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Complex Drop Impact Morphology Viktor Grishaev, carlo saverio iorio, Frank DUBOIS, and Alidad Amirfazli Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.5b02162 • Publication Date (Web): 14 Aug 2015 Downloaded from http://pubs.acs.org on August 22, 2015

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Complex Drop Impact Morphology

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Viktor Grishaev†, Carlo Saverio Iorio†, Frank Dubois†, and A. Amirfazli*‡

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†Service de Chimie-Physique EP, CP165-62, Université Libre de Bruxelles, 50 Av. F.D.

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Roosevelt 1050, Brussels, Belgium

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‡Department of Mechanical Engineering, York University, Toronto, Ontario, M3J 13P, Canada

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ACS Paragon Plus Environment

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ABSTRACT

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The aim of this work is to understand the changes in the observed phenomena during particle-

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laden drop impact. The impact of millimetre-size drops was investigated onto hydrophilic (glass)

4

and hydrophobic (polycarbonate) substrates. The drops were dispersions of water and spherical

5

and nearly iso-dense hydrophobic particles with diameters of 200 µm and 500 µm. The impact

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was studied by side and bottom view images in the range 148≤We≤744 and 7092≤Re≤16368.

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The particles suppressed the appearance of singular jetting and drop partial rebound, but

8

promoted splashing, receding break-up and rupture. The drops with 200 µm particles spread in

9

two phases: fast and slow, caused by inertial and capillary forces, respectively. Also, the increase

10

in volume fraction of 200 µm particle led to a linear decrease of the maximum spreading factor

11

caused by the inertia force on both hydrophilic and hydrophobic substrates. The explanation of

12

this reduction was argued to be the result of energy dissipation through frictional losses between

13

particles and the substrate.

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INTRODUCTION

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The impact of drops containing solid particles – particle-laden drops - on substrates is

16

relevant to many technologies, for example, to printed electronics1,2, additive manufacturing3–5,

17

spraying of liquid friction modifiers6,7 and plasma coating technology8. These technologies can

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benefit from a better understanding of impact phenomena for particle-laden drops through

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fundamental information gleaned from this work.

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To better understand the influence of particles on drop impact, first it is useful to consider the

21

range of phenomena that one sees for pure liquids. Then we will present a mini-review of the


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current studies dealing with the impact of particle-laden drops, to contextualize the work still

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needed to be done.

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Impact of drops without particles. The impact of liquid drops without solid particles on a

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surface shows a variety of phenomena: “prompt” or corona splash, receding break-up, rupture,

5

temporary dry spot in a lamella during the receding of a drop, singular jet during recoil, partial or

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complete rebound, and deposition (Figure 1).

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The prompt splash is characterized by the generation of droplets directly at the contact line,

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while in corona splash, the formation of droplets occurs around the rim of a corona, away from

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the solid surface.9 The prompt splash is mainly due to surface roughness while the corona splash

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is a result of instabilities produced by the surrounding gas.10

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The splash typically leads to drop fragmentation. However, this latter phenomenon is also

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characteristic of the dynamic associated with the receding breakup. The receding break-up

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results from an uneven motion of a receding contact line (Figure 1). This uneven motion often

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leads to finger-like perturbations, which can tear-off. The chance of tearing-off becomes higher

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with the decrease of liquid viscosity as well as with the increase of receding contact angle of the

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substrate, or the increase of impact velocity.9 Drop fragmentation could be observed also as a

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consequence of drop rupture.

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The rupture occurs due to formation of holes at the impact and their subsequent growth

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(Figure 1). These holes – often indicated as dry spots - form due to the break of air bubbles

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trapped between the impacting drop and the substrate.11 The rupture depends on substrate

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wettability, and Reynolds and Weber numbers.11 The Weber number = /

22

(1)

and Reynolds number


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= /

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(2)

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include the main parameters of drop impact: the diameter of drop before impact, , and impact

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velocity of the drop, , the density, , viscosity, , and surface tension, , of drop. On substrates

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with static contact angles 102° and 105°, the rupture have been observed to occur starting at

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= 5800 and = 800.11 Also, the rupture does not happen, when holes disappear during

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receding phase. In such cases, they are often reported as temporary dry spots.12–14

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The collapse of a temporary dry spot can cause the appearance of singular jets, breaking up

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into many small drops (Figure 1). Such jets happen during the receding phase of e.g. water drops

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on superhydrophobic surfaces at = (0.6 16).14 Sometimes, receding drops can also

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rebound from the solid surface.

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The drop rebound can be partial or complete (Figure 1). The partial rebound is promoted by

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the increase of the drop impact velocity or the receding contact angle of the liquid on the

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substrate (Table 3 in ref. [9]). If the receding contact angle is greater than 100° and 25 <
200 due to inertial effects overcoming capillary forces.15


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So, according to the literature above, the mentioned phenomena are mainly determined by the

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substrate wettability and roughness as well as Weber and Reynolds numbers for drop impact.

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However, addition of particles to the liquid can modify any of the above behavior and the

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question is to what degree and which phenomenon?

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Impact of particle-laden drops. Adding particles to a drop can result in three different types

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of systems: liquid marbles16–19, wet granular pellets20–22 and suspensions (see Figure 2). In this

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paper we will mainly study suspension drops, and henceforth will focus the discussion on such

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systems.

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The outcome of the impact of a suspension drop depends on the particle distribution which can

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be homogeneous or inhomogeneous. Homogeneous suspensions are those that have particles

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randomly and somewhat equally distributed throughout the drop, in the limit, such systems are

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dense (the particle concentration near random close packing of particles in 3D, i.e. ≈ 0.6 for

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spherical particles). A homogenous suspension can be verified by examing the images of drops

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before impact. Visual inspection was used to see suspensions were homogenious. If the particles

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seen to be uniformly distributed within the drop, then it was considered homogenious. If particles

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were not distinguishable by eyes, the assessment was based on the uniformity of the drop color

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(i.e. if drop color was uniform, the suspention was thought of homogenious). Additionally, if the

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suspension was treated by ultrasonic agitation before using it in a drop releasing system , it was

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considered as homogeneous.

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The distribution of particles in a drop of an inhomogeneous suspension may be random from

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test to test. In our opinion, the multiple experiments with such drops can help identifying patterns

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that are characteristic for the drops with a uniform particle distribution.


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In any case, further we consider separately works conducted with homogeneous and inhomogeneous suspensions.

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Studies of homogeneous dense suspensions were considered only in relation to splashing23,24

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and deposition24,25. Peters et al.23 studied the splashing for drop impact of monodisperse and

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bidisperse dense suspensions onto a glass substrate. The suspensions were dispersions of water

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with ZrO2 or/and glass particles with volume fraction from 0.59 to 0.65. According to the

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authors, splashing onset for suspension drops was not correctly described by the widely used

8

relationships for pure liquids, i.e., eq 3: / / =

9

where

!

!

(3)

is a constant which its value depends on substrate roughness.26–28 This was true even

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when viscosity of the liquid was substituted by effective viscosity estimated by the formula of

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Krieger and Dougherty29. Therefore, for dense suspensions, Peters et al.23 proposed a splashing

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criterion based on an energy balance at the level of the particles in the suspension. The energy

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balance led to particle-based critical Weber number (" ) definition of: " #" " =

(4)

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where " and #" are density and radius of particles, respectively. Peters et al.23 found splashing

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onset is when " = 14.3 ± 2, and did not depend on the roughness of glass substrates in

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contrast to the case for liquids without particles. Smaller particles were more likely to escape

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than larger ones in the bimodal suspensions (suspensions contain two type of particles with

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different diameters). The proposed splash criterion does not take into account the particle

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wettability and shape. In addition, the authors did not specify the character of splashing.

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Nevertheless, the proposed splashing mechanism assumes that it can happen far away from the


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drop contact line. The evidence for the latter point together with a splashing threshold

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corresponding to " = 14.3 ± 2, can be found in the data presented by Marston et al.24.

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Marston et al.24 investigated the spreading and splashing of particle-laden drops (diameter of

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26 mm) on glass surfaces. The suspension was a dispersion of water and sand particles with

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diameters of 350 µm. The particle volume fraction was 0.55. During drop splash, the speeds of

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particles ejected were ~2 times higher than the impact velocity. The authors do not discuss the

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splashing character. However, from the images in the paper (Figure 1, 4a24), we conclude that the

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splashing character was different from liquid without particles. The impact did not create corona

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and the particles detached from drop surface not only at contact line with the substrates, but also

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away from it. The splashing onset was in the interval of impact velocities from 1.35 to 1.86 m/s,

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corresponding to the particle-based Weber number of " = 11.7 22.3. Considering the

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range, these results can be roughly conform to the criterion proposed by Peters et al.23 (eq 4). In

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addition, the author found that the spreading factors of the suspension grew as (/ )/ at

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/ < 1 similar to liquid without particles where is time lapsed after a drop impact.

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The spreading of dense suspension was studied also by Lubbers et al.25. Lubbers et al.25

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investigated the evolution of impact of dense suspension drops on smooth glass surfaces. In this

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study, particles with diameter of 250 µm and volume fraction of 0.61 were used. The drops

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flattened into a rapidly expanding monolayer and particles grouped into clusters separated by

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particle-free regions. Models derived from balancing forces acting on individual particles

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explained both the expansion dynamics and the development of the spatial inhomogeneity

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quantitatively. However, no analytical expression (or correlations) for maximum splat diameter

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was provided.


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Whereas spreading of dense suspension drops showed some similarity with the pure liquids

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when / < 1, the splashing showed many differences. The splashing onset could not be

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described by the criterion of corona splashing, and it does not depend on the substrate roughness.

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To describe the splashing onset, the particle-based critical Weber number " ≈ 14 was

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proposed. However, it has not been verified for different particle wettabilities and shapes.

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Differences in the particle-laden drop impact with respect to pure liquids were also observed in

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the case of homogeneous dilute suspensions, containing nano- and micro-particles. It is worth

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mentioning that this is an scantly studied topic, especially for micrometer sized particles. Drop

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impact of suspension with nanoparticles was considered on heated30,31 and room temperature

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substrates32. At room temperature, only the complete rebound and spreading dynamics were

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studied.

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Zang et al.32 investigated the case of aqueous droplets containing 2% by weight 20 nm silica

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nanoparticles and/or 2% by weight polymer additives on superhydrophobic surfaces. The impact

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dynamics of the aqueous drops with silica nanoparticles was similar to pure water, despite the

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increase in the viscosity and its non-Newtonian behavior (Figure 832). Only for a drop with

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particles and polymer additives, the complete rebound was damped on superhydrophobic

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substrates at high impact velocities ( ≈ 150). The transition from rebound to deposition was

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attributed to the increase of the friction force between nanoparticles and polymer aggregates with

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the substrate. Also from the presented results (Figure 732), it may be deduced that nanoparticles

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reduced the maximum spreading factor of water with polymer additives and that the effect

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depends on Weber number. At = 1, the silica nanoparticles reduced the maximum spreading

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factor by ~19%. From = 1 to = 10 the effect decreased and it became imperceptible at


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= 10 to = 100. Similar result for the complete rebound was observed for homogeneous

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suspensions with microparticles by Ueda et al.33.

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Ueda et al.33 studied drop division during its complete rebound on a superhydrophobic surface

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for water with and without calcium carbonate powder. The powder particles were cylindrical in

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shape with diameters of ~100 nm and lengths of ~2 µm. The particles distributed

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homogeneously at 1% and 10% by weight (Figure 2, 333). Ueda et al.33 found that for 10% drop,

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the particles suppressed drop division during rebound. It was explained by viscosity increase.

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The results also showed that 1% or 10% by weight of the particles does not suppress the

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rebound of aqueous suspensions at ≈ 25, and it was similar to the observations by Zang et

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al.32 for 2% by weight of nanoparticles in water drops (0 < ≤ 150).

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The changes in the impact dynamics for homogeneous dilute suspension were also mentioned

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in works of Shen et al.30 and Lee et al.34, but many questions about the role of solid particles

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remain either due to the way the experiments were performed or due to the way results were

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discussed. As an example, in Shen et al.30, when analysing the drop spreading, in addition to

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solid particles also Arabic gum was added to the carrier fluid. The additional component

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contribute to substantial change in the viscosity of the liquid (Table 130), potentially masking the

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effective influence of the dispersed particles. Sometimes, also the experimental procedure is

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unclear. For example, in Lee et al.34, the choice of the time at which the drop contact area was

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considered as maximum was not evident. Looking at the image sequence shown in the paper, the

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drop appears to continue spreading after the time considered as the maximum spreading time. So,

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in these cases, the cause of changes in drop contact area is not clear.


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Thus, in the case of homogeneous suspensions, drop impact has been studied for splashing,

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complete rebound and impact dynamics. Nevertheless, it is not clear how even these phenomena

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depend on the particle volume fraction between 0.1 to 0.5, particles’ size, wettability and shape.

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In the case of inhomogeneous dilute suspensions, drop impacts were studied for partial rebound35, impact dynamics35,36, and splashing36.

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Ok et al.35 studied the effects of particles on impact dynamics and partial rebound of a single

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drop impacting onto a smooth substrates with different wettabilities. The particles had a diameter

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of 20.1 µm and were coated by calcium phosphate. Particle-laden drops partially rebounded on

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Teflon surfaces at ≈ 180 for ≤ 0.15 , while the rebound was suppressed for = 0.2 and

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0.3. The suppression of partial rebound was explained by high quantities of particles in the drop

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neck. It was argued that the particles prevented further thinning of the drop neck.

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At ≤ 0.15, particle quantities were not enough and pinch-off happened in the point devoid of

13

particles at the neck area. Also, the authors measured the spreading factor of the suspensions

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with volume fractions: 0.1 and 0.2 at = 0.01 m/s and = 2 m/s. The suspensions were

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compared with liquids, which viscosities matched to the effective viscosity of the suspensions.

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Ok et al.35 stated that the particles had a clear effect on the deposition and those effects cannot be

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explained simply by viscosity change due to particles. At the same time, the authors seemed not

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to have characterized the particle effect. The analysis of their data shows that at = 0.009 the

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particle effect was observed on the most hydrophilic substrate (static contact angle = 38°), on

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which the particles with = 0.2 reduced final spreading factor of the drops by 10% (Figure

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3a35). At = 170, the maximum spreading factor for suspensions with 0.2 (by volume) was

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less by 5 to 10% on all substrates (static contact angles were from 38° to 112°) than for liquid

23

without the particles (Figure 435). The final spreading factor decreased by less than 5% or


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unapparent for the substrates with static contact angles from 47° to 112° (Figure 435). On the

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most wettable substrate with the static contact angle of 38°, the final spreading factor of

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suspension with = 0.2 was 50% higher than that for the liquid without particles. So, the

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particles can change the maximum and final spreading factor, and the effect depends on particle

5

volume fraction, substrate wettability and drop impact velocity. The spreading of

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nonhomogeneous dilute suspension with microparticles was studied also by Nicolas36.

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Nicolas36 studied the spreading and splashing of suspension drops with density-matched

8

particles during impact onto glass substrates. Particles’ diameters were 380 µm, 640 µm and

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720 µm. The author found that the increase of particle volume fraction reduced the final

10

spreading factor at 79 < < 6000 and 10 < < 370 (the Reynolds number, , was

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calculated based on viscosity of liquid without particles). This was explained by an energy

12

balance model and the assumption that the viscosity, , in Reynolds number is given by the

13

effective viscosity, , , calculated by Krieger-Dougherty model36 as: , = (1 −

../0 ) 0.68

(5)

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To compare the spreading results from the works of Nicolas36 and Ok et al.35, we determined

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the Reynolds number for = 0.2 using eq 5. So, Nicolas36 observed the decrease of final

16

spreading factor due to the particles at 41 < < 1564 and 10 < < 370. This range

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includes = 870 and = 170, where Ok et al.35 observed the opposite behavior: 20.1 µm

18

particles increased final spreading factor on the most hydrophilic surface (static contact

19

angle was equal to 38°). Unfortunately, Nicolas36 did not present the information about substrate

20

wettability. So, the discrepancy may be caused by different substrate wettability or the different

21

particle size. In addition, it could be probably caused by a distorted drop contact area in the case


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of Ok et al.35. This was one of the reasons along with drop fragmentation used by Nicolas36 to

2

explain the increase of the maximum spreading factor at higher impact velocities (at ≥ 6000

3

and ≥ 370). Besides spreading changes, Nicolas36 found that the splashing threshold

4

decreased with the increase of . This observation cannot be explained by eq 3 and contradicts

5

the assumption that the suspension viscosity increases with larger values of according to eq 5.

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The particles in the suspensions stimulated the splashing instead of suppressing it. The author did

7

not see the influence of particle size on the splashing onset (Figure 4b36). We think that measured

8

data in spreading/splashing maps is not sufficient to arrive at such conclusion. In contrast, the

9

splashing maybe starts at lower impact velocity for 720 µm, than for 380 µm particles

10

(Figure 4b36).

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Thus, the survey of the literature shows that using the effective viscosity helps explain some of

12

the observed phenomena for the impact of drops containing solid particles; nevertheless its use

13

remains questionable for both nano‐ and micro-particles. In the case of nanoparticles, their

14

addition to a Newtonian liquid not only increases its viscosity, but also makes it dependent on

15

the shear rate, i.e. the liquid becomes non‐Newtonian and Eq. (5) is no longer applicable. In the

16

case of micro‐particles, the increase of the effective viscosity with the growth of particle volume

17

fraction allowed explaining the decrease of the spreading factor and the suppression of drop

18

splitting under its rebound. However, the concept of effective viscosity did not explain the

19

decrease of splashing threshold with the increase of particle volume fraction.

20

Moreover, the examined works of suspension drops show that there are the following

21

questions still open. How do solid particles influence the rupture, appearance of dry spot or

22

singular jets? How do particles’ size and their volume fraction influence all of the typical


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phenomena observed for pure liquids? How do particles’ wettability and shape influence the

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impact phenomena?

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In our work, we considered the two first questions for dilute inhomogeneous suspensions with

4

microparticles distributed randomly. To cover majority of the possible phenomena, we studied

5

the drop impact of suspensions on hydrophilic and hydrophobic surfaces.

6

MATERIALS AND METHODS

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Drops with diameter of 3.8 ± 0.1 mm were used. The millimetre drops are mainly used in

8

impact studies, so they are useful for comparative analysis. As carrier fluid, water was selected

9

(deionized reagent grade III, Acros Organics). The surface tension of water allows using

10

substrates with different wettability, thereby allowing to cover a maximum number of possible

11

phenomena seen for drop impact onto surfaces. Surface tension of water was measured to be

12

72.8 mN/m at room temperature by the pendant drop method (KRUSS DSA30S drop shape

13

analyzer). Drop impact studies were done at room temperature, when the density, , and

14

viscosity, , of water are 1 g/cm3 and 0.890 mPa·s, respectively (according to the manufacturer

15

and Kestin et al.37).

16

The impact velocity of the drop was chosen in the range from 1.7 to 3.7 m/s which

17

corresponds to 150 ≤ ≤ 750 and 7100 ≤ ≤ 16400 (see the Supporting Information for

18

details of the drop generation). This allowed us to examine the effect of the particles on various

19

possible phenomena (i.e. splashing, deposition, partial rebound, and jetting) occurring during

20

drop impacts onto substrates. At velocities below the studied range, only drop deposition will be

21

observed. At higher impact velocities, only drop fragmentation will be observed.

22

The influence of particles was studied for round microparticles (diameter of 200 and 500 µm)

23

from Cospheric (BLPMS-1.00 180-212 µm and BLPMS-1.00 425-500 µm). The particle


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diameters were chosen so that they lay in a range in which there are other published data to allow

2

comparison. Also, the selected particle sizes are easily distinguishable by high speed video

3

recording systems with a wide field of view (~30 × 30 mm), which are used in drop impact

4

studies. The microparticles were hydrophobic to study the influence of their wettability in

5

comparison with published data obtained for hydrophilic particles. The contact angles of water

6

based on eight measurements were 91±5° and 95±7° for the 200 µm and 500 µm particles,

7

respectively (see Grishaev38 for details of the measurements).

8

The particle-laden drops fell on transparent hydrophilic and hydrophobic substrates. As

9

hydrophilic substrates, cleaned borosilicate glass slides (Nexterion slides glass B, Schott) with

10

the size of 70 × 70 × 1 mm ( × 4 × 5) were used. The glass slides were cleaned in UV/ozone

11

system (PSD-UV4, Novoscan). Pre-cut polycarbonate plates (769 − 8720, RS components)

12

with same size as above were used as the hydrophobic substrates. Before experiments,

13

electrostatic charges were removed using ionized air generated by an anti-static gun (Milty Pro

14

Zerostat 3, Armourhome).

15

Wettability of the substrates was characterized by measurements of the advancing and receding

16

contact angles of deionized water using drop shape analyze system DSA30S (Kruss). For the

17

glass slides, advancing and receding angles were less than 5°. For the polycarbonate surfaces,

18

advancing contact angle was 102 ± 1°, and receding contact angle was 79 ± 2°. The surface

19

mean roughnesses of the substrates were less than 3 nm for glass (according to the manufacturer)

20

and less than 1µm for polycarbonate (typical value for such substrates).

21

The drop impact was studied by two high-speed cameras from side and bottom views. The

22

details of experimental set-up is presented in the Supporting Information. For every impact

23

velocity and particle diameter, 6 to 29 tests were done.


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The drop impact velocity was found by the measurement of drop displacement in two

2

successive images of side view and the division of this value by time between the frames

3

(1/2500 s in our experiments). The equivalent diameters of a drop before impact and a drop

4

contact area with a substrate were determined by the formula 64 ∙ 8/9, where 8 – drop areas on

5

side and bottom views, respectively (see the Supporting Information for details).

6 7

RESULTS

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We have obtained a large body of interesting data on various aspects of the drop impact

9

morphology. So, we present the results, and the discussions separately. In this section, the data

10

are categorized into two subsections for hydrophobic and hydrophilic substrates due to

11

substantial differences in the drop impact morphology.

12

Hydrophobic substrates

13

During a single event of water drop impact onto the hydrophobic substrate (polycarbonate)

14

multiple phenomena such as temporary dry spot, singular jet, and partial drop rebound can be

15

observed in a certain sequence, see Figure 3A ( = 150, which is calculated by using equation

16

(1)).

17

The probabilities of appearances of any of the phenomena decreased with the increase of the

18

impact velocity, and respectively, Weber number (Figure 4A). The reason for observed trend is

19

explained in Grishaev38 for interested readers.

20

The addition of 200 µm particles to the water drops with volume fraction up to 0.33,

21

suppressed the appearance of the singular jet in the range of Weber numbers 150 < < 750;

22

and the partial drop rebound was also suppressed for when the particle volume fraction was more

23

than 0.02 for the same range (Figure 3B).


15

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1

The appearance of dry spots was completely suppressed at Weber numbers equal to 710 ± 23;

2

and at Weber numbers = 153 ± 4 and = 440 ± 14 only for particle volume fractions

3

greater than 0.12 (Figure 4B). For the drops with the particle volume fraction less than 0.12, we

4

observed a tendency of reduced probability for dry spots to form in comparison with pure water

5

(Figure 4B). In some experiments the form of the dry spot had a different look (details can be

6

seen in Grishaev38).

7

The addition of 200 µm particles led to the splashing and drop receding break-up of the drops

8

upon impact onto the hydrophobic surfaces, which were not observed in the case of pure water.

9

During the initial stages of a water drop with 200 µm particles impact onto a hydrophobic

10

substrate, small drops or particles ejection can occur. In the case of a drop ejection, a particle is

11

often in them. The splashing can occur from the drop contact line, which is similar to the prompt

12

splash (Figure 5A), and far from it (Figure 5B). The splashing was not observed at Weber

13

numbers equal to 153 ± 4, and for = 440 ± 14 – when was less than 0.06

14

(Figure 4C). At = 710 ± 23, splashing can be seen only for particle volume fractions less

15

than 0.01 (Figure 4C).

16

The break-up of water drops with 200 µm particles was seen when the drop recoiled (Figure

17

3B); the particles were not uniformly distributed over the drop contact line during the spreading.

18

This caused disturbances at the drop edge in the form of fingers. These perturbations increased

19

when the drop recoiled as the liquid edge moved faster in the areas with less particles. The

20

nonuniform motion of the drop edge led to the stretching of one or more fingers containing

21

particles, from which satellite drops formed.

22

Figure 4D shows Weber numbers and particle volume fractions when receding break-up was

23

observed. The absence of the receding break-up (e.g. for = 150 and > 0.05) can be


16

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1

explained by a comparative analysis of the behavior of the liquid at the concentrations less and

2

greater than 0.05 (Figures 3B and 3C, respectively). As seen in Figure 3C, at high concentrations

3

the particles were located more uniformly along the edge of the drop. This led to less disturbance

4

of the drop edge at the maximum spreading, and to more uniform motion of the liquid during the

5

drop recoil, which does not cause the elongation of the fingers.

6

Based on the information about the receding break-up (Figure 4C) and the splashing (Figure

7

4D), one can determine when the drop fragmentation was not seen, i.e. when = 153 ± 4 and

8

> 0.05.

9

The spreading factors (/ ) for water, and water with 200 µm particles are shown in Figure

10

6A for = 152 ± 5; the maximum spreading factor on the hydrophobic surfaces decreases

11

with the increase of the particle volume fraction (Figure 6B). This trend was also observed for

12

= 450 and = 750. The linear regressions described 91 to 97% of the variance, so the

13

maximum spreading can be said to change linearly with the particle volume fraction. The slope

14

of the regression lines are presented in Table 1.

15

Similar to pure water, the splats of water with 200 µm had also the form of a circle with a

16

wavy edge contour at the maximum spreading (Figures 3B, C). The amplitude of the undulations

17

was not greater than 10 % relative to the equivalent drop radius for any of the systems. So, the

18

equivalent diameter of drop contact area is an appropriate descriptor for understanding the

19

changes in the spreading induced by 200 µm particles.

20 21

In contrast to the 200 µm particles, 500 µm particles were often in agglomerations before drop impact. Typically, the agglomeration composed of five or more particles.


17

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1

The singular jet was suppressed for systems with 500 µm particles at = 720 ± 20 and

2

< 0.07, = 450 ± 20 and < 0.3. It was also suppressed at = 720 ± 20 and

3

< 0.1 for most cases. The partial rebound was suppressed in all experiments.

4

Dry spots in the lamella might be formed during the spreading of particle-laden drops. At the

5

same time they can be temporary (disappearing during receding phase) or permanent (leading to

6

a rupture). The dry spot formation was different from the case of pure water. We did not find any

7

dependence of dry spots appearance upon or , except that the rupture mainly occurred at

8

= 150 and 450 (Figure 4E).

9

The splashing of water drops with 500 µm particles began at = 156 and = 0.05

10

(Figure 4F). The sizes of ejected drops and their quantities were greater for water with 500 µm

11

particles than for water with 200 µm at similar impact velocities and particle volume fractions. If

12

the splashing happened away from the contact line, detached particles (500 µm) or small drops

13

could rebound at large angles relative to the substrate plane.

14

The receding break-up for water with 500 µm particles was observed at = 450 and

15

= 750 in all experiments, and also at = 150 in the range of particle volume fraction

16

0.05 < < 0.1 (Figure 4G). The length and quantity of fingers were higher for 500 µm

17

particles than for 200 µm particles, so the probability of receding drop break-up was also higher.

18

The time dependencies of spreading factor of water, and water with 500 µm particles for

19

= 150 to 750 are given in the Supporting Information (Figure S4). The spreading factor

20

decreased with increasing particle volume fraction. The failure of this trend in some experiments,

21

for example at = 0.07 in Figure S4A or at = 0.06 in Figure S4C, may be due to the

22

presence of agglomerations in a drop before impact.

23


18

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1

Hydrophilic substrates

2

When a water drop impacts onto a hydrophilic substrate, it spreads in a symmetric thin layer

3

(Figure 7A). Dry spots, drop recoil, singular jet, or a partial rebound did not appear as in the case

4

of hydrophobic substrates; this behavior was observed for 150 < < 750.

5

Addition of 200 µm particles to water drops resulted in a disturbance of the drop contact line

6

after an inertial spreading onto hydrophilic substrates (Figure 7B), as well as, in some cases, its

7

splashing. Receding break-up, temporary dry spots or rupture was not observed, unlike for the

8

case of drop impact onto a hydrophobic substrate.

9

For hydrophilic substrates only one type of splashing was observed: particles or small droplets

10

ejected from the drop contact line. This character of splashing was similar to what occurred on

11

the hydrophobic surface in some cases (Figure 5B). The splashing did not occur at

12

= 153 ± 4, and at = 440 ± 14 or 710 ± 23 – when < 0.03 (Figure 8A).

13

For water with 200 µm particles we observed two stages of spreading: fast - within the first 12

14

ms, and slow – from 12 ms to 1 s (Figure 6C). The maximum spreading factor during fast stage

15

decreased with the increase of particle volume fraction. This reduction had a linear character for

16

Weber numbers from 150 to 750 (Figure 6D). The slope of the linear regressions did not depend

17

on the impact velocities (statistically verified see Table 1) unlike systems involving hydrophobic

18

surfaces.

19

At the maximum spreading, caused by inertia, the undulations of drop contact line were less

20

than 8% of radius for any system studied. As such, the equivalent diameter can be used to

21

describe the changes in drop spreading caused by particles.

22

Phenomena like receding break-up, dry spots or rupture was not observed for water drops with

23

500 µm particles impacting onto hydrophilic substrates. The splashing character of water with


19

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Page 20 of 40

1

500 µm particles was similar to the case of water with 200 µm particles on a hydrophilic surface,

2

only the size of detached drops and their or particles’ rebound angle from surface could be much

3

larger. The splashing was even observed at = 150. The increase of Weber number led to the

4

increase in splashing probability (Figure 8B).


20

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1

Langmuir

DISCUSSION

2

It was observed that adding particles suppressed the appearance of singular jetting and drop

3

partial rebound on hydrophobic substrates. Furthermore, particles caused early splashing,

4

receding break-up and rupture for impact on hydrophobic surfaces, and early splashing for

5

hydrophilic surfaces.

6

The splashing character of drops with particles was different from that observed in the case of

7

pure liquids9, and it was dependent on the substrate wettability. In the case of hydrophilic

8

substrates - particles or drops (with diameter of the same order as the particles) ejected from the

9

drop contact line, whereas in the case of hydrophobic surfaces, it can happen either from contact

10

line (as in prompt splash) or away from it. The ejection of particles away from the contact line

11

was similar to those observed in the impact of dense suspension with hydrophilic particles onto

12

hydrophilic substrates (e.g. see Figures 1a in Lubbers et al.25, and Marston et al.24). The main

13

difference from literature compared to our results was the observation of the ejection not only of

14

particles or liquid drops containing a particle, but also of drops without particles. It should be

15

noted that the diameters of the ejected drops were roughly a particle’s diameter.

16

The particles also initiate the rupture of the lamella and/or receding break-up for impact on

17

hydrophobic surfaces. The lamella rupture was due to the growth of dry spots, which in turn

18

appeared due to break-up of air bubbles attached to a substrate and a particle or only to a

19

substrate. The capture of the air bubbles occurred at the beginning of the spreading phase, and

20

bubbles’ diameters were between 150 and 250 µm. In turn, the receding break-up happened due

21

to the amplification of asymmetric drop motion during recoil. Table 2 summarizes the tendencies

22

seen in changing the morphology of drop impact due to presence of particles.


21

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Page 22 of 40

1

The probability of splashing increased with an increase in impact velocity, particle size or

2

particle volume fraction. The dependence on and :" were similar to that observed for dense

3

suspensions with hydrophilic particles impacting onto hydrophilic substrates23.

4

As well as splashing, the probability of receding break-up grew with increasing impact

5

velocity or particle size. Increasing the speed or particle size resulted in elongation of fingers

6

during spreading and receding phases.

7

Increasing the particle size also increased the probability of rupture. This was due to an

8

increase in the probability of capturing an air bubble on hydrophobic surfaces and/or the particles

9

at beginning of the impact.

10

In constrast to rupture, receding break-up and the splashing, the probability of partial rebound

11

decreased with the increase of impact velocity, particle diameter or volume fraction. This was

12

due to either the amplification of asymmetric motion of a drop during its recoiling (Figure 3A

13

and 3B), or the fragmentation of a drop (via splashing, receding break-up or rupture), or a

14

decrease in the recoil velocity (e.g. see the slope of curves in Figure 6A between 10 and 20 ms

15

for pure water and = 0.33). These reasons are different from mechanism proposed by Ok et

16

al.35. They explained the suppression of partial rebound under increasing via a large number of

17

particles in a drop neck.35 The difference in proposed mechanism can be caused by using only

18

side view images or lower Reynolds numbers in the work of Ok et al.35 ( < 2000 and

19

< 180).

20

While particles suppressed partial rebound, they caused drop fragmentation via splashing,

21

rupture and receding break-up. Therefore, with increasing impact velocity, the particle diameter

22

or concentration, the probability of drop deposition fell.

23


22

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1

Other dependencies, presented in Table 2 and marked by asterisks, had a complicated

2

character, i.e. their probability depended on several impact parameters. To understand them, it is

3

necessary to refer to appropriate regime maps in Figure 4. For instance, receding break-up had a

4

complex dependency on particle volume fraction in the case of 200 µm particles (Figure 4D). At

5

= 150, the increasing promoted the receding break-up at < 0.06, but at > 0.06 we

6

did not observe the receding break-up.

7

Adding particles also led to a change in the dynamics of the spreading factor for both types of

8

substrates. For hydrophilic substrates spreading of water drops with 200 µm particles had two

9

modes: fast and slow (Figure 6C). The first stage is caused by the action of inertial forces, and

10

the second - by the capillary forces, i.e. surface wicking. The slow (capillary stage) spreading

11

was not observed for pure water drops. Also, the maximum spreading factor, caused by inertia,

12

decreased linearly with the increase of particle volume fraction. This decrease did not depend on

13

the variation of the impact speed in the range of 1.7 to 3.7 m/s (Table 1).

14

The reduction of the maximum spreading factor is opposite to the observations of Nicolas36 for

15

the salt water with 380 µm and 720 µm particles of polystyrene at 6000 < < 10000 and

16

370 < < 1276. Nicolas36 linked the increase of maximum spreading factor to non-circular

17

form of drop contact line and the fragmentation of impacting drops due to their break-up. In our

18

experiments, the contact lines of drops with 200 µm particles were less disturbed than in the case

19

of Nicolas36. This is due to the smaller particle size.

20

On hydrophobic substrates, the maximum spreading factor of water with 200 µm particles also

21

decreased linearly with increasing particle volume fraction. Unlike the hydrophilic substrates, the

22

rate of decrease of spreading factor with increasing particle volume fraction grew with increasing

23

the impact velocity from = (1.7 2.9) m/s (Table 1). The reduction rates of spreading factor


23

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Page 24 of 40

1

with increasing volume fraction of the particles, are smaller on the hydrophobic than hydrophilic

2

substrates (Table 1). Since the rate of reduction for spreading factor depended on substrate

3

wettability and drop impact velocity, the decrease of spreading factor cannot be explained only

4

by the decrease of water volume fraction in a drop.

5

Other reasons for a reduced spreading factor can be an increase in viscous dissipation caused

6

by particles, as well as by energy dissipation due to the possible friction between the particles

7

and the substrate. To illustrate the latter factor, it is necessary to consider the behaviour of

8

particles during drop spreading.

9

When a drop spreads on a substrate, particles are mainly at its surface. This occurs due to the

10

deformation of the drop into a lamella and lift forces acting on particles by the fluid. When

11

particles appear at the drop surface, they are retained there as semisubmerged particles under the

12

action of capillary forces (since the static contact angle of water on a particle was ~ 90°). For

13

semisubmerged particles, the distance between their bottom and the top of the substrate is

14

determined by the thickness of the lamella. If the thickness of the lamella is less than the particle

15

radius, particles may contact with the substrate. In the contact area there is friction between

16

moving particles and the substrate (note there maybe a lubricating film, so the friction is not

17

necessarily a dry one). So, the probability of such mechanism and its contribution to energy

18

dissipation is determined by the thickness of a lamella.

19

The thickness of a lamella can be evaluated by the diameter of the drop contact area, and

20

using an assumption that a drop takes the form of a pancake when spreading over a substrate

21

surface. For hydrophilic substrates, at the lowest impact velocity = 1.7 m/s the lamella

22

thickness is already ~100 µm at the maximum spreading which means that particles can touch

23

the substrate. Obviously, for higher impact velocities, this would be even more apparent. So, on


24

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1

hydrophilic substrates, the decrease rate of spreading factor due to friction of 200 µm particles

2

with substrates should be generally the same at = (1.7 3.7) m/s. This was confirmed by

3

experiments (see coefficients 8 for hydrophilic substrates in Table 1).

4

In the case of the hydrophobic substrates, the lamella thickness is ~170 µm and 100 µm at

5

= 1.7 m/s and = 2.9 m/s, respectively. So, on hydrophobic substrates, the decrease rate of

6

spreading factor due to friction of particles with substrates should be less for = 1.7 m/s, than

7

for = 2.9 m/s and = 3.7 m/s. This was also confirmed by experiments (Table 1).

8

Thus, the results show that the explanation of the reduction of the maximum spreading factor

9

should take into account the mechanism of energy dissipation through frictional losses between

10

particles and the substrate.

11


25

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1

Page 26 of 40

CONCLUSION

2

Addition of 200 µm or 500 µm particles to water drop changed its impact behavior on

3

hydrophilic and hydrophobic surfaces. It was found that the particles suppressed the appearance

4

of singular jetting and drop partial rebound on hydrophobic substrates. Also, on hydrophilic

5

substrates the particles caused early splashing, and on hydrophobic - early splashing, receding

6

break-up and rupture.

7

The occurrences of these phenomena depended on the impact velocity, the particle diameter

8

and volume fraction. The increase of drop impact velocity led to an increase of the probabilities

9

for splashing and receding break-up. The increase of particle size caused the increase of the

10

probabilities for splashing, receding break-up and reduction of the probability for partial-

11

rebound. The increase of particle volume fraction increased the likelihood of splashing and

12

decreased the likelihood of partial rebound. So, the increase of mentioned parameters decreases

13

the probability of drop deposition without its fragmentation.

14

The particles changed the spreading dynamics as well. The addition of the 200 µm particles to

15

a water drop led to the fact that its spreading on a hydrophilic substrates happened in two phases:

16

fast and slow. The fast spreading was caused by the action of inertial forces, and slow – by the

17

capillary forces, i.e. surface wicking. The maximum spreading factor, caused by inertia, reduced

18

linearly with the increase of particle concentration on hydrophilic and hydrophobic substrates.

19

The explanation of this reduction was argued to be the result of energy dissipation through

20

frictional losses between particles and the substrate.

21 22


26

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1

ASSOCIATED CONTENT

2

Supporting Information. The details of experimental apparatus and image processing are

3

supplied as supporting information. Also, in supporting information you can find the image

4

sequence of splashing and the plots of drop spreading dynamics for water with 500 µm particles

5

on hydrophobic substrates. This material is available free of charge via the Internet at

6

http://pubs.acs.org.

7

AUTHOR INFORMATION

8

Corresponding Author

9

*To whom correspondence should be addressed, [email protected]

10

Author Contributions

11

The manuscript was written through contributions of all authors. All authors have given approval

12

to the final version of the manuscript.

13

Funding Sources

14

Transport Canada (Clean Rail program), the Natural Science and Engineering Research

15

Council of Canada (NSERC) and the Belgian Federal Science Policy Office (BELSPO).

16

ACKNOWLEDGMENT

17

We would like to thank Dr. Christophe Minetti (ULB) for providing the software of particle

18

counting and Patrick Queeckers (ULB) for helping with software issues for the syringe pump and

19

computers. Also, the authors acknowledge funding from Transport Canada (Clean Rail program),


27

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Page 28 of 40

1

the Natural Science and Engineering Research Council of Canada (NSERC), and from the

2

Belgian Federal Science Policy Office (BELSPO).

3 4

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Lubbers, L. a.; Xu, Q.; Wilken, S.; Zhang, W. W.; Jaeger, H. M. Dense Suspension Splat: Monolayer Spreading and Hole Formation after Impact. Phys. Rev. Lett. 2014, 113 (4), 2– 6.

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Stow, C. D.; Hadfield, M. G. An Experimental Investigation of Fluid Flow Resulting from the Impact of a Water Drop with an Unyielding Dry Surface. Proc. R. Soc. A Math. Phys. Eng. Sci. 1981, 373 (1755), 419–441.


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Mundo, C.; Sommerfeld, M.; Tropea, C. Droplet-Wall Collisions: Experimental Studies of the Deformation and Breakup Process. Int. J. Multiph. Flow 1995, 21 (2), 151–173.

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Cossali, G. E.; Coghe, A.; Marengo, M. The Impact of a Single Drop on a Wetted Solid Surface. Exp. Fluids 1997, 22 (6), 463–472.

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Krieger, I. M.; Dougherty, T. J. A Mechanism for Non-Newtonian Flow in Suspensions of Rigid Spheres. Trans. Soc. Rheol. 1959, 3 (1), 137–152.

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Shen, J.; Liburdy, J.; Pence, D.; Narayanan, V. Single Droplet Impingment: Effect of Nanoparticles. In ASME 2008 Fluids Engineering Division Summer Meeting collocated with the Heat Transfer, Energy Sustainability, and 3rd Energy Nanotechnology Conferences; 2008; pp 621–628.

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Murshed, S. M. S.; de Castro, C. a N. Spreading Characteristics of Nanofluid Droplets Impacting onto a Solid Surface. J. Nanosci. Nanotechnol. 2011, 11 (4), 3427–3433.

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Zang, D.; Wang, X.; Geng, X.; Zhang, Y.; Chen, Y. Impact Dynamics of Droplets with Silica Nanoparticles and Polymer Additives. Soft Matter 2013, 9, 394–400.

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Ueda, Y.; Yokoyama, S.; Nomura, M.; Tsujino, R.; Iguchi, M. Bouncing Behaviors of Suspension Liquid Drops on a Superhydrophobic Surface. J. Vis. 2010, 13 (4), 281–283.

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Lee, S. J.; Huh, H. K.; Kwon, D. H. Energy Dissipation of Graphene Colloidal Suspension Droplets Impacting on Solid Substrates. RSC Adv. 2014, 4 (14), 7216–7224.

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Ok, H.; Park, H.; Carr, W.; Morris, J.; Zhu, J. Particle-Laden Drop Impacting on Solid Surfaces. J. Dispers. Sci. Technol. 2005, 25 (4), 449–456.

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Nicolas, M. Spreading of a Drop of Neutrally Buoyant Suspension. J. Fluid Mech. 2005, 545, 271–280.

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Kestin, J.; Sokolov, M.; Wakeham, W. A. Viscosity of Liquid Water in the Range −8 °C to 150 °C. J. Phys. Chem. Ref. Data 1978, 7 (3), 941–948.

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Grishaev, V. Impact of Particle-Laden Drops on Substrates with Various Wettability. Ph.D. Thesis, Université libre de Bruxelles, 2015.

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Figure 1. Possible outcomes of a drop impact (without particles) on dry solid substrates. In each

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row, the panels should be read from left to right.


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Figure 2. Forms of particle-laden drops.

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Figure 3. Side and bottom views of drop impacts onto hydrophobic substrates. (A) Water at

3

= 150 ( = 3.82 mm and = 1.68 m/s). (B) Water with 200 µm particles at = 151

4

( = 3.79 and = 1.69 m/s) and = 0.04. (C) Water with 200 µm particles at = 154

5

( = 3.85 and = 1.70 m/s) and = 0.12. The white cross shows the point of a drop impact.

6


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1 2

Figure 4. Appearance probability, ;, and regime maps of drop impact phenomena on

3

hydrophobic substrates versus Weber number, W, and particle volume fraction, . (A) Water.

4

(B-D) Water with 200 µm particles. (E-G) Water with 500 µm particles.

5


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Figure 5. Side and bottom views for splashing of water drops with 200 µm particles on

3

hydrophobic (polycarbonate) surfaces. (A) = 437 ( = 3.77 mm and = 2.89 m/s) and

4

= 0.08. (B) = 725 ( = 3.87 mm and = 3.67 m/s) and = 0.04.

5


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1 2

Figure 6. Spreading of water drops with 200 µm particles: (A) on hydrophobic (polycarbonate)

3

surface versus time at = 152 ± 5 and = 7258 ± 170 ( = 3.83 ± 0.06 mm and

4

= 1.69 ± 0.02 m/s) and different particle volume fraction, ; (B) maximum spreading factor

5

of water drops with 200 µm particles on hydrophobic surface versus particle volume fraction, ;

6

(C) on hydrophilic glass substrates at = 153 ± 3 and = 7255 ± 116 ( = 3.83 ± 0.05

7

and = 1.69 ± 0.01); (D) maximum spreading factor of water drops with 200 µm particles on

8

the hydrophilic glass substrates versus . numbers were calculated by Eq. (2) using the

9

viscosity of pure water. These Figures are plotted in Figure S5 of the Supporting Information, in

10

the same scale for the interested reader.


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Figure 7. Side and bottom views of drop impact onto hydrophilic substrates. (A) Pure water at

4

= 152 ( = 3.81 mm and = 1.69 m/s). (B) Water with 200 µm particles at = 153

5

( = 3.83 and = 1.70 m/s) and = 0.05.

6


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Figure 8. Regime maps for splashing of drops on hydrophilic substrates. (A) Water with 200 µm

3

particles. (B) Water with 500 µm particles.

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Table 1. Coefficients A and B of the linear regression 8 + = for maximum spreading factor

2

caused by inertial force on hydrophilic and hydrophobic substrates (see Fig. 6). The error bars of

3

the estimated parameters are equal to two standard deviations. U (m/s)

Hydrophobic

Hydrophilic

A

B (pure water)

A

B (pure water)

1.7

-3.3±0.6

3.85±0.08

-5.1±0.5

4.94±0.04

2.9

-4.7±0.5

4.89±0.05

-6.2±0.6

5.76±0.04

3.7

-5.1±1.9

5.45±0.05

-5.5±0.5

6.11±0.06

4 5 6

Table 2. Tendency of the appearance of observed phenomena when water drops with solid

7

particles impact a surface as velocity (), or particle diameter (:" ), or particle concentration ()

8

increases.

9

The increase of

Splashing

Temporary dry spot

Rupture

Receding break-up

Partial rebound

Deposition

↑

*

*

↑

↓

↓

:"

↑

*

↑

↑

↓

↓

↑

*

*

*

↓

↓

* Complex dependence. See appropriate regime maps in Figure 4.

10


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Table of Contents Graphic

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Complex Drop Impact Morphology - ACS Publications - American

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