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Advances in Space Research 41 (2008) 2089–2093

Effect of evaporation and solutocapillary-driven flow upon motionand resultant deposition of suspended particles in volatile

droplet on solid substrate

I. Ueno a,*, K. Kochiya b

a Department of Mechanical Engineering, Faculty of Science & Technology, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba 278-8510, Japanb Division of Mechanical Engineering, Graduate School of Science & Technology, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba 278-8510, Japan

Received 3 November 2006; received in revised form 29 August 2007; accepted 29 August 2007

Abstract

Particle motion in a volatile droplet on a solid surface, especially the behavior of particles depositing in the vicinity of a solid–liquid–gas boundary line (contact line) is focused. This phenomenon is called the ‘coffee stain problem’. Motion and deposition of the particlessuspended in distilled water droplets and distilled water–ethanol mixture droplets are discussed. The spatio-temporal particle motion isanalyzed by the three-dimensional particle tracking velocimetry (3D PTV). A discussion of the morphology of the particles stuck to thesolid surface after the dryout of the droplet is also given.� 2007 COSPAR. Published by Elsevier Ltd. All rights reserved.

Keywords: Droplet; Evaporation; Particle; Coffee stain problem; Solutocapillary effect

1. Introduction

Droplet with tiny solid particles sitting on a solid sub-strate is a common system in daily lives as well as industrialapplications; rain droplet with minerals on the window,water droplet on dishes after the washing, colloidal crystalgrowth process, inkjet printing applications, etc. It must bequite familiar with ring-like stains left on the solid wallsafter drying out the droplet. Particles in the droplet pinthe contact line on the substrate, and non-uniform distribu-tion of the particles is realized. This phenomenon is gener-ally called a ‘coffee stain problem’, as shown in Fig. 1.Deegan et al. (1997, 2000) indicated a capillary flowtowards the pinned contact line in the drying droplet,which forms a ring stains. On a view point of industrialapplications, to control the particle behavior and to realizea uniform particle distribution are of great importance.Especially in the fields of protein crystal growth, it is

0273-1177/$34.00 � 2007 COSPAR. Published by Elsevier Ltd. All rights rese

doi:10.1016/j.asr.2007.08.040

* Corresponding author.E-mail address: ich@rs.noda.tus.ac.jp (I. Ueno).

strongly desired to produce uniform two-dimensional crys-tals. There are a number of works on pattern formation bydepositing particles (e.g., Denkov et al., 1992; Deegan,2000). There exist few works, however, upon the dynamicparticle behaviors in evaporating droplet, because it istoo small to detect their behaviors and the volatile droplethas deformable surface.

The authors focus in the present study upon the spatio-temporal particle behavior in a volatile droplet. By apply-ing the three-dimensional particle tracking velocimetry(3D PTV) they track the wandering particles in the dropletof O (1 mm). Effect of solutocapillary-driven flow upon theparticle behavior and resultant deposition of the particlesafter the dryout are discussed.

2. Experiments

Side and front views of the experimental apparatus areshown in Fig. 2. A droplet with and without particleswas set upon a solid plate of Pyrex� glass. The droplet vol-ume was varied from 1 to 8 mm3. The surface temperature

rved.

Fig. 2. Experimental apparatus: side view (left) and front view.

Fig. 1. Typical example of the ‘coffee stain’ on the solid substrate.

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of the substrate was controlled in a range of 20–60 �C byPeltier element fixed the backside of the plate. The surfacetemperature was measured by Al–Cr thermocouples of50 lm in diameter. The fluctuation of the temperaturewas kept less than ±0.2 K. Distilled water and ethanol–water binary mixture were employed as test fluids. Twomajor series of experiments were conducted; droplet sittingon the plate (i) in an open system and (ii) with a closed ves-sel around the droplet to control the evaporation of the testfluid. All experiments were carried out under an atmo-spheric pressure condition.

In the series of experiments with 3D PTV, Ag-coatedhollow spherical glass particles of 10 lm in diameter wereused as tracer particles. The particle motion in the fluidwas observed through a cubic splitter fixed beneath theplate. This observation system led a simultaneous captureof the particle motion by two CCD cameras (768 · 493 pix-els) in avoiding any influences of refraction by temporallydeforming free surface of the fluid on the glass plate. Theparticle images were captured at 30 fps with a shutter speedof 1/250 s. Particle motions in successively captured 2Dimages by each CCD camera were tracked by applyingthe triple pattern-matching algorithm provided by Nishinoand Torii (1993). Three-dimensional velocity field of theparticles was reconstructed by the results of the particletracking process with camera parameters, which wereobtained by the camera calibration procedure. Details ofthe procedures for the camera calibration and the recon-struction procedures of 3D particle motions were describedin Nishimura et al. (2005). The entire flow field in the drop-let was illuminated from above by continuous light sources.

Thus the captured views corresponded to the integratedfields in the direction of the droplet height.

In addition, the authors observed a morphological pat-tern by the deposited particles after the dryout of the drop-let. In this series of experiments, distilled water withorganic particles, and its mixture with ethanol wereemployed as another test system for the sake of more clearvisualization. A base of the test fluid is obtained by adding25 g organic powder to distilled water of 200 ml. Then thisbase fluid is thinned by adding water or ethanol. The vol-ume ratio of the base fluid to additional one is fixed as 6to 4. Pattern indicated in Fig. 1 was obtained from this ser-ies of experiments.

3. Results and discussion

Typical examples of pattern formation in the drieddroplet with organic particles are indicated in Fig. 3. Thisfigure consists of the results in the case of (a) distilled waterand (b) ethanol–water mixture (concentration of the etha-nol is of 30 wt%) droplets of 4 mm3. The substrate temper-ature is 20 �C. In the case of distilled water, one would havering-like thick deposition of the particles at the periphery.Width of the ring-like deposition is about 0.4 mm. In thedrying process, cracks at the almost constant intervalemerge on the ring region. In the case of ethanol–watermixture, on the other hand, the particles distribute almostuniformly; one cannot detect any ring-like thick depositionnear the periphery. The variation of the maximum outerperiphery of the droplet of 4 mm3 in the evaporating pro-cess is presented in Fig. 4. In this figure the variation ofthe distilled water droplet without any particles is also plot-ted. One can clearly see that the distilled water dropletwithout any particles keeps it is maximum size for a while,and abruptly shrinks after a while of sitting on the sub-strate, then finally disappears. On the contrary, the diame-ter of the maximum periphery of the droplet with particleskeeps its value at almost constant after the dryout. Notedthat the averaged diameter of the maximum periphery ofthe droplet with solutocapillary effect (distilled water–etha-nol mixture with particle case) is smaller comparing to thatof the droplet of distilled water with particles. This can beexplained by considering the net flow direction inside thedroplet. The detailed discussion is given in Figs. 5 and 6.

These different manners of particle distribution areexplained by considering the particle motion in the evapo-

Fig. 3. Pattern of the deposited particles after the dryout of the droplet. (a) Water droplet and (b) ethanol–water droplet. Scale bar in the both frames:1.0 mm.

Fig. 4. Progress of the averaged diameter of the drying droplet periphery.The diameter variations of the droplet of distilled water with organicparticles (named as tf2 in this figure), the one of distilled water–ethanolmixture with organic particles (tf2 + ethanol), and the other of distilledwater without any particles (tf1) are plotted.

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rating droplet. Now typical examples of particle behaviorsin the evaporating process of the droplet are presented in

Fig. 5. Typical example of reconstructed paths of different particles at differentand dashed line indicates the perimeter of the droplet. The droplet sits in thereconstruction period is for 9.5 s for both cases. Dashed arrows indicate the inimages.

Fig. 5 in the case of (a) distilled water and (b) ethanol–water mixture (concentration of the ethanol is of 30 wt%)droplets of 4 mm3. Both results were detected in an opensystem. The x–z plain corresponds to the surface of theplate on which the droplet sits. Dashed line indicates theperiphery of the droplet. The initial positions of the parti-cles when the image recording starts are pointed by dashedarrows in this figure and in following ones; the particles arelocated almost at 1.5 mm from the center of the dropletand at 0.6 mm in height for all cases in this figure. In thiscase the authors start obtaining the particle images at30 s after setting the droplet on the substrate. At this stagethe contact line of the droplet is already pinned by the par-ticles initially located closed to the contact line.

In Fig. 5(a) the authors track four different particles for9.5 s. All particles are aiming at the periphery of the dropletboundary at almost the same velocity. Averaged velocity isof 0.15 mm/s. As Deegan et al. (1997) reported there existsan outward convective motion due to the relatively higherevaporation rate around the pinned contact line. In theobservation period, all particles are stuck in the vicinityof the contact line. Through the present reconstruction of

initial locations. The x–z plain corresponds to the surface of the substrate,region of y > 0. (a) Water and (b) ethanol–water mixture droplets. The

itial positions of the particles when the authors start to obtain the particle

Fig. 6. Another example of particle motion in ethanol–water mixture droplet. The x–z plain corresponds to the surface of the substrate, and dashed lineindicates the perimeter of the droplet. (a) Whole view of the drying droplet and (b) zoomed view from a different observation angle in the vicinity of thecontact line where particle 2–4 travel. The reconstruction period is for 7.3 s for the particle 1, and for 5.0 s for other particles. Dashed arrows indicate theinitial positions of the particles as in Fig. 4.

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the particle motion inside the droplet, one can see that theparticles meander towards the contact line. The authorshave never found a clear condition of occurrence for thismeandering travel; it is surely found that the meanderingmotion disappears if the droplet is confined in a closed ves-sel. In the open system, on the other hand, this motion israndomly observed and is never predicted at any tempera-ture in the range of the present experimental conditions.The authors have also tried a semi-open systems; the drop-let is covered with opened cylinders with different size. Themeandering is also observed, but not regularly. Theauthors will continue the experiments to describe thisbehavior in a different opportunity.

In the case of ethanol–water mixture as shown inFig. 5(b), on the other hand, the particle never goestowards the contact line. At a very early stage of the dryingthe contact line is pinned by particles initially locatedaround the periphery. Once the contact line is pinned, therest of particles in the droplet mainly wander in the wholeregion of the droplet. In this figure a single particle istracked for 9.5 s. The x–z plain also corresponds to the sur-face of the main plate. Projected path of the particle is alsoplotted on the x–z plane for a help to understand its three-dimensional behavior in the droplet. The dashed line anddashed arrow also indicate the pinned contact line of thedroplet and the initial position of the particle when therecording of the particle images is started, respectively. Cir-cle marks are plotted on the particle trajectory with a con-stant time interval of 0.5 s to grasp a variation of theparticle velocity in its motion. Higher evaporation rateleads solutocapillary effect over the droplet free surface,and leads a vigorous convective motion of the fluid insidethe droplet. The averaged velocity is of 1.2 mm/s. Duringthe observation period the particle is never stuck in thevicinity of the contact line, and keep wandering in thedroplet, but descent in the middle region of the droplet.

Another example of the reconstruction of the particlebehavior is shown in Fig. 6. The authors start accumula-tion of the particle images at 40 s after setting of the dropletin this case. In this figure one has four particles; one islocated almost at the center of the droplet and the othersin the vicinity of pinned contact line (the opposite sidewhere the boundary line is drawn with the dashed line).The particle initially located at the center region wandersin a whole region, and is seldom stuck to the periphery dur-ing the observation period. The averaged velocity of wan-dering is about 1.6 mm/s. Once the particle flows alongthe contact line, it never flows towards the central regionof the droplet, but sweeps back-and-forth near the contactline at about 0.5 mm/s. Even the particles travel near thecontact line, they seldom decelerate to descend to theperiphery. In the binary mixture droplet case there mustbe an outward convective motion because the significantevaporation of the test fluid takes place in the vicinity ofthe contact line as in the water case. At the same time,the evaporation of the alcohol leads a non-uniform distri-bution of the alcohol concentration over the surface. Evenslight difference of the ethanol concentration over the freesurface of the droplet drives a fluid, which results in a com-plex flow all over the droplet. This complex convectivemotion results in almost uniform distribution of the depos-ited particles in the dried droplet as shown in Fig. 3(b). Inaddition, the difference of the convective motion inside thedroplet causes the difference of the averaged diameter ofthe maximum outer periphery as shown in Fig. 4. The out-ward flow dominates the convective motion inside thedroplet in the case of distilled water with particles, thusthe droplet tends to expand its area on the substrate com-paring to the droplet with solutocapillary effect.

Further research is surely needed to understand andcontrol the behavior of the particles suspended in thedroplet with solutocapillary effect. Such complex flow is

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driven by non-uniform distribution of the alcohol in thedroplet through the drying process of the droplet asaforementioned; the authors have never succeeded inmeasuring spatio-temporal distribution of the alcoholconcentration over the free surface. In addition, non-uni-form evaporation ratio of alcohol over the free surfacemight lead non-uniform distribution of temperature,which would result in the thermocapillary effect. It wouldbe needed to carry out numerical simulation takingaccount of evaporation, solutocapillary and thermocapil-lary effects for comprehensive knowledge on the convec-tive motion inside the volatile droplet. One needs tohandle interactions among the particle, suspension liquidand solid substrate to discuss the particle behavior andresultant distribution on the substrate.

4. Concluding remarks

Spatio-temporal particle motion in the flow field of theevaporating droplet of O (1 mm) in diameter is focused.Droplet with or without the solutocapillary effect is exam-ined. The particle behavior is reconstructed by applying thethree-dimensional particle tracking velocimetry (3D PTV).In the case of without the solutocapillary effect, the parti-cles flow towards the pinned contact line of the dropletas Deegan et al. (1997) indicated. The evaporation of thetest fluid results in a meandering motion of the particle.With the solutocapillary effect, on the other hand, the par-ticles wander in a whole droplet, and are seldom sucked tothe region of the pinned contact line.

Acknowledgments

The authors gratefully acknowledge Prof. Koichi Nishi-no (Yokohama Nat’l University), Prof. Hiroshi Kawamura(Tokyo University of Science) and Miss Yukiko Abe fortheir invaluable cooperation for carrying out 3D PTVexperiments. A part of the present study was financiallysupported by The Futaba Electronics Memorial Founda-tions. The author I.U. acknowledges Prof. Costas P. Grig-oropoulos and Dr. Seung Hwan Ko (University ofCalifornia, Berkeley) for inspiring to start this project.

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Deegan, R.D., Bakajin, O., Dupont, T.F., Huber, G., Nagel, S.R., Witten,T.A. Contact line deposits in an evaporating drop. Phys. Rev. E 62,756–765, 2000.

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