Fig. 3(b)), rul-ing out the existance of an air layer. A small amount of

alumina particles and milk ( 0.05 wt% and 0.01 wt%respectively) was added to silicone oil and water jets toact as light scatterers so that the laser path inside the

jet could be visualized, with insignificant change to the

!"

$"

%&

%'()!*+

,-.%

/+0

1!2+( %3!4 5!2+(

-6789 ::

;+0!?@(3;+0

!A B87 ::

1!2+(

FIG. 1. (a) A water jet can bounce off a hydrophilic gelatingel that is 98.5 wt% water. The inset shows the resultingcontact angle of 16 for a 10L water droplet. (b) A softPDMS gel (E=1.2 kPa) can repel both water and soap water,while a superhydrophobic (SH) surface loses its liquid repel-lence for soap water. The corresponding contact angles of10 L water/soap-water droplets shown in the insets are (leftto right, top to bottom): 90, 30, 150, 60.

surface tension (measured < 0.2 mN/m).Intuitively, we should expect the rebound behavior

of jet to depend on the size and geometry of the dim-ple. For example, just to accommodate the jet, thereshould be a threshold dimple size hmin, wmin D, for

jetting to occur. For small dimple, (w/2)/h tan i,i.e. w 2h tan i. This is well-obeyed when w < 2 mmfor a wide range of experimental conditons (Fig. 4(a)).

Since this indentation is an elastic response to the pres-sure of water impact V2, we expect h/D to dependon V2

/E, where is the density of the liquid and V

is the perpendicular component of the jet speed, i.e.V cos i. Note that according to the Buckingham-Pi the-orem, there can only be two non-dimensionless groups,which we have chosen here to be h/D and V2

/E.

The raw data (Fig. 4(b)) shows thath is linearly pro-portional to flow rate Q, which suggests that the correctscaling should be h/D (V2

/E)1/2. This was verified

experimentally for liquid jets (water and 30 wt% ethanolsolution,=35 mN/m) withD = 0.29-1.1 mm impingingon PDMS gels of E = 0.6-5 kPa for i = 30-50

, and

flow rates,Q = 5-250 ml/min (Figs.4(b), (c)). The bestfit line, indicated by dashed blue line on Fig. 4(c), is therelationh/D = 1.25(V2

/E)1/2 . Gels of different Eare

differentiated by different marker colors (See legend inFig.4(a)), while data points with different shades of thesame color represent jet impinging on gels of similar Ebut at different i. hmin/D was found to be 1.4, belowwhich jet rebound becomes unstable (dashed black line,Figs.4(c), (d)).

There is some departure from the general trend h/D =1.25(V2

/E)1/2 for h > 2.0 mm (see purple and green

unfilled circles in Figs. 4(b), (c)), because h starts toapproach the thickness of the PDMS gel, which was kept

!#

I

$ ! #$% &&

!i

!r

% ' % &()

II

III

*

FIG. 2. The pressure of impacting jet creates a dimple ofdepth h and width w on the PDMS gel (Inset I), facilitat-ing jet rebound. Inset II shows the eventual break-up of jetinto droplets (Plateau-Rayleigh instability). Inset III showsthe presence of three-phase line at the exit point for 70 wt%EtOH, ruling out the existence of an air layer separating jetand gel.


3/5

3

!"#"$%&' )'* +%,&$"&- %.

/"#"$%&' +0*120*'3 )'* +%,&$"&- %.

456! -'#

07 +7

89+0*1:;< =>/

89?'*@ =>/

89?'*@ =>/

#"A,"B

#"A,"B

#"A,"B

C'#0"3

FIG. 3. (a) Laser light (red) followed the contour of the

silicone oil jet as it bounced off a silicone oil bath, becauseof a stable air layer that separated the two. (b) In contrast,there was no air layer separating water jet bouncing off aPDMS gel. Hence, the laser light passed through undeflectedinto the PDMS gel.

at 7.5 mm for all the experiments. For a given incidenti, the rebound angle r is simply a function of h/D(Fig.4(d)), and below h/D = 1.4 (dashed vertical line),r approaches 90

precipitiously, i.e. jet transitions frombouncing (inset I) to trailing (inset II). Upon landing onthe gel, the trailing jet initially moves in a straight linebefore starting to meander[25].

Looking at the data for 30 wt% ethanol solution(green diamonds), we see that does not affect dimple

size/shape and rebound direction. This is becauseh andw mm; The effect ofbecomes important only whenthe dimple size approaches the elasto-capillary length,|S|/E, where |S| is the spreading parameter [15, 26].Typically, |S| 10 mN/m, and for E 1 kPa, thislength 10 nm[27].

Finally, we would like to point out that many strategiesused in designing liquid-repellent surfaces, such as adding

roughness and infusing surface with lubricant [28, 29],can be applied to soft substrates to create surfaces thatcan repel liquid droplets and jets. To illustrate this, weswell a PDMS gel by placing it in a petri-dish of siliconeoil. After two days, the gel has absorbed some of the sil-icone oil, causing its weight to increase by 22%. There isalso now a silicone oil layer on top of the gel, resulting ina decrease in contact angle hysteresis, , from 30 to 5.The tilting angle for 30 L droplets (Fig. 5) has also de-creased from 20 to 4. The detailed mechanism for thisdroplet repellence has been described elsewhere [2830].Such surfaces have been used for numerous applications,including anti-icing and anti-fouling surface [3133].

In conclusion, we have shown that a liquid jet with awide range of = 24-72 mN/m can bounce off a softgel, by following the contour of the dimple formed uponimpact. The size and geometry of the dimple determine1) whether jetting is possible and 2) the direction of jet-ting. We have further shown that this jet rebound phe-nomenon is possible even when there is direct liquid-gelcontact. This is unlike other jet rebound phenomenawhich require a stable air layer separating the jet andthe substrate.

We wish to thank Kenneth Park for useful discussions.The work was supported partially by the ONR MURIAward No. N00014-12-1-0875 and by the Advanced Re-search Projects Agency-Energy (ARPA-E), U.S. Depart-

ment of Energy, under Award Number DEAR0000326.We acknowledge the use of the facilities at the HarvardCenter for Nanoscale Systems supported by the NSF un-der Award No. ECS-0335765.

[1] D. Quere, Rep. Prog. Phys. 68, 2495 (2005).[2] T.-S. Wong, T. Sun, L. Feng, and J. Aizenberg, MRS

Bulletin 38, 366 (2013).[3] X. J. Feng and L. Jiang, Adv. Mater. 18, 3063 (2006).[4] D. Richard, C. Clanet, and D. Quere, Nature 417, 811

(2002).

[5] J. C. Bird, R. Dhiman, H.-M. Kwon, and K. K. Varanasi,Nature 503, 385 (2013).

[6] Y. Liu, L. Moevius, X. Xu, T. Qian, J. M. Yeomans, andZ. Wang, Nature Phys. 10, 515 (2014).

[7] C. Antonini, I. Bernagozzi, S. Jung, D. Poulikakos, andM. Marengo,Phys. Rev. Lett. 111, 014501 (2013).

[8] L. Chen and Z. Li,Phys. Rev. E 82, 016308 (2010).[9] J. Eggers and E. Villermaux, Rep. Prog. Phys. 71, 036601

(2008).[10] F. Celestini, R. Kofman, X. Noblin, and M. Pellegrin,

Soft Matter 6, 5872 (2010).

[11] A. Yarin, Annu. Rev. Fluid Mech. 38, 159 (2006).[12] X. Deng, F. Schellenberger, P. Papadopoulos, D. Vollmer,

and H.-J. Butt, Langmuir 29, 7847 (2013).[13] J. Kolinski, L. Mahadevan, and S. Rubinstein, EPL108,

24001 (2014).[14] C. Extrand and Y. Kumagai, J. Colloid Interface Sci.

184, 191 (1996).[15] B. Roman and J. Bico, J. Phys.: Condens. Matter 22,

493101 (2010).[16] R. W. Style, Y. Che, S. J. Park, B. M. Weon, J. H. Je,

C. Hyland, G. K. German, M. P. Power, L. A. Wilen,J. S. Wettlaufer, and E. R. Dufresne,Proc. Natl. Acad.Sci. USA 110, 12541 (2013).

[17] N. Vogel, R. A. Belisle, B. Hatton, T.-S. Wong, andJ. Aizenberg, Nat. Commun. 4 (2013).

[18] Add Phils paper (2014).[19] A. Collyer and P. Fisher, Nature 261, 682 (1976).
http://dx.doi.org/%2010.1557/mrs.2013.99http://dx.doi.org/%2010.1557/mrs.2013.99http://dx.doi.org/%2010.1557/mrs.2013.99http://dx.doi.org/%2010.1557/mrs.2013.99http://dx.doi.org/10.1103/PhysRevLett.111.014501http://dx.doi.org/10.1103/PhysRevLett.111.014501http://dx.doi.org/10.1103/PhysRevLett.111.014501http://dx.doi.org/10.1103/PhysRevE.82.016308http://dx.doi.org/10.1103/PhysRevE.82.016308http://dx.doi.org/10.1103/PhysRevE.82.016308http://dx.doi.org/10.1073/pnas.1307122110http://dx.doi.org/10.1073/pnas.1307122110http://dx.doi.org/10.1073/pnas.1307122110http://dx.doi.org/10.1073/pnas.1307122110http://dx.doi.org/10.1073/pnas.1307122110http://dx.doi.org/10.1073/pnas.1307122110http://dx.doi.org/10.1103/PhysRevE.82.016308http://dx.doi.org/10.1103/PhysRevLett.111.014501http://dx.doi.org/%2010.1557/mrs.2013.99http://dx.doi.org/%2010.1557/mrs.2013.99


4/5

4

[20] M. Versluis, C. Blom, D. van der Meer, K. van der Weele,and D. Lohse, J. Stat. Mech. Theor. Exp. 2006, P07007(2006).

[21] S. Lee, E. Q. Li, J. O. Marston, A. Bonito, and S. T.Thoroddsen,Phys. Rev. E 87, 061001 (2013).

[22] M. Thrasher, S. Jung, Y. K. Pang, C.-P. Chuu, and H. L.Swinney,Phys. Rev. E 76, 056319 (2007).

[23] E. Lorenceau, D. Quere, and J. Eggers, Phys. Rev. Lett.93, 254501 (2004).

[24] N. Wadhwa, P. Vlachos, and S. Jung, Phys. Rev. Lett.110, 124502 (2013).

[25] N. Le Grand-Piteira, A. Daerr, and L. Limat, Phys. Rev.Lett. 96, 254503 (2006).

[26] P.-G. de Gennes, F. Brochard-Wyart, and D. Quere,Capillarity and wetting phenomena (Springer-Verlag,New York, 2008).

[27] C. Duez, C. Ybert, C. Clanet, and L. Bocquet,Phys.

Rev. Lett. 104, 084503 (2010).[28] T.-S. Wong, S. H. Kang, S. K. Tang, E. J. Smythe, B. D.

Hatton, A. Grinthal, and J. Aizenberg, Nature477, 443(2011).

[29] A. Lafuma and D. Quere, EPL 96, 56001 (2011).[30] J. D. Smith, R. Dhiman, S. Anand, E. Reza-Garduno,

R. E. Cohen, G. H. McKinley, and K. K. Varanasi, SoftMatter 9, 1772 (2013).

[31] P. Kim, T.-S. Wong, J. Alvarenga, M. J. Kreder, W. E.

Adorno-Martinez, and J. Aizenberg, ACS nano 6, 6569(2012).

[32] A. K. Epstein, T.-S. Wong, R. A. Belisle, E. M. Boggs,and J. Aizenberg, Proc. Natl. Acad. Sci. USA 109, 13182(2012).

[33] D. Daniel, M. N. Mankin, R. A. Belisle, T.-S. Wong, andJ. Aizenberg, Appl. Phys. Lett. 102, 231603 (2013).
http://dx.doi.org/%2010.1103/PhysRevE.87.061001http://dx.doi.org/%2010.1103/PhysRevE.87.061001http://dx.doi.org/%2010.1103/PhysRevE.87.061001http://dx.doi.org/%2010.1103/PhysRevE.76.056319http://dx.doi.org/%2010.1103/PhysRevE.76.056319http://dx.doi.org/%2010.1103/PhysRevE.76.056319http://dx.doi.org/%2010.1103/PhysRevLett.104.084503http://dx.doi.org/%2010.1103/PhysRevLett.104.084503http://dx.doi.org/%2010.1103/PhysRevLett.104.084503http://dx.doi.org/%2010.1103/PhysRevLett.104.084503http://dx.doi.org/%2010.1103/PhysRevLett.104.084503http://dx.doi.org/%2010.1103/PhysRevLett.104.084503http://dx.doi.org/%2010.1103/PhysRevE.76.056319http://dx.doi.org/%2010.1103/PhysRevE.87.061001


5/5

5

!" $"

%" &"

V2/E

'( )*$(+,&

i r

i r

r = 16

Ih/D = 3.5

h/D = 1II

r = 90

FIG. 4. (a) Dimple width,w , plotted against 2h tan i, where, h, is the dimple depth and, i, is the incident angle, for liquidjets withD = 0.29-1.1 mm impacting PDMS gels of youngs moduli, E= 0.6-1.5 kPa at flow rates Q = 5-250 ml/min. Theliquid used was water, except for data labeled with green diamonds, which were obtained for 30 wt% ethanol (surface tension,= 35 mN/m). (b)h increases with increasing flow rateQ, albeit at different rates depending on exact experimental conditions.

(c) The results in (b) can be collapsed into one curve, when h/D is plotted againstV2

/E, where is the density of the

liquid and V is the perpendicular component of the jet speed, i.e. V cos i. (d) The rebound angle, r, for a fixed i is afunction of the ratioh/D. The transition from a bouncing jet (inset I) to a trailing jet (inset II) occured at around h/D = 1.4.

!"# %&' ()*''&+ %&'

,-."/01+2 '1#&"

= 5

= 30

FIG. 5. shows 30L droplets on unswollen, dry (left) andswollen (right) PDMS gel at tilting angles of 20 and 4 re-spectively, just before they start to slide down. The contactangles hysteresis, , is determined from the droplet imagesto be 30 and 5 respectively.

Documents

160 Liquid jet rebound upon impact on a soft gel