Patterns in Drying Drops Dictated by Curvature-Driven Particle

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Patterns in Drying Drops Dictated by Curvature Driven Particle Transport Ranajit Mondal, Shivani Semwal, Logesh Kumar, Sumesh P Thampi, and Madivala G Basavaraj Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b02051 • Publication Date (Web): 26 Aug 2018 Downloaded from http://pubs.acs.org on September 2, 2018

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Patterns in Drying Drops Dictated by Curvature Driven Particle Transport Ranajit Mondal1 , Shivani Semwal1 , P Logesh Kumar1 , Sumesh P Thampi1 , Madivala G Basavaraj1∗ 1

Polymer Engineering and Colloid Science Laboratory, Department of Chemical

Engineering,Indian Institute of Technology Madras, Chennai-600036, Tamilnadu, India E-mail: [email protected],[email protected]

Abstract Patterns generated by controlled evaporation of droplets containing colloids are dictated by internally generated flows. This advective particle transport is crucial to the efficacy of printing and coating processes and is also an elegant route to the self-assembly of particles. We propose a novel particle transport route which involves adsorption of particles to the interface and subsequent curvature driven migration of the particles along the interface. This interface mediated transport can be exploited to control the distribution of particles in the dried patterns, which we experimentally elucidate by achieving gravity induced drop shape changes. Our experiments demonstrate that the interplay between the bulk and the interfacial transport leads to strikingly different patterns: while dried aqueous sessile drops of colloidal dispersions produce well known “coffee-rings”, dried pendant drops lead to “coffee-eyes”. We support our experimental findings using scaling arguments. In previous studies, the effect of gravity-induced change in drop shape on the patterns formed in drying drops have been neglected. However, we show that the structure of the patterns formed by the

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colloidal particles after solvent evaporation are markedly different when the drops are deformed by gravity.

Keywords: Coffee-ring, Coffee-eye, Drop deformation, Evaporative self-assembly, Interfacial flow, Interface Buckling, Viscoelastic Interface

Introduction Plethora of dried deposit patterns generated by controlled evaporation of drops and the self-assembly of colloids in these patterns rely on the transport of particles by internally generated flow fields. The evaporation of a particle laden sessile drop on a solid substrate leads to a “coffee-ring”, the formation of a ring like deposit of particles near the pinned contact line (Figure 1d), which is undoubtedly the most striking example of this phenomena. 1 The widely accepted mechanism of coffee ring formation is the transport of particles to the pinned contact line of the drop as a result of the outward radial flow of the solvent. Typically, such patterns form when sessile drops are dried on hydrophilic substrates which is the most studied configuration to date. 1–6 We show that both the orientation 7,8 and wettability 9–11 of the substrate, which are often neglected, are the two prime factors that significantly influence the patterns in dried drops. This is often the case encountered in several applications. For example, in agriculture, 12,13 multicomponent nutrient or insecticide drops sprayed on crops land on leaves orientated at various angles. Moreover, the wettability of the leaf may vary depending upon the crop type. Similarly, the orientation and wettability of surfaces in printing 14,15 and coating applications 16,17 can also be arbitrary. As shown in Figure 1, strikingly different patterns – “coffee-eyes” in Figure 1e and asymmetric particle distribution in Figure 1f – form when drops in pendant configuration (Figure 1b) and drops on vertical substrates (Figure 1c) are dried compared to the “coffee-rings” left by sessile drops (Figure 1a). The natural candidate to explain the contrasting patterns shown in Figure 1 is the grav2


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Figure 1: Contrasting patterns by drying drops containing colloidal particles on a hydrophilic substrate (θ = 30±5◦ ). Top panel – Configuration of drying drops (a) sessile mode (b) pendant mode and (c) drop on a vertical substrate. Bottom panel– Corresponding 3D view of the dried patterns obtained by re-construction of 2D images (see supporting information section 1) (d) coffee-ring (accumulation of particles at the drop edge) in dried sessile drop (e) coffee-eye (accumulation of particles at the drop center) in dried pendant drop (f ) asymmetric distribution of particles in deposits left on a vertical substrate showing more particles at the advancing side. itational settling of particles. However, this is not the case as the patterns in Figure 1 are obtained from drops that contain colloidal particles which do not sediment during the life time of the drying drops. However, gravity can still induce subtle changes in the shape of small drops (for a 1µl water drop, Bond number (Bo) = Rd2 ρg/σ ≈ 0.1, where Rd is the characteristic length of the drop, g is the gravitational acceleration, ρ is the density and σ is the interfacial tension between the drop and the surrounding air). We show that such small deviations in the drop shape can bring curvature driven migration of particles that get adsorbed to the interface during drying. In sessile drop evaporation, this interface mediated particle transport constitutes an additional mechanism that leads to “coffee-ring” deposits. However, this is not the case for drops on substrates oriented differently as shown in Figure 1e − f . 3


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We attribute the formation of such intriguing patterns to the existence of interface mediated particle transport which is elucidated through both experiments and scaling analysis. In our experiments, we deliberately use highly charged dispersions of hematite nano-ellipsoids because (1) these dispersions always form coffee-ring deposits irrespective of particle shape and aspect ratio when dried in sessile configuration 6 (2) due to inherent reddish brown color, hematite particles in the drying drops allow easy visualization of distribution of particles. The latter aspect is crucial to unravel the novel particle transport mechanism.

Materials and Methods Synthesis of hematite ellipsoids Hematite (α − F e2 O3 ) ellipsoidal particles were synthesized using the forced hydrolysis of F e+3 in presence of urea. 18 High resolution scanning electron microscope (HR-SEM) characterization of the hematite ellipsoids (Figure S1 in supporting information) revealed that the particles are highly monodisperse. The aspect ratio of the ellipsoids can be controlled by tuning the quantity of sodium di-hydrogen phosphate (N aH2 P O4 ). 18 In all our experiments, particles of fixed aspect ratio 4.3±0.33 were used.

Preparation of the substrate The substrates of four different wettabilities were prepared using the following protocols and characterized by measuring the contact angle of a water drop. (1) To obtain highly hydrophilic substrate of contact angle (θ=12±3◦ ), the glass substrates were cleaned with piranha solution (70% H2 SO4 and 30% H2 O2 by volume) followed by rinsing multiple times with water and dried using N2 gas prior to use. (2) Instead of piranha cleaning, if the glass substrates were cleaned with acetone, the water drops made a contact angle of 30±5◦ . Further, the glass substrates were rendered hydrophobic by coating a thin polymer layer. (3) The polystyrene (PS) film coated the glass substrate leads to a contact angle of 90±2◦ . In 4


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order to coat a piranha cleaned glass substrate with PS, a 10% (w/w) extended polystyrene (PS) dissolved in toluene was spin coated at 500 rpm. (4) Commercially available Teflon tape stuck on a glass substrate leads to a contact angle θ=120±5◦ .

Droplet evaporation experiment Aqueous dispersions of hematite ellipsoids at a concentration of ∼ 0.12% (w/w) were used in all experiments. By varying the pH of the dispersion, the surface charge density on hematite particles can be controlled. In our experiments, the pH of the dispersion was adjusted to 2.0 by the addition of HN O3 . Under these conditions, the particles are highly charged with a zeta potential of +40 mV (measured in 0.0001 M N aCl) and therefore the dispersions are stable against gravity settling. 6 The dried patterns of these dispersions are known to form “coffee-ring” in sessile drop configuration. As the dispersions are inherently reddish brown in color, a qualitative analysis of the distribution of particles in the drying drops and the final deposits can be made by simple visualization. Therefore this is a good model system to investigate the influence of substrate orientation and wettabiliy on the pattern formation in drying drops. The evaporation experiments were performed by placing a drop of colloidal dispersion of known volume on an oriented solid substrate of desired wettability. All experiments were carried out under constant temperature of 25±3◦ C and relative humidity of 50±5%.

Imaging of drying drops To investigate the evaporation modes of the drying drops, the drying kinetics was monitored by capturing the video of an evaporating drop. The side view of the drop was captured using Dino-Lite digital microscope (AnMo electronics corporation, Taiwan). The recorded video was converted to 2D images and the temporal evolution of the contact diameter and the contact angle were measured using IMAGE-J software. The adsorption of particles and the subsequent transport of particles along the interface 5


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were also assessed from the 2D images of the drying drops. To this end, the reflected light intensity variation in the vicinity of the interface was measured using IMAGE-J software. Ensuring that the optical path is constant, a thin strip of 10 pixel (1 pixel≈ 0.01 mm) width along the interface, as shown in Figure 7b, was considered to measure the variation in intensity at different time intervals plotted in Figure 7 (See supporting information section 4).

Analysis of the dried deposit The final deposits left after the complete evaporation of water shown in Figure 2 were imaged using a Dino-Lite digital microscope (AnMo electronics corporation, Taiwan). The images were analyzed using IMAGE-J by plotting the radial variation in the reflected light intensity (Figure 3) to determine the spatial distribution of particles in the dried patterns. The height profile of dried particulate deposits were also measured using an optical surface profile meter (Bruker, contour GT-1, Germany).

Results and Discussion Substrate orientation and wettability dictate patterns in drying particle laden drops The final deposit patterns obtained after the evaporation of drops containing colloidal ellipsoids on four different substrates at three different orientations are shown in Figure 2. As shown in Figure 2a1 − c1, the sessile drops that made a contact angle (θ) less than or equal to 90◦ leaves a “coffee-ring” deposit upon drying. 1,5,6 The nature of pattern is further confirmed by plotting (1) the radial variation in the height of the dried deposit measured from an optical surface profiler and (2) radial variation in the reflected light intensity obtained from the digital images of the dried deposit as shown in Figure 3a2 − c2. As the

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concentration of particles at the periphery of the deposit is the largest, the height profile shows spikes and corresponding intensity profile shows sharp dips. However, drops dried on a partially hydrophobic substrate (θ=120±5◦ ), showed a suppression of the coffee-ring as evident in Figure 2d1 and Figure 3d2, which is consistent with previous reports. 19–21 As

Figure 2: Substrate orientation and wettability dictate the final deposit patterns. Top panel – Evaporating sessile drops of 2µl volume containing hematite ellipsoids at a concentration of ∼ 0.12 wt% on substrates of different wettability characterized by initial contact angle, θ = 12 ± 3◦ , 30 ± 5◦ , 90 ± 2◦ , 120 ± 5◦ . Corresponding images (top view) of the dried deposits for drops evaporated in sessile mode (second row, a1 to d1), pendant mode (third row, e1 to h1) and on vertical substrates (fourth row, i1 to l1). The darker the color, the higher is the concentration of particles. The scale bar in each image corresponds to 500 µm and its length is largest in the images in the last column. shown in Figure 2e1 and Figure 3e2, the pendant drops dried on a highly hydrophilic substrate (θ≈ 12 ± 3◦ ) also leaves a coffee-ring deposit identical to that dried in sessile mode. In marked contrast, pendant drops dried under identical conditions on other three substrates 7


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shows a large concentration of particles at the center of the deposit along with particles deposited at the pinned contact line, as shown in the images in Figure 2f 1 − h1. With increase in θ, the color in the central region of the drop becomes darker corresponding to an increase in the particle concentration. This is corroborated further by the intensity and the height profiles shown in Figure 3f 2 − h2. It must be noted that the dried hanging drops leave a deposit of uneven distribution of particles with a high particle concentration at the center. The formation of central dome in the dried deposits is referred to as “coffee-eye”. Such patterns have been reported earlier in sessile drops evaporated on a hot substrate by Li et. al. 22 and in drops dried in pendant configuration by Hampton et al., 8 however, the reason for the formation of such deposits in our experiments are very different as discussed in subsequent sections. Hampton and co-workers 8 attribute the formation of “coffee-eye” to the aggregation of particles in the drying drop and their subsequent gravity settling. While for the drops dried on vertical surfaces, deposit patterns are known to exhibit an asymmetric distribution of particles. 7 This is attributed due to the continuous depinning of the contact line of the drying drop at the receding side and continuous growth of the deposit at the advancing side due to pinning. In our experiments, the patterns formed upon evaporation of drops on vertical substrates are typically elongated with most of the particles deposited at the advancing side of the drop irrespective of the wettability of the substrate as shown in Figure 2i1 − l1 and Figure 3i2 − l2. With decrease in substrate wettability, the asymmetry in the distribution of particles increases due to the deposition of more particles at the advancing side of the drop. While “coffee-ring” and “coffee-eye” deposits obtained respectively in sessile and pendant drop evaporation exhibits angular symmetry with respect to distribution of particles, this symmetry is clearly broken for drops dried on vertical substrates. However, the patterns still shows a reflection symmetry with respect to the elongated axis of the drop, but not with respect to the short axis, indicating the role of gravity, which will be discussed further.

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Figure 3: Analysis of distribution of particles in the dried deposits. a2 to l2 show the variation of the normalized height profile (black line) and the normalized reflected intensity profile (red line) along the diameter (long axis for drops on vertical substrates) as a function of normalized distance x/R of the dried deposits shown in Figure 2a1 to l1. The plots confirm the formation different patterns such as coffee-ring (a2 to c2, e2), uniform deposit (d2), coffee-eye (f 2 to h2) and asymmetric distribution of particles (i2 to l2).

Modes of evaporation kinetics Further clue of the influence of gravity on dried deposits comes from the differences observed in the evaporation kinetics of drying drops at various substrate orientations. We monitor the temporal evolution of the diameter of the contact line 2R(t) and contact angle θ(t) of the evaporating drops at different substrate orientations as shown in Figure 4. Sessile drops, irrespective of substrate wettability, evaporates in constant contact radius (CCR) mode 23 wherein the contact radius of the drop remains constant and the three phase contact angle decreases monotonically for majority of the drying period, as shown respectively in Figure 4a and b. It is also evident in Figure 4a that pendant drops exhibit CCR mode for a shorter duration ≈ 0.75tf , where tf is the total evaporation time and correspondingly an earlier depinning of the contact line. It must be noted that, for a given substrate, a pendant drop always has a lower contact diameter compared to a sessile drop indicating gravity induced drop deformation.

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Figure 4: Evaporation kinetics of drying drop. Evolution of (a) diameter of the contact line, 2R(t) and (b) contact angle, θ(t) for drops dried in sessile (open symbols) and pendant (filled symbols) modes on substrates of different wettability. A drop drying on a vertical substrate is characterized by monitoring the evolution of (c) length of the major axis of the contact line, 2L(t) and (d) advancing contact angle, θA (t) (open symbols) & receding contact angle, θR (t) (filled symbols). For majority of drop lifetime, all the drops show constant contact radius/length mode evaporation accompanied by a decrease in contact angle. An early depinning is observed in case of drops in pendant configuration and drops on vertical substrates compared to that of sessile drops. On the other hand, the drops residing on vertical substrates elongate in the direction of gravity and therefore they are characterized by two different contact angles, namely, an advancing (θA ) and a receding (θR ) contact angle. The long axis of the elongated drop is always greater than the contact diameter of the sessile and the pendant drops of same volume residing on substrate of same wettability. We analyze the temporal variation of the length of major axis of the contact line 2L(t) as well as the two contact angles θA (t), θR (t) as shown in Figure 4c and d respectively. Analogous to the CCR mode in sessile and pendant drops, we observe a constant contact length (CCL) mode in drops drying in vertical configuration on hydrophilic and neutrally wetting substrates (θ ≤ 90◦ ). From Figure 4a and c, it is clear that

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Figure 5: Lifetime of drying drops. The lifetime, tf (defined as the total evaporation time) of 2µl drops at different substrate orientation (α). tf is largest for drops on vertical substrates and it increases with decrease in wettability. the CCL mode lasts longer than the corresponding CCR mode in sessile and pendant drops. In contrast, the contact length on a partially hydrophobic substrate (θ ≈ 120◦ ) continuously decreases during the course of drying. In all the cases, θA is always greater than θR at any given instant and they exhibit nearly similar temporal variation as shown in Figure 4d. The influence of gravity on evaporation kinetics is also evident from the measurement of the lifetime (total drying time, tf ) shown in Figure 5 for the drops dried in different configurations. The life time of the drop increases significantly when dried on vertical substrates compared to the other two configurations on all substrates. This non-monotonic variation of the life time of particle laden drops with substrate orientations is similar to that of particle free water drops. 24 This unusual behavior is attributed to (1) the gravity driven shape changes and the consequent changes to the kinetics of the depinning of the contact line (2) the difference in the evaporative flux at the advancing and receding sides of inclined drops. 7 Moreover, for a given drop volume and substrate orientation, tf increases as the substrate 11


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wettability decreases due to the smaller interfacial area available for evaporation.

Interface mediated particle transport in drying drops Radial flow does not explain contrasting deposit patterns: Coffee-ring patterns are typically explained based on the transport of particles to the drop periphery due to the radially outward flow of the carrier fluid. In a drying drop of contact radius R, the evaporative flux at any radial location r is given by 1 J(r) ∝ (R − r)−λ where λ = (π − 2θ(t))/(2π − 2θ(t)). The radial flow arising from this spatially inhomogeneous evaporative flux causes the advection of the particles to the pinned contact line. This inhomogeneity in the evaporative flux completely vanishes for θ = 90◦ . Thus the advection of particles to the pinned contact line reduces with the increase in contact angle resulting in the accumulation of particles in the interior of the dried drop as well. We confirm this by plotting radial variation in the height of the dried deposit obtained from dried sessile drops as shown in Figure 6 (For details see section 5 in the supporting information). However, the radial bulk flow mechanism fails to explain the formation of central domes in the patterns resulting from dried pendant drops and asymmetric distribution of particles in drops dried on vertical substrates. Contrasting deposit patterns are not due to gravity settling: We first rule out the possibility of gravitational settling of particles as the cause for the difference in the distribution of particles in the dried deposits. The experimental conditions are such that the gravity driven settling time of nano ellipsoids is negligible compared to that of Brownian and surface tension forces: the ratio of gravity to Brownian force is ≈ 10−9 and the ratio of gravity to surface tension forces is ≈ 10−3 . Therefore, during the lifetime of the evaporating drop (∼ 10-40 min), the gravitational settling of particles both in the bulk as well as along the interface are irrelevant. This is experimentally verified as shown in supporting information (Figure S2), wherein the gravitational settling does not occur even after 24 h.

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Figure 6: As wettability of the substrate decreases, the height profiles show the accumulation of more particles in the interior region (r = ±0.5R) of patterns formed by evaporating drops in sessile mode. Novel route of particle transport in drying drops: We now propose and demonstrate the existence of a new mechanism responsible for the strikingly different patterns observed in our experiments. In contrast to the bulk flow advecting the particles, the novel particle transport route involves (1) the adsorption of particles to the interface during evaporation and (2) the subsequent migration of the particles along the interface to the regions of higher surface curvature. In our experiments, the particles are highly charged, and therefore, they do not spontaneously adsorb at the drop surface. This is due to the image charge repulsion. 6,25 Therefore, irrespective of the drop orientation, the adsorption of particles on the drop surface occur as a result of the sweeping of the particles by the descending interface. 26–28 Once the particles are captured by the descending interface, the local curvature of the drop interface which is orientation dependent plays an important role in the transport of particle along the surface of the droplet. Therefore, this transport mechanism is expected to be ubiquitous and contributes to the accumulation of particles at the contact line for sessile drops, but leads to different patterns in the case of drops dried in other configurations.

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Visualization of interface mediated particle transport: We now elucidate the adsorption of particles to the interface and their eventual transport along the interface. To this end, we present 1) Figure 7a - qualitative evidence by monitoring the occurrence of buckling instability in particle laden interfaces 2) Figure 7b and c - quantitative evidence via the analysis of the distribution of particles in the vicinity of the liquid-air interface. Figure 7a shows snapshots of the drop at various instances during evaporation in both sessile and pendant configurations for θ = 120◦ . It is evident that the particles adsorb to interface and at later stages (t ≥ 0.5tf ) of the evaporation, this results in an elastic deformation of the drop surface in sessile mode while the buckling/wrinkling instability occurs at the interface in pendant mode (See supporting information Movie S1 and Movie S2). Such interface instabilities have been previously reported in particle laden drops subjected to external compression. 6,25,29,30 In the absence of evaporation, the highly charged hematite particles in the drop (zeta potential of +40 mV in 0.0001 M N aCl) do not adsorb to the interface due to the image charge repulsion. 6 Therefore, the adsorption of particles as seen in Figure 7a is purely a result of the interfacial capture of particles by the descending interface due to evaporation. 26 The elastic nature of the interface as evident in Figure 7a is due to the large concentration of adsorbed particles on the drop surface. 25 Figure 7b and c show the variation of the intensity of reflected light in the vicinity of the liquid-air interface obtained from projected 2D images of the drying drops for θ = 30◦ at t = 0.2tf , 0.7tf and for θ = 90◦ at t = 0.2tf , 0.8tf . In order to obtain this reflected intensity variation, a thin 10 pixel (1 pixel≈ 0.01 mm) wide strip as shown schematically in the inset of top right plot in Figure 7b is considered. As the optical path along the strip is constant, the intensity variation provides information of the distribution of particles adsorbed at the interface: lower the reflected intensity, higher is the particle concentration. For sessile drops, at any given time, the reflected intensity at the interface close to the drop edge (r/R ≈ 1) is much lower than the intensity at any other location on the interface. This indicates that

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there is a higher concentration of adsorbed particles at the interface near the contact line. Now, comparing the profiles at t = 0.2tf and 0.7tf , we observe similar intensity in the central region, but has a larger dip near the contact line at 0.7tf which shows a higher concentration of particles at the interface close to the contact line. On the other hand, for a pendant drop, the reflected intensity at the interface near the drop center progressively decreases compared to that of near the contact line showing an accumulation of particles at the drop apex. This spatio-temporal variation of reflected intensity clearly suggests the adsorption of particles to the interface and their subsequent transport along the interface. However, the particle transport is towards the pinned contact line in sessile drops while away from the contact line i.e., towards the drop apex for the pendant drops as shown schematically in Figure 7d. We now explain that this difference in behavior originates from the curvature driven migration of particles. Physics of curvature driven migration of particles: There are two aspects that dictate the curvature driven particle migration observed in our experiments: (a) the gravity induced deformation of the drop and (b) the particle induced deformation of the interface. (a) Gravity induced drop deformation: In the absence of gravity, drop takes the shape of a spherical cap which can be characterized by a constant mean curvature (average of two principal radii of curvature) and zero deviatoric curvature (the difference of the two principal radii of curvature). However, gravity changes the shape of the drop from a spherical cap. 31 This deviation scales with Bond number (Bo) and thus both mean and deviatoric curvatures vary along the drop surface (For details see supporting information section 8). (b) Particle induced deformation of the interface: A particle hosted at a fluid-fluid interface deforms the interface to simultaneously satisfy both Young’s equation at the contact line and the Young-Laplace equation at the deformed interface. 32–34 In particular, on a curved host interface, the deformed interface around an adsorbed particle fights against the deviatoric curvature of the host interface yielding locally flat regions around the adsorbed particle. 35–38 Therefore, compared to a particle trapped at a planar interface, the free en-

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Figure 7: Interfacial adsorption of particles and subsequent transport along the interface. (a) Snapshots of drying sessile and pendant drops on a partially hydrophobic substrate, θ = 120◦ . The adsorption of particles to interface results in an elastic deformation of the drop surface for t ≥ 0.5tf . The variation of the intensity of reflected light in the vicinity of the liquid-air interface (inset in top right plot in b) obtained from projected 2D images (side view) of the drying drops for (b) θ = 30◦ at t = 0.2tf , 0.7tf and for (c) θ = 90◦ at t = 0.2tf , 0.8tf . (d) Schematic of the particle transport due to radial bulk flow (white arrow), which is towards the contact line and the new transport route arising due to interfacial adsorption (yellow arrow) followed by the migration of particles along the interface towards the regions of higher curvature (black arrow). The dashed line represents the location of the interface at t = 0. ergy of the system with particle at a curved interface is smaller. 35,36 Thus it is energetically favorable for the particles to migrate to the regions of higher curvature to minimize the free energy of the host interface irrespective of the configuration of the drying drop. Though the mean curvature variation can also lead to migration of the particles along the interface, this contribution is not significant in our experiments (See supporting information). In our experiments, the interface curvature is not constant. For sessile drops, both the 16


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mean and deviatoric curvature do not vary in the azimuthal direction as the drop is axisymmetric, however they vary with the height ( vertical location of the interface) due to the change in hydrostatic pressure. Analogous to the mean curvature, the deviatoric curvature increases from apex towards the contact line (See supporting information) and thus particles migrate along the interface to the pinned contact line. Therefore, the interface mediated particle transport is an additional mechanism that enhances the coffee-ring formation in dried sessile drops. In sharp contrast, for a pendant drop, similar to the mean curvature, the deviatoric curvature increases from the contact line towards the apex leading to migration of particles away from the pinned contact line. This results in a central dome of particles in the dried deposit. For drops on substrates orientated differently, the interface curvature variation is more complex, therefore, the accumulation of particles depends on competing contributions generated by the bulk flow and interface mediated particle transport.

Scaling analysis We now present scaling arguments to support our experimental findings. The interfacial energy (E) associated with a colloidal ellipsoid of semi-minor and major axis Rp and Hp respectively is given by: 35,36 σHp Rp2 E∼− Rc (h)

(1)

where Rc (h) is the deviatoric curvature at height h. Analogous to the mean curvature, the deviatoric curvature also varies with respect to the drop height (Refer supporting information),

Rc (h) ∼

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σ ρgh


(2)

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Therefore, the capillary force arising from the interface deformation that is responsible for the migration of the particles is,

F =−

dE ∼ Hp Rp2 ρg dh

(3)

As the capillary force must balance the viscous force (∼ µUi Rp ), the particle migration velocity (Ui ) along the interface can be estimated as,

Ui ∼

Hp Rp ρg . µ

(4)

On the other hand, the bulk fluid velocity (Ub ) due to the inhomogeneity in the evaporation flux can be estimated as, 39

Ub ∼

D∗ p θ(t) R(R − r)

(5)

where D∗ is the effective diffusivity of the evaporating carrier liquid driving the bulk flow. Substituting typical values of the variables that correspond to experimental conditions in equation 4 and 5, we calculate Ui ≈ 0.125µm/s and Ub (r = 0.5R) = 0.366µm/s. This suggests that both the bulk flow and the interface mediated mechanisms have comparable contributions to the particle transport in the drying drops containing colloids.

Dried patterns independent of droplet volume and particle shape Influence of droplet volume on dried patterns: In the absence of gravity (Bo = 0), drop deposited on a substrate takes the shape of a spherical cap. As gravity acts, drop deforms and the shape of the drop is determined by the balance of gravity and surface tension forces. ρgh = γ

1 1 + R1 R2 18

−σ

2 R0


(6)

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Figure 8: The shape of sessile and pendant drops at different Bond numbers (Bo) for θ = 90◦ . x and y are scaled with capillary length. where σ is the interfacial tension, ρ is the fluid density, g is the acceleration due to gravity, R0 is the radius of curvature at the apex of the drop, h is the height measured in the direction of gravity from apex and R1 , R2 are radii of curvatures measured at any h. In equation 6, term on the left hand side is the contribution of hydrostatic pressure due to gravity and the terms on the right hand side arise from Laplace pressure. 31 Using equation 6, the shapes of sessile and pendant drops on a neutrally wetting substrate (contact angle, θ = 90◦ ) calculated as a function of Bo is shown in Figure 8. When the effect of gravity is small, i.e., Bo = 0.0001 both sessile and pendant drops have identical, hemispherical shape. As Bo increases, significant deviations in the drop shape arise: sessile drops flatten in the direction perpendicular to the gravity and pendant drops elongate in the direction of gravity. Consequently, both mean curvature and deviatoric curvature change at every location on the drop surface. This is expected to affect the the migration of particles along the interface and consequently on the dried patterns. One of the simplest way to test this hypothesis is to carry out drying drop experiments by changing the droplet volume as

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Figure 9: Effect of drop volume on drying patterns: The optical microscopy images of the drops containing hematite ellipsoids dried on a hydrophilic substrate (θ=30±5◦ ) are shown. In (a) and (b), the dried deposits after complete evaporation of solvent from 2µl (a1, b1) and 10µl (a2, b2) drops dried respectively in sessile mode and droplet on vertical substrate are shown. The bottom panel, (c), corresponds to the dried deposits for the drops evaporated in pendant mode of varying droplet volume - 2µl (c1), 10µl (c2), 20µl (c3), 30µl (c4) and 50µl (c5). In all the images darker the color, higher is the concentration of particles. The increase in the concentration of particles in the central region of the dried deposits formed in pendant mode drying is highlighted by dashed circle. The scale bar in each image corresponds to 1mm. discussed below. To this end, experiments are conducted at identical conditions by drying drops on a hydrophilic substrate (θ=30±5◦ ) at three different orientations namely, sessile, pendant and in vertical substrate configuration. The initial volume of the particle laden drop is varied from 2 µl to 50 µl. Similar to that of evaporating 2 µl drops, the drying of 10 µl drops also shows highest life time when dried on a vertical substrate while the least life-time in sessile and pendant configurations (For details see supporting information). The de-pinning behavior of large volume droplets were also found to be analogous to that observed for the 2 µl drop. The final dried deposits generated by drying drops of different initial volumes 20


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are shown in Figure 9. Both the 2µl and 10µl drops dried in sessile mode (Figure 9a) are observed to form “coffee-ring” while dried in vertical configuration (Figure 9b) leaves a deposit with asymmetric distribution of particles. However, in vertical mode, a depletion of the concentration of particles at the receding side and a clear increase in the concentration of particles at the advancing side of the drop was observed. In the pendant configuration, the final dried deposit is always a “coffee-eye” irrespective of drop volume, however, the concentration of particles in the central dome is observed to increase with increase in drop volume as highlighted by dashed circle in Figure 9c. These results also clearly demonstrate that the patterns formed by drying of larger drop volume are a manifestation of the effect of gravity on the drop shape. The patterns formed by drying particle laden drops of larger volume can further reiterate the role of gravity. Influence of particle shape on dried patterns: In the previous sections, we showed that the adsorption of colloidal ellipsoids to the interface is evident from the reflected light intensity profile close to the drop surface, which is further confirmed by the buckling of the drying drops. However,the interfacial adsorption of particles due to descending interface in drying drops occurs even if the particles are spherical 26 and is therefore expected to be independent of particle shape. As long as the particles are captured by the descending interface, the curvature of the drop which is orientation dependent facilitates the transport of particle along the surface of the droplet. To elucidate this, we perform drying experiments under identical drying conditions, however, by considering dispersions containing spherical polystyrene (P S) particles (3µm diameter, concentration ∼ 1 wt %). A 1µl drop is dried on a neutrally wetting substrate (θ=90±2◦ ) in three different orientations, namely, sessile, pendant and vertical. As the particles are highly negatively charged (zeta potential ∼ −92 mV ), similar to hematite particles, they do not spontaneously adsorb to the interface. The final deposit patterns obtained, which are shown in Figure 1, are similar to that of those observed in the dried drops containing hematite ellipsoids. Though there are subtle differences in the self assembly and specifics of distribution of particles in the final deposit, the

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Figure 10: Patterns left by polystyrene sphere laden 1µl drops dried on a neutrally wetting substrate (θ=90±2◦ ). The dried deposit patterns in a1, b1 and c1 are obtained by bright field optical microscopy. The surface profiles shown in a2, b2, c2 and three dimensional height profiles of the deposits shown in a3, b3 and c3 are the results of optical surface profile study. Top panel corresponds to images of the deposit dried in sessile mode, the center panel corresponds to images of the deposit dried in pendant and the bottom panel corresponds to images of the deposit dried on vertical surface. The scale bar in a1, b1 and c1 corresponds to 500µm. macroscopic appearance of dried patterns remain same. Therefore, the influence of interface driven particle transport on the patterns formed in drying drops is shape independent.

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Conclusions We have demonstrated that the patterns left by the particle laden drops dried on oriented substrates are significantly different compared to the patterns generated in the most studied configuration, namely, sessile drops. While sessile drops produce a coffee ring, pendant drops leave a central dome. At any other substrate orientations, the dried deposits show a larger accumulation of particles at the advancing side of the contact line. These observations show that the underlying mechanism of particle transport in drying drops is fundamentally different from that solely due to the capillary flow of the solvent. The noticeable differences in the patterns are explained by considering the effect of gravity on the drop shape. Gravitational effects in drying problems have always been neglected for (small) ∼ mm sized drops considering that the change in the drop shape is not significant. However, we have shown that a small deviation from a spherical cap shape is sufficient to significantly alter the distribution of particles in the dried patterns. The consequence of the gravity induced drop deformation reveals a new transport mechanism which relies on (i) adsorption of particles to the drop surface during evaporation and (ii) the subsequent migration of the particles along the interface to the regions of higher curvature. Based on the scaling analysis we demonstrated that the contribution of interface mediated particle transport is equally strong as the bulk particle transport. For a sessile drop, the direction of particle transport due to capillary flow in the bulk and due to curvature differences along the interface is same. Thus, the two contributions add up to the coffee ring formation. However, for a pendant drop, the directions of particle transport are in the opposite direction - the advection by bulk flow is directed towards the contact line while the interface mediated transport is directed towards the drop center. The progress we have elucidated by understanding the interplay of the two particle transport mechanisms will have significant impact in several fields including disease diagnostics, separation technology, spray painting and agricultural applications. The effect of new particle transport mechanism on pattern formation opens new opportunities in the investigation 23


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of desiccation cracks and colloidal lithography. The particles in drops dried on oriented substrates can also lead to plethora of interesting and novel self-assembly patterns. Furthermore, by manipulating the mobility of particles in different transport mechanisms, novel particle separation techniques can be designed.

Author Information Corresponding Author *Email:[email protected], [email protected]

Notes The authors declare no competing financial interest.

Acknowledgement We acknowledge Microelectronics and MEMS laboratory, Department of Electrical Engineering (IIT Madras) for the optical surface profilometry and Department of Chemical Engineering (IIT Madras) for the SEM facility. Authors thank Dr. Anand K Kanjarla, MME, IIT Madras and Dr. Dillip K Satapathy, Physics, IIT Madras for useful discussions.

Supporting Information Experimental details and analysis (pdf) Drying sessile drop (Movie S1) Drying pendant drop (Movie S2)

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Patterns in Drying Drops Dictated by Curvature-Driven Particle

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