Deposition of Colloidal Drops Containing Ellipsoidal Particles

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Deposition of Colloidal Drops Containing Ellipsoidal Particles: Competition Between Capillary and Hydrodynamic Forces Dong-Ook Kim, Min Pack, Han Hu, Hyoungsoo Kim, and Ying Sun Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.6b03221 • Publication Date (Web): 27 Oct 2016 Downloaded from http://pubs.acs.org on November 1, 2016

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Deposition of Colloidal Drops Containing Ellipsoidal Particles: Competition Between Capillary and Hydrodynamic Forces

Dong-Ook Kim1, Min Pack1, Han Hu1, Hyoungsoo Kim2, and Ying Sun1,* 1

Department of Mechanical Engineering and Mechanics, Drexel University, Philadelphia, PA

2

Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ

ABSTRACT. Ellipsoidal particles have previously been shown to suppress the coffee-ring effect in millimeter-sized colloidal droplets. Compared to their spherical counterparts, ellipsoidal particles experience stronger adsorption energy to the drop surface where the anisotropy-induced deformation of the liquid-air interface leads to much greater capillary attractions between particles. Using inkjet-printed colloidal drops of varying drop size, particle concentration, and particle aspect ratio, the present work demonstrates how the suppression of the coffee-ring is not only a function of the particle anisotropy, but rather a competition between the propensity for particles to assemble at the drop surface via capillary interactions and the evaporation-driven particle motion to the contact line. For ellipsoidal particles on the drop surface, the capillary force ( Fγ ) increases with particle concentration and aspect ratio, while the hydrodynamic force ( Fµ ) increases with particle aspect ratio but decreases with drop size. When Fγ / Fµ > 1, the surface ellipsoids form a coherent network inhibiting their migration to the drop contact line and the coffee-ring effect is suppressed, whereas when Fγ / Fµ < 1, the ellipsoids move to the contact line resulting in coffee-ring deposition.

*

Corresponding author. Tel.: +1(215)895-1373; Fax: +1(215)895-1478; E-mail:[email protected]. 1

ACS Paragon Plus Environment

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1. Introduction Uneven depositions left behind by drying coffee drops or dish stains are common everyday phenomena familiar to everyone since they occur naturally. However, for industrial processes such as printing and coating technologies, the careful tuning of the deposition from colloidal drops is not only desirable, but a prerequisite for the final functional products.1,2 An evaporating colloidal drop with a pinned contact line induces an outward radial flow from the drop center to the edge causing particles to aggregate near the contact line promoting the well-known “coffeering effect”.3 Numerous methods have been proposed to suppress the coffee-ring effect by balancing the carrier liquid removal rate with the evaporation-driven particle motion,4,5 introducing Marangoni flows,6,7 or tuning the capillary interaction energy at the drop surface by changing the particle shape.8,9 Coffee-ring suppression was demonstrated using micrometer-sized polystyrene ellipsoids dispersed in single-solvent microliter droplets (millimeter drop diameter), where the anisotropyinduced deformations of the liquid-air interface led to particle aggregation on the drop surface as the inter-particle attraction forces are two orders of magnitude greater than those between spheres.10 Confocal microscopy images have shown that the depositions of spherical particles often form a multi-leveled thick ring at the contact line, whereas the deposition thickness of ellipsoids is rather uniform and thin due to the inter-particle locking at the drop surface.8,11 Many parameters may affect the deposition morphologies of ellipsoidal particles. While Yunker et al.8 have shown the influence of particle anisotropy on the suppression of the coffee ring by increasing the aspect ratio, volume fraction, and polydispersity of ellipsoidal particles, the effects of particle size, surface chemistry12,13, and carrier liquid properties (e.g., pH value14 and complex fluid mixture7) on particle deposition morphologies have also been recently demonstrated. In

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addition to the experimental studies, the capillary interactions between ellipsoids at the liquid-air interface15 have been modeled and simulated.16 Other anisotropic particles such as silica microrods have been used previously to create smectic and nematic orderings near the drop edge17. However, hydrophilic ellipsoids and rods cause fundamentally different capillary attractions, namely, ellipsoids cause a rise of the meniscus on the particle sides and a depression at the particle tips where the reverse is true for rods. Such interfacial deformations lead to strong capillary attractions that encourage tip-to-tip aggregation for rods and either tip-to-tip or side-toside aggregation for ellipsoidal particles depending on particle wettability and surface charge.9,17,18 For microliter drops previously used to study the coffee-ring suppression caused by ellipsoids,8 the evaporation time scale is much longer than the time for particles to self-assemble at the liquid-air interface via capillary interactions, finally leading to an even deposition. What if the evaporation time scale is curtailed? What is the relationship between the evaporation-driven and capillary interaction-induced particle motions in ellipsoidal particle-laden droplets? How does this competition between the hydrodynamic force acting on the particle and the interparticle capillary interactions affect the final deposition morphologies of ellipsoids? In this study, we aim to address these issues by directly observing the deposition process of inkjet-printed drops containing polystyrene prolate-spheroidal micro-particles dispersed in water and varying the droplet volume from pico- to nano-liters to control the hydrodynamic forces acting on the particles. The volume fraction and particle aspect ratio are also varied to examine the effect of the capillary interactions among ellipsoidal particles on the liquid-air interface. In addition, a model is developed that accounts for the ellipsoids near the liquid-air interface where the interparticle capillary ( Fγ ) to hydrodynamic ( Fµ ) force ratio dictates whether the particles are in a

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capillary-dominated regime, which leads to coffee-ring suppression, or in a hydrodynamicdominated regime, which drives the particles to deposit at the contact line.

2. Experimental Methods A custom-built inkjet printing setup, integrated with a synchronized flash photography system for side-view imaging and a fluorescence microscope for bottom-view observations, was used in our experiments, as shown in Figure 1(a). Pico-liter volume drops were generated by using a waveform generator (JetDrive) to signal a piezoelectric inkjet print-head with orifice diameters of 60 and 80 µm (MicroFab MJ-Al-01). To produce repeatable nano-liter volume drops with a drop diameter in the range of 0.3 - 1.2 mm, a custom-built drop generator was used, consisting of a piezoelectric disk (CUI CEB-35D26, diameter 35 mm), a fluid chamber (a cylinder of 28.6 mm diameter and 25.4 mm depth), a nozzle (Makerbot MK8), and an adjustableheight fluid reservoir. The drop diameter measurements for 20 droplets generated with the same operating parameters were within 0.2% for all drop sizes tested. Constant pressure in the nozzle was maintained by a pneumatic control device (MicroFab, Plano, Texas). A high resolution (0.5 µm per pixel) SensiCam QE CCD camera (Romulus, Michigan) with a Navitar 12x Zoom lens (Rochester, New York) and a halogen strobe light (Perkin Elmer) were used to capture the sideview images of drop deposition. The waveform generator, SensiCam CCD camera, and the strobe light were synchronized with a delay generator (SRS DG645, Sunnyvale, California). The custom-built XYZ stage controlled the location of the nozzle and an automated XY stage controlled the substrate location. Prolate ellipsoids were obtained by uniaxial stretching of spherical carboxylate-modified polystyrene particles (Invitrogen) 1 µm in diameter, essentially by following the method of Ho et

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al.19 To confirm that the fabrication of ellipsoids and treatment with polyvinyl alcohol (PVA) did not affect the particle surface properties, we performed a separate set of experiments by using polystyrene spherical particles that were treated by the same fabrication process as used for the ellipsoids but without any stretching. The resulting deposition patterns for these chemically treated spheres were the same as those without any treatment. The particle aspect ratio, defined as k = b/a (b is the semi-major axis and a is the semi-minor axis), was varied from 1 (sphere) to 6.5 (see Figure 1(b) and 1(d)). The colloidal suspensions of ellipsoids were diluted from volume fraction of 0.001 to 0.01 using deionized water. The substrates used in the experiments were glass microscope coverslips (Bellco, ∼150 µm thick). The substrates were initially cleaned by rinsing sequentially in acetone, ethanol, isopropyl alcohol, and deionized water; this process was repeated three times before finally rinsing the substrates three times with deionized water. All experiments were carried out at an ambient temperature of 22°C with the relative humidity of 40% inside a custom-built environmental chamber.

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Figure 1. (a) Schematic of the inkjet printing experimental setup. (b) Scanning electron microscopy images of polystyrene ellipsoidal particles of aspect ratio k = 6.5 and (c) spherical particles. (d) Schematics of the water contact angle ( θ ) on the ellipsoidal particle surface and the distance between the particle center of mass and the liquid-air interface (h) shown in a side-view depiction (left), as well as the semi-major axis b and semi-minor axis a of a prolate ellipsoid from a top view for an ellipsoid at the liquid-air interface (right).

During evaporation of the colloidal drops, the particle motion and deposition were observed by using a Zeiss inverted fluorescence microscope (Axio Observer A1) with a 40× oil objective. Bottom-view 8-bit grayscale images were captured by a Sony XCL-5005CR CCD camera (Park Ridge, New Jersey) at 10 frames per second. A scanning electron microscope (SEM, Zeiss Supra 50VP) and an optical profilometer (Zygo 7100) were used for the analysis of the particle

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deposition

morphologies.

The

LB-ADSA

drop

analysis

plugin

of

ImageJ

(http://rsbweb.nih.gov/ij/) was used to determine the contact angle of a sessile drop on a glass substrate. Moreover, ImageJ was used to plot the light intensity profile of the particle deposition from fluorescent images. An inverted confocal microscope (Olympus FV1000) was utilized to directly measure the distribution of ellipsoids during drop evaporation, where cross-sectional images starting from the glass slide (~0 µm) to ~30 µm into the droplet were taken in ~1.5 µm increments along the z-axis near the contact line of the droplet.

3. The Model In this section, a model is developed to predict the deposition morphology of a colloidal droplet containing ellipsoidal particles based on an analysis of the forces on the particles straddling the liquid-air interface of the drop. The following assumptions are made: i)

At the end of drop spreading, some ellipsoidal particles originally dispersed homogeneously dispersed in a drop are adsorbed to the liquid-air interface. During drop evaporation, a significant amount of ellipsoids continue to stay on the liquid-air interface.

ii) The particle motion is determined by two effects, i.e., the capillary forces between particles and hydrodynamic forces caused by evaporation-driven flow. iii) The contact line of the drop is pinned and the liquid-air interface of the drop is assumed to be a spherical cap. Gravitational effects are neglected during evaporation because the Bond number is Bo = ρ gd0 / γ < 0.2 , where ρ is the density of water, g is the gravitational 2

acceleration, d 0 is the drop in-flight diameter (see Figure 1(a)), and γ is the surface tension of water.

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iv) The evaporation process is assumed to be diffusion-limited where the drop surface is assumed to be in phase equilibrium.20 v)

Ellipsoidal particles have strong long-ranged attractions to each other and remain on the liquid-air interface.10 Once particles form clusters at the interface, these clusters are large enough to resist evaporation-driven flow so they do not move or break up. In order to justify assumption (i), the adsorption energy of colloidal particles at the liquid-air

interface is estimated. It has been shown previously that the adsorption energy of a hydrophilic ellipsoidal particle increases with aspect ratio when keeping particle volume constant.21 Assuming a planar liquid-air interface, the adsorption energy of a prolate spheroid with its semimajor axis parallel to the interface is expressed as21

E ad = 4πa 2 Gγ [

k (1 − h 2 ) + cos θ ⋅ Ap (h )] 4G

(1)

where h = h / a is the dimensionless height, h is the distance between the particle center of mass and the interface, θ is the water contact angle on the particle surface (see Figure 1(d)),

(

)

G = 1 / 2 + [ k / 2 1 − k − 2 sin −1 ( 1 − k − 2 )] is a geometrical correction factor of a prolate spheroid 1

( k ≥ 1), and AP (h ) = (k / πG ) ∫ [1 − (1 − h 2 )(1 − k −2 ) x 2 ](1 − h 2 ) tan −1[(1 / h ) (1 − h 2 )(1 − x 2 ) ]dx 0

is the areal fraction of the particle immersed in water. Based on Eq. (1), for a particle with a contact angle of 35°, the adsorption energy of an ellipsoidal particle with an aspect ratio of 6.5 is over 6 times that of a spherical particle of the same volume, indicating a much lower energy state of ellipsoids at the liquid-air interface and hence a relatively higher possibility of ellipsoids to be adsorbed to the drop surface. Once at the drop surface, an ellipsoidal particle deforms the liquidair interface, which in turn produces strong inter-particle capillary stresses15,22,23 that move ellipsoidal particles towards each other along the interface to minimize the surface excess

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energy. In the following, we focus on the interactions between ellipsoids on the liquid-air interface of a drop. Botto et al.18 extended the work of Stamou et al.24 for the capillary interaction energy between two neighboring ellipsoidal particles A and B on a fluid-fluid interface, following

12π H P2 rP4 EAB = −γ cos(2ϕ A + 2ϕ B ) Lm4

(2)

where H P is the amplitude of the interface distortion along the particle surface, rP is the effective particle radius and rP = ak 1 / 3 for prolate ellipsoids, Lm is the center-to-center distance between the two particles, and ϕ A and ϕ B are the angles between the centerline linking two particles and the semi-major axes of particles A and B, respectively. Assuming homogeneously dispersed particles, Lm = ( 4πrP 3 / 3φ )1 / 3 where φ is the initial volume fraction of particles in the drop. For ellipsoidal particles, stretched from spherical polystyrene particles of 1 µm in diameter, on a liquid-air interface, Loudet et al.23 experimentally estimated the interface distortion Hp ≈ 25, 45, and 55 nm for micrometer-sized ellipsoids of aspect ratio 1.8, 3.5, and 6.5, respectively. For a given value of the inter-particle distance Lm , the capillary interaction energy EAB is minimized when ϕA = −ϕB , for quadrupoles arranged in any mirror-symmetric configuration regardless of particular angles. The force due to capillary attraction between two mirror-symmetric particles is hence given by

∂E 48πH P rP Fγ = − AB = γ 5 ∂Lm Lm 2

where Fγ ~ Lm

−5

4

(3)

and this scaling has been confirmed by experiments using ellipsoidal15 and

cylindrical25 particles. Equation (3) indicates that, when fixing the particle size, particle

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wettability, and liquid surface tension, the inter-particle capillary force ( Fγ ) depends on the particle volume fraction ( φ ) and aspect ratio ( k ). Meanwhile, stationary ellipsoidal particles at the liquid-air interface also experience hydrodynamic forces due to evaporation-driven flow inside the drop and this hydrodynamic force may be approximated using the following shape-corrected Stokes formula26  6πµν a, k =1  r Fµ ≈   6πµν r aK ′, k ≠ 1

(4)

where µ is the dynamic viscosity of water, ν r is the radial velocity of the evaporation-driven outward flow on the drop surface, and K ′ is a shape-dependent correction factor given by

(

) {

K ′ = 8 k 2 −1 / 3 (2k 2 − 3) / (k 2 −1)1/2  ln k + (k 2 −1)1/2  + k

}

for

prolate

spheroids

aligned

preferentially side-by-side as observed in our experiments as well as others27; K ′ increases with the particle aspect ratio k. We note that the approximation symbol in Eq. (4) is caused by only a fraction of the ellipsoid being submerged in water. For an evaporating colloidal drop with a pinned contact line, particles are advected by the fluid flow inside the drop mainly due to the non-uniform evaporative flux along the drop surface. Following the Hu−Larson model28, the initial radial velocity of the evaporation-driven outflow inside the sessile drop is given by

[

 3 1 ν r = − ~ (1 − ~ r 2 ) − 1− ~ r2  8 r

(

)

Θ / π −1 / 2

]

2 r~z 0 ~z  ~ 1  − J − Θ /π  1− ~ r2 2   2 Rdepo   2 

(

)

Θ / π −3 / 2

  Rdepo + 1    t f

(5)

where r~ = r / Rdepo is the dimensionless radius, Θ is the apparent contact angle of the droplet

{

}

and is assumed be between 0 and 90°, Rdepo = πd 0 /[3π tan(Θ / 2)] 3

1/ 3

is the droplet deposition

~ z = z / z 0 is the dimensionless height, z 0 is the initial height of the droplet, J (~ r ) is the radius, ~ local

evaporation

flux

and 10


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(

~ J = (t f / ρz 0 ) 1 − r~ 2

)

Θ / π −1 / 2

(Dc

v

(

)

(1 − RH ) / Rdepo ) 0.27Θ 2 + 1.3 [0.6381 − 0.2239(Θ − 4 / π ) ] 2

is

obtained from curve fitting numerical solutions of an evaporating pinned sessile drop28. Here, the total drying time is t f = πρRdepo tan(Θ / 2) /[8D(1 − RH )c v ] , where D is the diffusivity of vapor 2

in air, c v is the saturated vapor concentration, and RH is the relative humidity. Combining Eqs. (4) and (5), it is noted that, when fixing the substrate and liquid (namely, the wettability, surface tension, and liquid viscosity) and the drying environment (e.g., relative humidity and temperature), the hydrodynamic force ( Fµ ) on the particle depends on the drop size ( d 0 ) and particle aspect ratio ( k ). Using Eqs. (3) and (4) to evaluate the particle-particle capillary attraction force ( Fγ ) and the hydrodynamic force ( Fµ ) respectively, for stationary ellipsoidal particles at the liquid-air interface, the ratio of capillary attraction ( Fγ ) to hydrodynamic force ( Fµ ) is hence given by Fγ Fµ

2

≈γ

8H P a 3 k 4 / 3 µv r K ′Lm 5

(6)

which predicts the competition between two major forces acting on the ellipsoids and hence the motion of the ellipsoids along the drop surface. Based on this relation, the resulting deposition morphologies are mainly affected by the drop size, particle aspect ratio, and particle concentration, among others. In the next section, the model predictions using Eq. (6) are compared with our experimental results. Both the inter-particle capillary interactions and the hydrodynamic forces in the model predictions are based on using the drop size, contact angle, and particle concentration at the end of drop spreading.

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4. Results and Discussion In order to understand the deposition morphologies of ellipsoids with different aspect ratios, Figure 2 shows successive snapshots of inkjet-printed colloidal drops containing particles of aspect ratio k = 1 (spheres), 3.5, and 6.5 evaporating on a glass substrate with a 0.005 initial particle volume fraction at a controlled relative humidity of 40%. For a drop diameter d 0 =70 µm, the time at which evaporation is completed, t f , is about one second, regardless of the particle aspect ratio. As shown in Figure 2, spherical particles start to move to the drop edge at t = 0.1t f and continuously move to the pinned contact line during evaporation until t = t f . For

the cases of ellipsoids, some particles move to the drop edge at t = 0.1t f , similar to spheres, and the rest of the particles self-assemble due to strong capillary interaction forces between particles. Once ellipsoids form a coherent network near the center of the drop surface at t = 0.5t f for the case of k = 6.5, they stop moving until they are finally deposited with increasing aggregation at the drop center at t = t f . The experiments thus demonstrate that the final depositions of spheres and ellipsoids differ significantly; in particular, spheres are in continuous motion to the drop contact line whereas ellipsoids have a time period where they are trapped in an immobile network.

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Figure 2. Snapshots of the particle deposition process in inkjet-printed colloidal drops with particle aspect ratio k = 1 (spheres), 3.5 and 6.5 all at a 0.005 volume fraction. The drop diameter d 0 =70 µm. The scale bar represents 20 µm.

To compare the deposition pattern with varying particle aspect ratio, Figure 3 shows the edge to center particle number density ratio, ρ edge / ρ mid , of the final deposition for ellipsoids of aspect ratio k = 1 (spheres), 1.8, 3.5, and 6.5 for colloidal drops of 0.005 particle volume fraction and drop diameter d 0 = 70 µm. Here, ρ edge is the average particle number density close to the drop edge (0.75 < r / Rdepo < 1) and ρ mid is the average particle number density in the middle of the drop ( r / Rdepo < 0.75), based on counting the number of particles in that area. As shown in the inset of Figure 3, spherical particles are primarily deposited at the drop edge, resulting in

ρ edge / ρ mid = 11.5. As the aspect ratio of the ellipsoidal particle increases, ρ edge / ρ mid decreases monotonically and for ellipsoids of k = 6.5 (as shown in the inset of Figure 3), ρ edge / ρ mid is about unity. This transition from a coffee ring to increasing deposition at the center, due to

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increasing particle aspect ratio, is also consistent with results observed from 1 µl or larger drops.8 We therefore classify the deposition as “coffee ring” when the edge-to-center particle density ratio ( ρ edge / ρ mid ) and the edge-to-center light intensity ratios are greater than two. Otherwise, the deposition is classified as “no coffee ring”.

Figure 3. The local particle density at the drop edge, ρ edge , normalized by the density in the middle of the drop, ρ mid , plotted for the particle aspect ratios of k = 1 (spheres), 1.8, 3.5 and 6.5. The drop diameter d 0 =70 µm and the volume fraction is 0.005. Error bars are obtained on the basis of three independent experiments. The scale bar represents 20 µm.

To quantify the deposition morphology shown in Figure 2, Figure 4(a) shows the normalized light intensity of the deposition profiles as a function of normalized radial distance, r / Rdepo , from the drop center for particles with k = 1 (spheres), 1.8, 3.5 and 6.5 and the drop

diameter d 0 =70 µm with a 0.005 initial particle volume fraction. The light intensity profile I (r) is normalized by the maximum intensity I max for each deposition. For spheres, the particle number density is low from the drop center to r ≈ 0.9 Rdepo and increases significantly near the

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edge ( 0.9Rdepo < r ≤ 1.0Rdepo ). As the particle aspect ratio k increases, the deposition of particles becomes more uniform along the radial direction as more particles are deposited in the drop center. To compare the final deposition patterns of different drop sizes, the relative light intensity profiles of the deposition as a function of the normalized radius, r / Rdepo , are shown in Figure 4b for drop diameters d 0 =70, 390, and 650 µm and particle aspect ratio k = 6.5 with volume fraction of 0.001. Here, the light intensity is scaled with the cube root of the total particle number ( 3 N r ) for each drop size and then divided by ( I max / 3 N r )

d 0 = 70 µm

in order to demonstrate the

relative intensity peak of the coffee ring with drop diameter. As shown in Figure 4(b), as the drop diameter increases, the normalized light intensity at the drop edge decreases, as such the coffee-ring effect is shown to decrease with the drop size.

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Figure 4. (a) Normalized light intensity of the deposition profile as a function of the normalized radial distance, r / Rdepo , for particle aspect ratio k = 1 (spheres), 1.8, 3.5 and 6.5 of a drop with d 0 = 70 µm and 0.005 particle volume fraction. The intensity profile I (r ) is normalized with the maximum intensity for each deposition. (b) Relative light intensity of the deposition profile as a function of the normalized radial distance, r / Rdepo , for drops of diameter d 0 =70, 390, and 650 µm and particle aspect ratio k = 6.5 all at 0.001 particle volume fraction. The intensity I (r ) is scaled with a cube root of the total number of particles in a drop ( 3 N r ) and then divided by ( I max / 3 N r )

d 0 = 70 µm

.

To better understand the forces acting on the particles at the liquid-air interface, Figure 5(a) shows the inter-particle capillary ( Fγ ) and hydrodynamic ( Fµ ) forces acting on the ellipsoids as 16


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a function of the particle volume fraction for a drop of d 0 =1.2 mm and

containing

ellipsoids of k = 6.5, calculated using Eqs. (3) and (4) at a relative humidity of 40%. Based on Eq. (5), the maximum radial velocity of the evaporation-driven flow along the liquid-air interface is located at the drop contact line and is estimated by setting z = a and r = Rdepo − h / tan( Θ) . For the conditions considered here, the inter-particle capillary force acting on the ellipsoids increases monotonically with the particle volume fraction while the hydrodynamic force remains the same. When the particle volume fraction reaches 0.0013 (see Figure 5(a)), the capillary attraction between particles becomes stronger than the hydrodynamic force to prevent ellipsoids from moving to the contact line and hence the coffee-ring effect can be suppressed. Figure 5(b) shows a confocal microscopy image near the drop contact line depicting the distribution of ellipsoids during evaporation for a drop of 1.2 mm in diameter containing ellipsoids of k = 6.5 with a 0.005 volume fraction and an instantaneous contact angle ( Θ ) of 7°. The confocal microscopy result confirms our earlier assumption that the majority of ellipsoids are located on the liquid-air interface as opposed to the bulk liquid due to the strong adsorption energy and inter-particle capillary interactions. In contrast, for spherical particles of the same size, volume fraction, and evaporation conditions, no significant accumulation of spheres is observed on the drop surface.

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Figure 5. (a) Comparison of the capillary force ( Fγ ) and hydrodynamic force ( Fµ ) as a function of the particle volume fraction for particle aspect ratio k = 6.5 in a drop of d 0 = 1.2 mm at 40° contact angle and 40% relative humidity. (b) Distribution of ellipsoids (red dots) near the drop contact line for particle aspect ratio k = 6.5 and 0.005 initial volume fraction of an evaporating drop obtained by confocal microscopy. The black line depicts the liquid-air interface.

As discussed in Section 3, the competition between the inter-particle capillary force ( Fγ ) and hydrodynamic force ( Fµ ) acting on the surface of the ellipsoids during drop evaporation determines whether the coffee-ring is formed or suppressed. Figure 6 shows the deposition patterns for different drop sizes and particle volume fractions containing ellipsoids of k = 6.5, together with the calculated ratio of Fγ / Fµ , where Fγ / Fµ < 1 denotes the hydrodynamic force dominant regime where the coffee-ring is formed and Fγ / Fµ > 1 indicates the capillary force dominant regime suppressing the coffee-ring effect. The model prediction is consistent with experimental results, where red symbols are for coffee-ring formation and blue symbols are for no coffee ring. As the drop size increases, the hydrodynamic force decreases monotonically as predicted by Eq. (5), while as the volume fraction increases, the capillary force increases sharply

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with Lm

−5

due to the increased particle density in the drop. The deposition morphology hence

transitions from a coffee ring to more uniform as the volume fraction and drop size increase.

Figure 6. Dependence of deposition morphology (coffee ring vs. no coffee ring) on drop size and particle volume fraction for colloidal drops containing ellipsoids of aspect ratio k = 6.5. The symbols denote experimental results and the black solid line represents Fγ / Fµ = 1 .

For colloidal drops of d 0 = 70 µm in diameter, Figure 7 shows the experimentally obtained and model predicted dependence of deposition morphology on particle aspect ratio and volume fraction. As the aspect ratio of the ellipsoidal particle increases, both the hydrodynamic and capillary forces increase, as characterized by Eqs. (3) and (4), while the capillary force mainly increases with the volume fraction. In this study, we ignore Brownian motions of the particles, which are found to be negligible compared to the evaporation-driven flow. For a drop of d 0 = 70 µm, the hydrodynamic force acting on the ellipsoids is stronger than that for bigger drop sizes, leading to a larger coffee-ring region ( Fγ / Fµ < 1) in the deposition phase diagram. The model

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prediction is validated by the experimental results also showing transitions in the vicinity of

Fγ / Fµ = 1 (see the solid line in Figure 7). We note that, for spheres, the Fγ / Fµ = 1 line is reached at ~0.083 particle volume fraction where the drop surface is saturated with particles.8 The three insets in Figure 7 show the experimentally obtained deposition patterns on glass substrates, suggesting the validity of using Fγ / Fµ in predicting the coffee-ring deposition morphology while varying the particle aspect ratio and volume fraction.

Figure 7. Dependence of deposition morphology (coffee ring vs. no coffee ring) on particle aspect ratio and volume fraction for colloidal droplets of d 0 = 70 µm. The scale bar represents 20 µm. The symbols denote experimental results and the black solid line represents Fγ / Fµ = 1 .

5. Conclusion The competition between the inter-particle capillary interactions near the drop surface and the hydrodynamic force induced by evaporation-driven flow predicts well the final deposition morphologies of inkjet-printed sessile drops containing polystyrene ellipsoids. In this study, the

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hydrodynamic force was controlled via the drop size and the particle aspect ratio, and the interparticle capillary interactions were tuned via the particle volume fraction and the particle aspect ratio. The drop size ( d 0 ) was carefully controlled in the range of 60 µm to 1.2 mm in diameter with monodisperse micrometer-sized ellipsoidal particles suspended in pure water and printed directly on to glass substrates in a humidity controlled environmental chamber. The results show that the particle deposition patterns agree well with the model prediction governed by the capillary to hydrodynamic force ratio Fγ / Fµ , where Fγ / Fµ < 1 promotes the coffee-ring effect and Fγ / Fµ > 1 suppresses the coffee-ring effect. By increasing the drop size, particle volume fraction, and particle aspect ratio, the deposition uniformity of evaporating colloidal drops containing ellipsoids is increased. The results of this study will be useful for future developments in inkjet printing applications as well as aiding the understanding of particulate deposition patterns containing anisotropic particles.

ACKNOWLEDGMENT We thank Prof. Howard A. Stone at Princeton University for providing valuable comments and his contribution to this study. Support for this work was provided by the National Science Foundation under Grant No. CMMI-1200385 and CMMI-1401438.

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Deposition of Colloidal Drops Containing Ellipsoidal Particles

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