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Tuning the Receding Contact Angle on Hydrogels byAddition of Particles

François Boulogne, François Ingremeau, Laurent Limat, Howard A. Stone

To cite this version:François Boulogne, François Ingremeau, Laurent Limat, Howard A. Stone. Tuning the RecedingContact Angle on Hydrogels by Addition of Particles. Langmuir, American Chemical Society, 2016,32 (22), pp.5573-5579. �10.1021/acs.langmuir.6b01209�. �hal-01629084�

Tuning the receding contact angle on hydrogels by addition of particles

Francois Boulogne1,2, Francois Ingremeau1,3, Laurent Limat2, and Howard A. Stone1

1Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ08544, USA

2Laboratoire Matiere et Systemes Complexes (MSC), UMR 7057 CNRS, Universite ParisDiderot, Batiment Condorcet, 10 rue Alice Domon et Leonie Duquet, Paris, France

3LIPhy, CNRS, and Universite Grenoble Alpes, 140 Rue de la Physique, 38402Saint-Martin-d’Heres, France

May 24, 2016

Abstract

Control of the swelling, chemical functionalization, and adhesivity of hydrogels are finding new applications ina wide range of material systems. We investigate experimentally the effect of adsorbed particles on hydrogels onthe depinning of contact lines. In our experiments, a water drop containing polystyrene microspheres is depositedon a swelling hydrogel, which leads to the drop absorption and particle deposition. Two regimes are observed: adecreasing drop height with a pinned contact line followed by a receding contact line. We show that increasing theparticles concentration increases the duration of the first regime and significantly decreases the total absorptiontime. The adsorbed particles increase the pinning force at the contact line. Finally, we develop a method tomeasure the receding contact angle with the consideration of the hydrogel swelling.

1 Introduction

Hydrogels are promising materials for numerous appli-cations such as superabsorbant materials, soft contactlenses [1, 2], drug delivery systems [3], human implantsor tissue engineering [4]. The control of interfacial prop-erties represents a major breakthrough in technologicalinnovations with a particular focus on the control ofroughness, adhesion [5], friction [6], wetting [2] or opticalproperties. However, it is challenging to control theseinterfacial characteristics due to the complexity of thephysical and chemical properties of hydrogels. Amongthe possibilities to control these properties, some tech-niques consist in grafting polymers at the gel surface soas to control adhesion properties [7, 8] or in patterningthe surface to tune the adhesion [9].

In the literature on colloidal deposition, it is well-known that particles can pin a contact line [10, 11, 12,13]. Thus, synthetic textured surfaces have been de-signed to achieve control of the roughness and to studycontact angle hysteresis [14, 15, 16, 17]. The effect of de-fects on a receding contact line has been studied theoret-ically [18, 19, 20, 21, 22, 23] and observed experimentally[24, 25, 26, 27, 28, 29]; see [30, 31] for reviews.

Surprisingly, despite the fact that hydrogels contain alarge quantity of water, a water drop deposited on itssurface has a non-zero contact angle. This effect is dueto the free polymer chains, which are present at the gelinterface and pin the contact line [32]. Therefore, to

tune the wetting properties of hydrogels, we propose toinvestigate the functionalization of gel interfaces by thedeposition of particles.

Previously, we have studied hydrogels, which swell fol-lowing the absorption of a water drop containing a di-lute suspension of micron-size particles [33]. Unlike theso-called coffee stain effect observed during the evapo-ration of such drops on non-porous substrate, we haveshown that the absorption leads to a nearly uniform de-position of particles. In our earlier study, we highlightedthat the final deposition is the result of a combinationof two successive regimes: a pinned contact line followedby a receding contact line as the absorption proceeds.We argued and observed that solvent absorption into thehydrogel occurs with a nearly homogeneous flux that de-cays as t−1/2 for most of the absorbing surface. Thelarger flux observed near the contact line brings moreparticles to the drop edge during the pinned contact lineregime. However, the second regime of the time depen-dent dynamics populates the center of the wetting areamore than the edge, which finally erases the larger con-centration at the drop edge.

In this paper, we show that a higher particle concen-tration leads to a stronger pinning of the contact line, i.e.a smaller depinning contact angle. As a result, it delaysthe transition between the two regimes and it affects thefinal deposition morphology. Moreover, we quantify thiseffect, by measuring the liquid-gel contact angle with anovel method based on the detection of the hydrogel in-

1

~J z

r

R ≈ 1.1 mm

Psat

3 mm

Figure 1: Experimental setup. A drop is dispensed on anabsorbing hydrogel in an environment saturated in vaporto prevent evaporation. The light green area shows thetypical swelling front [33].

terface on which particles are adsorbed. We rationalizeour findings with the literature related to the pinning ofa contact line on surfaces containing defects.

2 Experimental details

Our experiments consist in a colloidal drop containingmicron-size particles, dispensed on a swelling hydrogel(figure 1). We made a fully closed glass cell constitutedof two concentric compartments. The gel is placed in thecenter and is surrounded by a reservoir of water. There-fore, the environment is maintained at a relative humid-ity of 100% to prevent evaporation of the drop and thehydrogel.

2.1 Hydrogels

Absorbing substrates are made of polydimethyl acry-lamide (PDMA) hydrogel [34]. We denote mmono themass of monomer (N,N-dimethylacrylamide) and mw

the mass of water. In addition, [MBA] and [mono]are, respectively, molar concentrations of the crosslinker(N,N’-methylene-bis-acrylamide) and the monomer. Thecomposition of the gel is set by mmono/(mmono +mw) = 0.15 and [MBA]/[mono] = 2%. The quan-tity of initiator (potassium persulfate and N,N,N’,N’-tetramethylethylenediamine) is set to a molar ratio of0.01 of the monomer quantity. All chemicals are pur-chased from Sigma-Aldrich, USA. The solution is pouredin a mold made of two glass plates (75 × 50 cm2, DowCorning) separated with a rubber spacer of 3 mm thick-ness (McMaster-Carr). Hydrogels are stored in a vaporsaturated environment and they are used three days afterpreparation.

2.2 Colloidal drop

Colloidal suspensions consist of hydrophilic fluorescentparticles of 2a = 1 µm diameter (Lifetechnologies, Or-ange with absorption/emission wavelengths at 540/560nm) purchased as an aqueous suspension containing 0.02% thimerosal. The suspension is diluted with deionizedwater at a concentrations Cp from 2×106 to 1×109 par-ticles/ml, which corresponds to a volume fraction range

of [9× 10−6, 4× 10−3]. In all experiments reported here,the drop volume is 0.8 µl. For complementary investiga-tions (see the appendix), we used hydrophilic fluorescentparticles of 2a = 0.2 µm diameter (Lifetechnologies, Or-ange (540/560 nm), 2 mM azide). Blended suspensionsof non-fluorescent and fluorescent particles were preparedby mixing polystyrene-carboxylated particles of 2a = 1µm diameter (Polysciences, Polybead carboxylate) withfluorescent particles of 2a = 1 µm diameter. The con-centration of fluorescent particles is set to 5 × 106 par-ticles/ml and the non-fluorescent particle concentrationsis adjusted to obtain a given final concentration.

2.3 Optical microscopy

Bright field and fluorescent images are captured witha Hamamatsu camera (Digital camera ORCA-Flash4.0C11440, 2048× 2048 pixels) mounted on an inverted mi-croscope (Leica DMI4000 B) with a 5× objective. Theacquisition is automated with the software Microman-ager [35].

To measure the gel interface position, we use a confo-cal microscope Leica TCS SP5 with a dry objective PLFluotar, 10×. The microscope is equipped with a trans-lation stage and a z-piezo stage.

3 Observations

3.1 Absorption regimes

For a drop deposited on an absorbing hydrogel, tworegimes can be distinguished, independently of the pres-ence or absence of particles [36]. During regime I, thecontact line is pinned, the drop has a constant radius Rand the drop height decreases in time. At the end ofthis regime, at t = tI , the contact line recedes (regimeII) toward the center of the wetting area until the dropvanishes at time t = tf .

The schematic illustrations in figure 2(a) depict thequalitative effect of the particle concentration on the tworegimes of drop dynamics. As the particle concentrationincreases, particles reinforce the pinning of the contactline already observed on bare hydrogels. Thus, the dura-tion tI of regime I increases, which allows more efficientabsorption of the drop solvent over a large surface area(figure 2(b)). When the contact line recedes, the areafor liquid absorption decreases. However, for larger par-ticle concentrations, the remaining volume of water inthe drop is smaller at t = tI and a shorter absorptiontime tf is observed, as reported also in figure 2(b).

For different particle concentrations Cp, at low parti-cle concentrations, typically Cp < 1 × 107 particles/ml,tI and tf are comparable to the values obtained for apure water drop of the same volume. At such low con-centrations, the particles weakly affect the transition ofregimes I and II. For a larger concentration, the duration

2

Regime I

Regime II

Low Cp High Cp(a)

102

103

104

106 107 108 109

(b)

t I,t f

(s)

Cp (particles/ml)

tItf

Figure 2: (a) Schematics illustrating the two regimes forlow and high particle concentrations. (b) Durations ofregime I, tI , and the total absorption time, tf , as a func-tion of the particle concentration Cp. The error barsrepresent the standard deviation.

of regime I increases while the total absorption time de-creases. For Cp > 2 × 108 particles/ml, the drop heightat t = tI is comparable to the particle size (figure 2(a)and SI Movie). Therefore, we observe tI ≈ tf .

3.2 Particle deposition

As the gel absorbs water, particles are carried toward thegel interface. In our experiments, we observed that theparticles are irreversibly absorbed on the gel, i.e. parti-cles are never resuspended once they are adsorbed evenwhen the contact line recedes. Thus, the final deposi-tion pattern depends on the absorption flux J(r, t) andon the transition between regimes I and II, which drivesthe wetting area where particles can be deposited [33].

The final deposition patterns for four different concen-trations ranging from Cp = 2 × 106 to 109 particles/mlare shown in figure 3(a). To quantify the effect of theparticle concentration on the particle deposition profile,we used mixtures of non-fluorescent and fluorescent par-ticles. In the fluorescent mode of the microscope, wedetect the individual positions of fluorescent particles.The blended suspension allows us to apply the same al-gorithm regarding the particle concentration. In figure3(b), we show the radial concentration profile obtainedfrom binning the deposit area in concentric rings of thesame areas. For a particle concentration of Cp = 107

particles/ml, we recover the profile obtained previously

[33], which shows a small decay along the radius. We ex-plained this profile from the combination of the particledeposition that occurs during regimes I and II. As theparticle concentration increases, the trend of absorbedparticle number density versus radii is inverted. A nearlyflat profile is observed for Cp = 108 particles/ml and alarger deposition is obtained near the contact line forCp = 109 particles/ml. Indeed, the radial profile is sim-ilar to the observation made at the end of the regime Ifor a low particle concentration [33]. Thus, for tI ≈ tf ,a peak at the drop edge is observed because of a largerabsorption flux near the contact line. However, for lowerconcentrations, additional particles are deposited whenthe contact line recedes for t > tI , which allows moreparticles to deposit in the center.

In the next sections, we rationalize the effect of theparticle concentration on the duration of the regime I,namely tI . In particular, we investigate how the parti-cle concentration affects the contact angle of the liquidon the hydrogel when the contact line depins. It is par-ticularly challenging to measure the liquid contact angleθliq(t) on the hydrogel because the substrate continu-ously deforms as the absorption proceeds. Also, directoptical methods are difficult to employ here for two rea-sons. First, the contrast of refractive index between thehydrogel and the drop is low, such that the position ofthe gel-liquid interface cannot be measured by methodsbased on refraction. Second, as we study the effect ofparticles, these particles may interfere with direct visu-alization. Thus, we developed another method relying onthe presence of particles to measure the gel-liquid inter-face position and, with further modeling, we obtain theliquid contact angle θliq(t) for any particle concentration.

4 Results and interpretation

4.1 Model for the contact angle dynam-ics

We now consider the change in the contact angles withthe notations presented in figure 4. We denote θcap theapparent contact angle of the liquid drop, which is de-fined as

θcap(t) = θliq(t) + θgel(t), (1)

where θliq is the angle between the gel and the liquid-vapor interface and θgel is the angle of the gel at thecontact line.

We now consider the time evolution of a spherical capvolume defined as Vcap = Vliq + Vgel where Vliq is theliquid volume during the regime I and Vgel is the swollenvolume of gel beneath the drop (figure 4). The drophas a radius R smaller than the capillary length `c =√γ/(ρ`g) ≈ 2.7 mm, where γ is the liquid-vapor surface

tension, ρ` is the liquid density and g is the gravity. Thus,the drop shape is approximated as a spherical cap, and

3

(a)

0.1 mm

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 0.2 0.4 0.6 0.8 1

(b)

N/N

tot

r/R

Cp = 107 particles/mlCp = 108 particles/mlCp = 109 particles/ml

Figure 3: (a) Final deposit for four initial concentrations(from the top right, in the clockwise order): Cp = 2×106,107, 108 and 109 particles/ml. Images are obtained byfluorescent microscopy. (b) Number of particles N non-dimensionalized by the total number Ntot as a functionof the radial position for three different concentrations.

θgel

θliqVcap

VliqVgel

hgel(r, t) hcl

Figure 4: Notations for the calculations including theeffect of the swelling of the gel on the liquid contact angle.The volume Vgel represents the volume of the swollen gelin the spherical cap drawn in black.

for small angles, we have

Vcap =πR3θcap

4= Vliq + Vgel. (2)

During regime I, we have shown previously that theflux J(r, t) of water from the drop to the gel is spatiallyhomogeneous in the center of the drop [33]. The flux islarger near the contact line but this deviation is localizedto 1/10 of the drop radius [33]. Therefore, we neglect thisdeviation and we consider the time evolution of the fluxas

J(t) ≈√Dδ√t, (3)

where D = 250 µm2/s is an effective diffusion coefficientand δ ≈ 0.18 is the swelling ratio. The swelling ratio is

defined as δ =V wsw

V totsw− V w

i

V toti

, where V wi and V wsw are, re-

spectively, the volumes of water in the initial and swollenstates, and V toti and V totsw are, respectively, the volumesof gel at the initial and swollen states. Thus, the timeevolution of the liquid volume Vliq during this regime is

Vliq(t) ≈ V0 − 2δS√Dt, (4)

where V0 is the initial volume and S = πR2 is the wettingarea. By combining equations (2) and (4) into equation(1), we obtain

θliq(t) ≈4

πR3

(V0 − 2πR2δ

√Dt+ Vgel(t)

)−θgel(t). (5)

Also, we remark that neglecting the swelling of the sub-strate is equivalent to set Vgel(t) = 0 and θgel(t) = 0 inequation (5), i.e.

θliq(t) ≈4

πR3

(V0 − 2πR2δ

√Dt). (6)

By inspection of equations (5) and (6), we can see that

the swelling correction Vgel(t) − πR3

4 θgel(t) included inequation (5) is the difference between the actual shapeof the gel and a spherical cap with the gels angle at thecontact line. In the next section, we present the mea-surements to obtain θgel(t) and Vgel(t) to compute θliq(t)from equation (5).

4.2 Measurement of θliq(t)

To estimate the quantities Vgel(t) and θgel(t), we firstmeasure the time evolution of the gel-liquid interface po-sition hgel(r, t); see figure 4. To describe the depinningtransition, we assume that the absorption dynamics isindependent of the particle concentration. This is a rea-sonable assumption since the highest concentration ofparticles leads to a deposit that covers around ≈ 20% ofthe surface. This deposit has a permeability very highcompare to the one of the hydrogel. Therefore, the par-ticles cannot apply a significant resistance to the flowand can be neglected when considering the absorption

4

0

20

40

60

80

100

120

140

0 0.2 0.4 0.6 0.8 1 1.2

t ↗

hgel(µ

m)

r (mm)

0

50

100

150

0 25 50 75 100hcl(µ

m)

t (min)

Figure 5: Time evolution of the gel interface positionhgel(r, t). The reference is the vertical position of thecontact line hcl(R, t), which is set to zero. Times rangefrom t = 2 min to t = 20 min, with a time incrementof 3 min. The inset shows the time evolution of thecontact line vertical position hcl(t). The vertical dashedline represents t = tI ≈ tf ≈ 20 min.

dynamic. Thus, the measurement of θliq(t) is also inde-pendent of Cp. Since tI increases with Cp, the measure-ment of θliq(t) for the largest concentration will provideθliq(tI).

To measure hgel(r, t) (see figure 4), we use a suspensionat a concentration Cp = 1 × 109 particles/ml. As someparticles are rapidly adsorbed at the gel interface, we usetheir fluorescence to detect the position of the interface.

With a confocal microscope, we take images in a ver-tical plane perpendicular to the gel surface by scanningalong the z direction with steps of 2.7 µm. Images aretaken along the drop radius with a resolution of 512 pix-els and with a width of 50 pixels. At this magnifica-tion, 512 pixels represent 1.5 mm (i.e. a resolution of3µm/px), which is larger than the drop radius R ≈ 1.1mm. The z-scan is repeated every 30 s.

For each picture, the sum of pixel intensities is calcu-lated in a sliding windows of (30×50) pixels moving alongthe radius with a step of 10 pixels (≈ 30 µm). Thus,we obtain an intensity i(r, z, t) for which the radial po-sition corresponds to the center of the sliding windows.For a given radial position ri and time ti, the intensityi(ri, z, ti) presents a maximum located at the gel-liquidinterface due to fluorescent particle adsorption. The po-sition of the maximum is determined from a fit with aLorentzian curve to achieve a subpixel precision. As a re-sult, we obtain the interface position of the gel hgel(r, t)reported in figure 5.

From figure 5, we use a trapezoidal method to cal-

culate the volume Vgel(t) = 2π∫ R0hgel(r, t) r dr and we

also calculate the gel angle θgel(t) from the tangent ofhgel(r, t) at the contact line. These values are reported

0

10

20

30

40

50

0 200 400 600 800 1000 1200 1400

θ(◦)

t (s)

θliq no swelling approxθliqθgel

θgel + θliq

Figure 6: Time evolution of the liquid contact angle θliqon the gel for data shown in figure 5. The solid linerepresents equation (6) where the swelling of the gel isneglected and the green points are given by equation (5)accounting for the gel swelling. Blue points represent thetime evolution of the gel angle θgel at the contact line andthe orange points, the sum θgel + θliq.

in figure 6 and shows only a small variation during ourobservations. The first minute of swelling is not availabledue to the time resolution of our experiment.

Then, with equation (5), we estimate θliq(t), which isgiven in figure 6. We also plot in figure 6, the estimateof θliq(t) from equation (6), which does that not accountfor the swelling effect. For a given volume of liquid, i.e. agiven time (see equation (4)), the contact angle is smallerdue to the inclined position of the gel interface. Never-theless, both curves have a similar trend and the correc-tion coming from the swelling of the hydrogel remainssmall.

4.3 Effect of the particle concentrationon the contact line depinning

In the literature on contact line hysteresis, it is commonto define the hysteresis H as the difference between theadvancing and the receding force that has been appliedon a contact line to trigger its motion. A clever measure-ment of this hysteresis has been provided by di Meglioand Quere for contact line motion on fibers [24]. For asurface covered with dilute defects, is has been showntheoretically [18, 19] and experimentally [37] that thehysteresis is proportional to the density of defects. Forlarger defect surface concentration Cs, numerical and ex-perimental studies [25, 38] indicate that the hysteresisgrows as C0.7

s .As we established the evolution of the liquid contact

angle θliq(t) on the hydrogel (figure 6), we can interpretthe durations of regime I that depends on the particleconcentration (figure 2(b)), as a critical receding contact

5

0.96

0.97

0.98

0.99

1

1.01

1.02

106 107 108 109

Saturation

cos(θ l

iq(t

I))

Cp (particles/ml)

0.96

0.98

1

1.02

108 109 1010 1011 1012

C0.7s

Cs (particles/m2)

Figure 7: The points represent cos(θliq(tI)) as a functionof the initial particle concentration Cp for 1 µm diam-eter particles. The error bars represent the uncertaintyreported from data presented in Figure 2(b). The solidline is a guide for the eye. The inset shows cos(θliq(tI))as a function of the defect surface concentration Cs cal-culated from equation (7). The solid line represents theequation cos(θliq(tI)) ∝ C0.7

s .

angle. Thus, using tI(Cp) from figure 2(b) and θliq(tI)from figure 6, we derive cos(θliq(tI)) at the receding timeas a function of the particle concentration Cp as repre-sented in figure 7.

For particle concentrations typically larger than 5 ×107 particles/ml, the direct particle identification andcounting is particularly difficult. To estimate the particlesurface concentration at time tI for all experiments, weconsider the absorbed volume of the drop 2δS

√DtI [33].Thus, the particle surface concentration adsorbed at thesurface at t = tI is

Cs = 2δ√DtICp. (7)

Our data shows that the hysteresis increases with theparticle concentration and then saturates for Cp > 2×108

particles/ml or for an average coverage of Cs ≈ 3× 1010

particles/m2. At this concentration, the particles apply asufficient force to maintain pinned the contact line duringthe entire absorption process. Furthermore, as suggestedby the experimental literature on solid surfaces, a power-law cos(θliq(tI)) ∝ C0.7

s also successfully describes ourresults.

Our observations are in agreement with the results ob-tained by Kajiya et al. [36] for pure liquid water drops.For very dilute suspensions, the critical liquid contact an-gle below which the contact line recedes is small. Never-theless, this angle is not zero and for our gels is θliq ≈ 14◦.The results presented in figure 7 shows that the presenceof micron size particles at the contact line allows us toreduce continuously this critical angle to zero.

5 Conclusion

In this paper, we studied the effect of the particle con-centration on the dynamics of a drop absorbed by aswelling hydrogel. The dynamics of a pure water dropis composed of a first regime where the contact line ispinned on the hydrogel and a second regime where thecontact line recedes. As the particle concentration in-creases, the duration of regime I increases. Since theabsorption area is larger during this first regime, thetotal absorption time decreases with the particle con-centration. For micron size particles, we observed thatabove a surface concentration of 2 × 1010 particles/m2,the contact line remains pinned throughout the entireabsorption process. To quantify the critical receding con-tact angle θliq(tI), we developed a method based on thedetection of the gel-water interface position. We haveshown that cos(θliq(tI)) ∝ C0.7

s , in agreement with theliterature related to the contact line hysteresis on solidsubstrates containing defects [25, 38] .

The results reported here illustrate that the additionof particles on the surface of a hydrogel modifies the re-ceding contact angle. In the situation of a colloidal dropabsorbed by the hydrogel, we have shown that the parti-cle surface concentration profile is modified by changingthe initial particle concentration. We related this effectto the variation of the receding contact angle due to theparticles adsorbed during the swelling process. In par-ticular, we found for our system that a concentrationof Cs ≈ 3 × 1010 particles/ml leads to an homogeneouscoating, while a lower concentration generates a largerdeposition in the center of the deposit.

These results extend our previous findings on the ho-mogeneous coatings of particles on hydrogels [33], whichcan be useful for the realization of functionalized in-terfaces of hydrogels. In terms of applications, thesequestions are particularly crucial for biomedical applica-tions such as soft contact lenses [1, 2], functional biogels[40, 41] or tissue engineering [5]. More generally, we be-lieve that adsorption of particles can inspire future stud-ies to tune the wetting properties of hydrogels. From thefundamental point of view, the field of solid capillarityraises important questions on the wetting of soft mate-rials, the role of soft solid interfaces and the importanceof physical and chemical properties [39].

Future work will be devoted to the importance ofchemical and physical properties of the particles on thefinal wetting properties. Indeed, we expect that the sizeof the defects as well as the hydrophilicity of the chemicalgroups grafted on the particles are significant. Since theexperiments described in this paper allows measurementof the pinning force caused by the defects, it is possible tocompare this force for different particle sizes or differentparticle surface chemistry. These measurements mightbe useful to predict how a deposit of particles changesthe spreading of water on a hydrogel surface.

6

102

103

104

106 107 108 109 1010

(a)t I,t f

(s)

Cp (particles/ml)

tItf

0.95

0.96

0.97

0.98

0.99

1

1.01

1.02

106 107 108 109 1010

(b)

cos(θ l

iq(t

I))

Cp (particles/ml)

0.940.960.98

11.02

108 109 1010 1011 1012 1013

C0.7s

Cs (particles/m2)

Figure 8: Data for 0.2 µm diameter particles. (a) Dura-tions of regime I, tI , and of the total absorption time tfas a function of the particle concentration Cp. (b) Thepoints represents cos(θliq(tI)) as a function of the ini-tial particle concentration Cp. The solid line is a guidefor the eye. The inset shows cos(θliq(tI)) as a func-tion of the defect surface concentration Cs calculatedfrom equation (7). The solid line represents the equa-tion cos(θliq(tI)) ∝ C0.7

s .

6 Appendix

In addition to the results presented in the main text,which are obtained for 1 µm diameter particles, we re-produced the experiments for 0.2 µm diameter particles.Figure 8 shows equivalent data to figures 2(b) and 7.Both plots show trends similar to the observations madefor 1 µm diameter particles. However, the particle con-centration must be increased by a factor ≈ 10 to obtaintI ≈ tf .

7 Acknowledgements

F.B. acknowledges that the research leading to theseresults received funding from the People Programme

(Marie Curie Actions) of the European Union’s SeventhFramework Programme (FP7/2007-2013) under REAgrant agreement 623541.

References

[1] F.J. Holly and M.F. Refojo. Wettability of hydrogelsI. Poly(2-hydroxyethyl methacrylate). J. of Biomed.Mater. Res., 9:315–326, 1975.

[2] H. Ketelson, D. Meadows, and R. Stone. Dynamicwettability properties of a soft contact lens hydro-gel. Colloids and Surfaces B: Biointerfaces, 40:1–9,2005.

[3] T. Hoare and D. Kohane. Hydrogels in drug de-livery: Progress and challenges. Polymer, 49:1993–2007, 2008.

[4] J. Hunt, R. Chen, T. van Veen, and N. Bryan.Hydrogels for tissue engineering and regenerativemedicine. J. Mater. Chem. B, 2:5319–5338, 2014.

[5] S. Rose, A. Prevoteau, P. Elziere, D. Hourdet,A. Marcellan, and L. Leibler. Nanoparticle solutionsas adhesives for gels and biological tissues. Nature,505:382–385, 2014.

[6] B. Stoimenov, V. Fridrici, P. Kapsa, H. Kosukegawa,and M. Ohta. Bioengineering materials and condi-tions for obtaining low friction with PVA hydrogels.Tribology Online, 8:140–152, 2013.

[7] M. Molina, C. Rivarola, M. Broglia, D. Acevedo,and C. Barbero. Smart surfaces: reversible switch-ing of a polymeric hydrogel topography. Soft Matter,8:307–310, 2012.

[8] G. Sudre, L. Olanier, Y. Tran, D. Hourdet, andC. Creton. Reversible adhesion between a hydro-gel and a polymer brush. Soft Matter, 8:8184–8193,2012.

[9] C. Poulard, F. Restagno, R. Weil, and L. Leger.Mechanical tuning of adhesion through micro-patterning of elastic surfaces. Soft Matter, 7:2543–2551, 2011.

[10] R. Deegan. Pattern formation in drying drops. Phys.Rev. E, 61:475–485, 2000.

[11] E. Rio, A. Daerr, F. Lequeux, and L. Limat. Movingcontact lines of a colloidal suspension in the presenceof drying. Langmuir, 22:3186–3191, 2006.

[12] H. Bodiguel, F. Doumenc, and B. Guerrier. Stick-slip patterning at low capillary numbers for an evap-orating colloidal suspension. Langmuir, 26:10758–10763, 2010.

7

[13] B. Weon and J. Je. Self-pinning by colloids confinedat a contact line. Phys. Rev. Lett., 110:028303, 2013.

[14] S.M.M Ramos, E. Charlaix, and A. Benyagoub.Contact angle hysteresis on nano-structured sur-faces. Surface Science, 540:355–362, 2003.

[15] D. Quere. Wetting and roughness. Annual Reviewof Materials Research, 38:71–99, 2008.

[16] P.H. Forsberg, C. Priest, M. Brinkmann, R. Sedev,and J. Ralston. Contact line pinning on microstruc-tured surfaces for liquids in the Wenzel state. Lang-muir, 26:860–865, 2010.

[17] A. Paxson and K. Varanasi. Self-similarity of con-tact line depinning from textured surfaces. NatCommun, 4:1492–, 2013.

[18] J.F. Joanny and P.G. de Gennes. A model for con-tact angle hysteresis. Journal of Chemical Physics,81:552–562, 1984.

[19] Y. Pomeau and J. Vannimenus. Contact angleon heterogeneous surfaces: Weak heterogeneities.Journal of Colloid and Interface Science, 104:477–488, 1985.

[20] A. Rosso and W. Krauth. Roughness at the depin-ning threshold for a long-range elastic string. Phys.Rev. E, 65:025101, 2002.

[21] S. Moulinet, A. Rosso, W. Krauth, and E. Rolley.Width distribution of contact lines on a disorderedsubstrate. Phys. Rev. E, 69:035103, 2004.

[22] P. Le Doussal, K.J. Wiese, S. Moulinet, and E. Rol-ley. Height fluctuations of a contact line: A directmeasurement of the renormalized disorder correla-tor. EPL, 87:56001, 2009.

[23] P. Le Doussal and K. Wiese. Elasticity of a contact-line and avalanche-size distribution at depinning.Phys. Rev. E, 82:011108, 2010.

[24] J.-M. di Meglio and D. Quere. Contact angle hys-teresis: a first analysis of the noise of the creepingmotion of the contact line. EPL, 11:163, 1990.

[25] J.-M. di Meglio. Contact angle hysteresis and inter-acting surface defects. EPL, 17:607, 1992.

[26] G.D. Nadkarni and S. Garoff. An investigation ofmicroscopic aspects of contact angle hysteresis: pin-ning of the contact line on a single defect. EPL,20:523, 1992.

[27] E.L. Decker and S. Garoff. Contact line structureand dynamics on surfaces with contact angle hys-teresis. Langmuir, 13:6321–6332, 1997.

[28] M. Reyssat and D. Quere. Contact angle hystere-sis generated by strong dilute defects. Journal ofPhysical Chemistry B, 113:3906–3909, 2009.

[29] M. Delmas, M. Monthioux, and T. Ondarcuhu. Con-tact angle hysteresis at the nanometer scale. Phys.Rev. Lett., 106:136102, 2011.

[30] P.-G. De Gennes. Wetting: statics and dynamics.Rev. Mod. Phys., 57:827–863, 1985.

[31] D. Bonn, J. Eggers, J. Indekeu, J. Meunier, andE. Rolley. Wetting and spreading. Rev. Mod. Phys.,81:739–805, 2009.

[32] M.A. Cohen Stuart, W.M. de Vos, and F.A.M. Leer-makers. Why surfaces modified by flexible polymersoften have a finite contact angle for good solvents.Langmuir, 22:1722–1728, 2006.

[33] F. Boulogne, F. Ingremeau, J. Dervaux, L. Limat,and H.A. Stone. Homogeneous deposition of parti-cles by absorption on hydrogels. EPL, 112:48004,2015.

[34] G. Sudre. Tunable Adhesion of Hydrogels. PhDthesis, Universite Pierre et Marie Curie - Paris VI,2011.

[35] A. Edelstein, N. Amodaj, K. Hoover, R. Vale, andN. Stuurman. Computer Control of Microscopes Us-ing Micromanager. John Wiley & Sons, Inc., 2010.

[36] T. Kajiya, A. Daerr, T. Narita, L. Royon,F. Lequeux, and L. Limat. Dynamics of the con-tact line in wetting and diffusing processes of wa-ter droplets on hydrogel (PamPs–PaaM) substrates.Soft Matter, 7:11425–11432, 2011.

[37] J.A. Marsh and A.M. Cazabat. Dynamics of contactline depinning from a single defect. Phys. Rev. Lett.,71:2433–2436, 1993.

[38] J. Crassous and E. Charlaix. Contact angle hys-teresis on a heterogeneous surface: solution in thelimit of a weakly distorted contact line. EPL, 28:415,1994.

[39] B. Andreotti, O. Baumchen, F. Boulogne, K. E.Daniels, E. R. Dufresne, H. Perrin, T. Salez, J. H.Snoeijer, and R. W. Style. Solid capillarity: Whenand how does surface tension deform soft solids?Soft Matter, 12:2993–2996, 2016.

[40] N. A. Peppas, Y. Huang, M. Torres-Lugo, J. H.Ward, , and J. Zhang. Physicochemical foundationsand structural design of hydrogels in medicine andbiology. Annual Review of Biomedical Engineering,2(1):9–29, 2000.

8

[41] D. Seliktar. Designing cell-compatible hydrogels forbiomedical applications. Science, 336(6085):1124–1128, 2012.

9