DOI: 10.1007/s13367-019-0017-2
Spreading behaviors of high-viscous nanofluid droplets impact on solid surfaces
Hai Long Liu, Xuefeng Shen, Rui Wang, Yuanping Huo, Changfeng Li, and Junfeng Wang*
School of Energy and Power Engineering, Jiangsu University, Zhenjiang 212013, China (Received March 11, 2019; final revision received July 6, 2019; accepted July 22, 2019) In this work, the impact dynamics of high-viscous nanofluid droplets onto a solid surface has been inves- tigated experimentally by means of high-speed camera visualization technique. We dispersed various nanoparticles (multiwall carbon nanotube (MWCNT), nano-graphene, and nano-graphite powder) into high- viscous base fluid (epoxy resin) to obtain the stable and homogenous nanofluids without surfactant addi- tives. The well dispersed nanofluids show different degree of shear-thinning behaviors, and the shear-thin- ning properties of those fluids have been characterized by the power-law rheology model. The dynamic contact angle (DCA), transient dimensionless height, and transient contacting factor along with the spread- ing time under different Weber numbers (We) have been investigated. The results show that the nanofluid with a lower shear viscosity over the entire range of the shear rates results in larger variations of the con- tacting factor and the dimensionless height. The effect of surface wettability on droplet impact behaviors is more significant for the fluid with higher shear viscosity and less shear-thinning degree during the reced- ing phase. The latter spreading and receding motions of the droplet with higher shear viscosity and shear- thinning degree are suppressed significantly, regardless of the Weber numbers in current study. Finally, a model based on experimental data has been proposed to predict the maximum spreading factor of high-vis- cous droplet impact on solid surface.
Keywords: nanofluids, droplet impact, shear-thinning, spreading dynamics
1. Introduction
The phenomenon of a liquid droplet impacting on solid surface is not only an interesting phenomenon in nature, but also plays a crucial role in a variety of engineering applications such as 3D printing (Jiao et al., 2018), ink-jet printing (Yoo and Kim, 2015; Zhang et al., 2018), spray coating (Srikar et al., 2009), fabrication of micro-lens (Bertola, 2015), biological tissue manufacturing (Derby, 2012), and efficient heat transfer (Breitenbach et al., 2018;
Richter et al., 2005). In general, the impact process could be classified into five time-sequential phases: kinematic, spreading, relaxation, wetting, and equilibrium (Rioboo et al., 2002) and the outcomes include spreading, receding, splashing, and bouncing (Yarin, 2006). The impact dynam- ics are determined by both the properties of the droplet and the physicochemical characteristics of the solid sur- face. These effects can be described in terms of several dimensionless numbers: the Reynolds number (Re = DV/
) which represents the competition between inertial and viscous forces, and Weber number (We = DV2/) which represents the ratio of inertial to surface tension forces.
Alternatively, the Ohnesorge number (Oh = / ) and Capillary number (Ca = V/) are also used in related lit- erature (Josserand and Thoroddsen, 2016). Substantial work has focused on the droplet spreading with Newto- nian fluids which can be found in the review articles (Jos-
serand and Thoroddsen, 2016; Yarin, 2006). However, a large amount of liquids used in industries always contain different kinds of additives such as surfactants, polymers, and particles, and those fluid flows are essentially non- Newtonian (Liu et al., 2012; Masiri et al., 2019).
Since Choi (1995) first introduced “nanofluids” which are the suspensions of nanometer-sized particles, those engineering media have been used in numerous applica- tions. It has been found that the nanoparticles can bring prominent thermal and electrical property enhancement to the base fluid (Mehrali et al., 2015; Özerinç et al., 2010).
The major obstacle of preparing nanofluid is the produc- tion of a homogeneous suspension of nanoparticles, mostly because the particles always tend to aggregate due to the van der Walls forces among particles (Mehrali et al., 2015). For instance, CNT are prone to entangle and aggre- gate in fluids due to their nonreactive surfaces, very large specific area and aspect ratio which cause the high surface effect and interactions (Park et al., 2002). Duan et al.
(2012) found that the graphite water nanofluids might have the particle aggregation just after the preparation and the size of aggregation in nanofluids would increase with the increase of the particle volume concentration and the holding time. Surfactants are often used to improve the dispersity of nanoparticles. However, the addition of sur- factant can also change the rheological behavior of the base fluid and becomes non-Newtonian. In the present experiment, the high-viscous epoxy resin was used as base fluid to avoid particle agglomeration caused by Van der
D
*Corresponding author; E-mail: [email protected]
Waals force (Yearsley et al., 2012), allows one can ana- lyze the pure effect of nanoparticles without surfactants.
Therefore, the effect of nanoparticle on droplet spreading can be studied independently.
The viscosity is a key property of nanofluids in indus- trial applications. It is found that the nanofluids exhibit significantly higher viscosity compared to their base fluids (Kole and Dey 2013; Moghaddam et al., 2013), and demonstrate different degree of non-Newtonian behaviors depending on nanoparticle concentration, temperature, base fluids fluidity, shear rate, and stress, as well as type and size of nanoparticles (Murshed and Estellé, 2017).
Several researchers investigated the rheological character- istics and reported that the nanoparticles can bring the sig- nificant shear-thinning phenomenon (Hadadian et al., 2014; Kole and Dey, 2013). Yearsley et al. (2012) mea- sured the detailed rheological behaviors of nanofluids with MWCNT and reported remarkable shear viscosity and oscillatory linear viscoelasticity. Duan et al. (2012) observed the non-Newtonian shear-thinning behavior when measur- ing the effective dynamic viscosity of graphite water based nanofluids. Their experimental results suggested that the increase on effective dynamic viscosity of nano- fluids is related to the graphite nanoparticle aggregation in the fluids.
Several researchers have studied the impact of droplets of various surfactant solutions on solid substrate (Mou- rougou-Candoni et al., 1999; Rozhkov et al., 2010). Gen- erally, the presence of surfactants would slow down the lamella retraction to an extent which depends on their nature. Bergeron et al. (2000) first discovered that with the addition of polymer additives, the recoiling phase of drop- let on smooth dry surfaces was suppressed. They attributed the suppression of rebound to the high extensional viscos- ity inherent in high-molecular weight polymeric solutions.
After that, a few studies have been conducted to investi- gate the advantages of polymer additives in improving spread or inhibiting rebound and splash from a solid sub- strate (Bartolo et al., 2007; Boyer et al., 2016; Finotello et al., 2018; Vega and Castrejón-Pita, 2017). Due to the high performance in efficient heat transfer and high thermal conductivity material preparation, the impact dynamics of nanofluids droplet has received increased attention these years. Wasan and Nikolov (2003) reported that the pres- ence of nanoscale particles has effects on the wetting behaviors of nanofluids containing sodium lauryl sulphate surfactant compare to that of base fluid. Li et al. (2015) found that the dynamic spreading can be slowed down by increasing nanoparticle volume fraction because of the enhancement of viscus force, which plays an important role during the spreading process. Hao et al. (2016) reported that the presence of silica nanoparticles can sig- nificantly increase the viscous energy dissipation inside the liquid droplets, suppressing the jumping from surfaces.
Some researcher believed that the transition from receding to equilibrium stage is mainly due to the friction forces between the nanoparticles and impact surface (Zang et al., 2013). However, the relationship between the rheological properties of non-Newtonian nanofluids and the impact dynamics of droplets have not been investigated explicitly and quantitively.
The maximum spreading factor max (ratio of maximum spreading diameter of a droplet to initial diameter) of droplet impact on a surface is an important parameter to select the best operating conditions. Numerous relations between the maximum spreading factor and the impact conditions have been established by considering the bal- ance between inertia, viscous, and surface tension contri- butions (Clanet et al., 2004; Eggers et al., 2010; Roisman et al., 2009; Scheller and Bousfield, 1995). It is necessary to emphasize that all those models show reasonable agree- ments with their experiments or numerical simulations.
However, they rarely considered rheological properties of fluid and complex flow physics during droplet impact.
(Mandani et al., 2018) investigated the impact dynamics of Boger droplets on solid surfaces experimentally, they found that the maximum spreading factor of water drop- lets is much greater than that of Boger fluid and glycerin but Boger fluid is slightly larger than that of the glycerin droplet. Moon et al. (2013) and Andrade et al. (2015) showed that the classical model failed to predict the max- imum spreading factor accurately for non-Newtonian (shear-thinning) droplets. An and Lee (2012) found that the maximum spreading factor of a shear-thinning droplet appears larger than that of a Newtonian drop having the same zero-shear viscosity, but smaller than a Newtonian drop with the same infinite-shear viscosity. It should be noted that when a shear-thinning fluid droplet impacts on a solid surface, the shear viscosity continuously varies between zero-shear viscosity and infinite-shear viscosity associated with shear deformation. Therefore, it is worth to carry out a further study on the maximum spreading factor of the non-Newtonian fluid droplet.
In the present study, the impact of droplets containing nanoparticle additives on solid surfaces with different wet- tability was investigated and compared to that of pure epoxy resin droplet. The nanofluids were prepared by dis- persing various nanoparticles (carbon nanotubes, graphene, nano-graphite powder) to the epoxy resin with two-step method. Then the rheological characteristics of prepared nanofluids were investigated by a rotational rheometer. By employing the high-speed camera visualization technique, we captured the impact process of droplets. The contact- ing factor, dimensionless height, and dynamic contact angle (DCA) of those droplets under different Weber num- bers (We) were studied to examine the effects of nanopar- ticle additives and surface wettability on impacting dynamics of droplet. Moreover, an empirical model will be proposed
to predict the maximum spreading factor of high-viscous droplets impacting on solid surface.
2. Materials and Experimental Methods
It has been found that the shape of nanoparticles has significant effects on the properties of nanofluids. In order to investigate the influence of nanoparticle shape on the impact dynamics of nanofluids droplet on solid surfaces.
The tube-liked carbon nanotube, sheet-liked graphene, and sphere-liked graphite powder were used in preparing the epoxy resin based nanofluids. Three kinds of nanoparti- cles (chemically treated carbon nanotubes, graphene, and nano-graphite powder) were dispersed homogeneously in the epoxy resin at levels of 0.05, 0.1, and 0.2 wt.% by means of ultrasonic technique. The detailed information of liquids’ properties and abbreviations in this study has been listed in Table 1.
A two-step method has been adopted in the synthesis of nanofluids and the available commercial nanoparticles supplied by several companies were dispersed to the base fluid. The outer diameter of chemically treated carbon nanotubes is less than 8nm and the inner diameter ranges from 2-5 nm. The length scale is 0.5-2 m and the -COOH functional group content is 3.86 wt.% (Chengdu Organic Chemicals Co. Ltd, purity of >99.5%). The graphene particle has average thickness of 5nm and diam- eter of 25 m (Tanfeng Tech. Inc, purity of >98%). The graphite powder has average size of 40 nm (Aladdin Industrial Corporation, purity of >99%).
In this work, the nanoparticles were initially dispersed into ethanol with different weight fractions using a soni- cator for 30 minutes. Then it mixed with the epoxy resin and disrupted in the sonicator for 4 h. Finally this mixture will be kept in an ultrasound apparatus for 3 days with heat of 80°C to remove the ethanol. To analyze the
nanoparticle dispersion and agglomeration of prepared nanofluids, the optical microscopy observations were car- ried out by using an inverted microscope (Leica DMI4000B), as well as the scanning electron microscopy (SEM) stud- ies (JEOL JSM-7800F).
To investigate the impact behaviors of a nanofluids droplet, we designed the experiment system to capture the impact process as sketched in Fig. 1. The droplets with uniform size were generated by a syringe pump to supply the test liquid through a stainless steel needle with inner diameter of 0.5 mm (G21). The dynamic behaviors of a droplet that fell freely down from the needle onto a solid surface were visualized by using the high-speed camera (Phantom V1611, Dantec Dynamics) with a microscopic zoom lens (NAVITAR, 12X) at 10000 fps. A LED cold light source is placed horizontally ahead of the high-speed camera and the angles between the camera and the surface were fixed at 0o so that horizontal images can be captured in a very short exposure time. The impact process of four droplets was recorded and examined at each falling con- ditions to verify the experimental repeatability. Based on the resolution (1080×720 pixels) of the images, both mea- surements of the impacting droplet diameter and the impact velocity were estimated to be accurate within
±2.0%. The contact angle, dimensionless height, and con- tacting factor along with the spreading time of droplets under different Weber numbers (We) were calculated in post-image processing with an accuracy of ±3%. Error bars represent an average obtained from three individual measurements and the measurements are repeated twice, and the error bars indicate the 95% confidence interval of the averages. In addition, the dynamic contact angles were obtained by a B-Spline Snake approach (Stalder et al., 2006).
The droplet has densities , dynamic viscosities , sur- face tension , and impact velocity V. The impact velocity of a falling droplet was controlled by changing the dis- tance between the tip of the needle and the surface. And it was estimated based on the moving distance in the ver- tical direction between two (or multiple) successive images just before impact. Likewise, the size of the drop- Table 1. Surface tension and rheological parameters of test liq-
uids.
Test Liquids Surface Tension [mN/m]
[Pa·sKn] n 0
[Pa·s] [Pa·s]
Epoxy resin 55.12 1.56 1 1.56 1.56
0.05 wt.%MWCNT 54.83 4.11 0.98 4.83 3.90 0.1 wt.%MWCNT 54.62 5.87 0.97 7.03 5.50 0.2 wt.%MWCNT 52.57 7.48 0.95 11.43 6.75 0.05 wt.%Graphene 54.08 3.60 0.95 5.22 3.23 0.1 wt.%Graphene 53.81 3.76 0.90 8.87 3.32 0.2 wt.%Graphene 53.26 4.21 0.87 11.67 3.62 0.05 wt.%Powder 54.37 2.58 0.90 4.47 2.15 0.1 wt.%Powder 53.23 2.67 0.89 8.26 2.23 0.2 wt.%Powder 52.35 3.86 0.88 10.30 3.32
Fig. 1. (Color online) Experimental setup.
let before the impingement was measured directly from the post image processing. The impacting droplets had an 2.45 ± 0.05 mm initial equivalent droplet diameter, calcu- lated from Eq. (1), where Dh and Dv are the horizontal and vertical dimensions, respectively. However, the differ- ences between Dh and Dv are nearly negligible, so that all drops were considered to have spherical shapes with an equilibrium initial diameter D, given by,
(1) The surface tension data of test nanofluids were mea- sured with a surface/interface tension meter (Dataphysics, DCAT11). The Weber number is defined with the liquid properties as We = DV2/. The hydrophilic (glass) and hydrophobic (teflon) substrates were used as the solid sur- faces. In this study, we choose two impact velocities of individual droplets: 1.71 m/s ( ) and 3.43 m/s
( ).
The measurements of liquid properties and the drop impact experiments were conducted at temperature of 25oC. The density of test liquids is 1100 ± 1 kg/m3. The shear viscosities of the epoxy resin and nanofluids were measured with a rotational rheometer (TA, DHR 1) with 50 mm parallel plate, a gap size of 500 m under the shear rate varying from 102 to 102 s1. The power-law model (Macosko, 1994) as shown in Eq. (2) has been employed to describe the shear-thinning characteristics and related discussion can be found in section 3.1.
(2) where K is the consistency coefficient and n is the dimen- sionless power-law index.
3. Results and Discussion
3.1. Morphological and rheological characters of prepared nanofluids
Obtaining a homogeneous and stable dispersion of the nanoparticles is one of the greatest challenges in the preparation of nanofluids. Optical micrographs of 0.2 wt.% chemically treated MWCNT, graphene, and graphite powder suspensions are given in Fig. 2. To compare the dispersion status between the chemically treated MWCNT and untreated MWCNT, we also prepared the 0.2 wt.%
untreated MWCNT using the identical method.
The average diameter of chemical treated MWCNT, graphene, and graphite particles dispersed in the nanoflu- ids after the ultrasonic breaker is up to 10 m as observed in Figs. 2a, 2c, and 2d. Though the mixtures are well dis- persed in microscale, the nanoparticles are still larger than those specified by the supplier in the powder form. It sug- gests that the nanoparticles have been aggregated into a certain size even in the high viscosity epoxy resin, resulted from the high surface effect of nanoparticles and the inter-
particle attraction (Jiang et al., 2003; Duan et al., 2012).
Moreover, the carbon nanotubes were significantly aggre- gated if the nanotubes are untreated, as shown in Fig. 2b.
The size of aggregated untreated MWCNT is larger than
2 1/3
( h v) . D D D
We 200 We 800
· = K·n 1–
Fig. 2. (Color online) Optical micrographs of 0.2 wt.% nanoflu- ids after dispersion. (a) chemically treated MWCNT in epoxy resin, (b) untreated MWCNT in epoxy resin, (c) graphite powder in epoxy resin, and (d) graphene in epoxy resin.
Fig. 3. (Color online) SEM images of MWCNT in epoxy resin.
(a) 14000×, (b) 27000×.
100 m at least. In the following sections which discuss the nanofluids droplet, only nanofluids containing chem- ically treated MWCNT, graphene, and graphite powder are used. SEM images of the chemical treated MWCNTs which are dispersed in the epoxy resin are shown in Fig.
3. The dotted lines highlight the existence of single nano- tube in prepared fluids which indicates the breakdown of agglomeration in nanoscale.
Figure 4 presents the shear viscosity of the test liquids.
The epoxy resin is a constant value of 1.56 Pa·s which indicates a Newtonian fluid. However, the nanofluids are characterized by shear-thinning behaviors and approach to a constant viscosity at high shear rates. With a higher mass fraction of nanoparticles, the shear viscosity increases throughout the entire shear rate range. Meanwhile, the non-Newtonian shear-thinning feature becomes more prominent. The spherical graphite powder nanofluids are more likely to exhibit lower infinite shear viscosity, while nanoparticles having sheet and tube shapes show distinct larger infinite shear viscosity. Typically, it is expected the shear viscosity containing low shear 0 and high shear viscosity plateaus with a shear-thinning region in between should describe the steady shear behavior of homogenous stable nanofluids. However, the Fig. 4 demonstrates that the shear viscosity sharply decreases in the low shear region and doesn’t show plateau behavior while an appar- ent plateau occurs in the high shear region ( ). We conjecture that in the prepared nanofluids, the nanoparticle clumps and the dispersed individual particles entangle with each other, causing the viscosity to increase. The entanglement is relatively strong at very small shear rates ( ) and becomes weaker at higher shear rates due to alignment of some particles to the flow and break up of clumps. In this work, the viscosities at
and were chosen as the zero-shear viscosity 0
and infinite-shear viscosity , respectively. The shear- thinning behaviors caused by nanoparticle additives might be different from the previous study about shear-thinning polymeric droplet since typically the shear-thinning region of the droplet containing polymer is much larger than the droplet containing nanoparticle (Ma et al., 2009). The rhe- ological properties of shear-thinning fluids have been characterized by using the power-law model as given by Eq. (3). The fitting parameters, the consistency coefficient K and power-law index n as listed in Table 1, suggest that the consistency coefficient K increases with the mass frac- tion of nanoparticles. However, the power-law index n reduces slightly. In other words, the fluids become more viscous at low shear rate and show more evident shear- thinning behaviors as increasing the nanoparticle mass fractions (Fig. 4). The oscillatory test indicates that the fluids used in this study exhibit an apparent fluidic behav- ior. Thus, we didn’t consider the viscoelasticity as a major effect on droplet impact dynamics in this study.
3.2. Visualization of the transient impact process Figure 5 shows the droplet impact sequences of the test droplets with different nanoparticle additives. The defor-
· 1 s –1
· 0.01 s –1
· 0.01 s –1
· = 1 s–1
Fig. 4. (Color online) Shear viscosity tests of different nanoflu- ids: (a) Multiwall carbon nanotube/epoxy resin, (b) nano-graphite powder/epoxy resin, and (c) graphene/epoxy resin.
mation process of a droplet impact on a solid surface at small to medium Weber number could be divided into four main phases: the kinematic phase, the spreading phase, the receding phase, and the equilibrium phase (Rioboo et al., 2002). After a droplet impinging on the surface, it rapidly begins spreading along the surface until it reaches a max- imum contacting factor with minimum dimensionless height, and then begins to recede. The ‘bounce-off’ phe- nomena are significantly modified due to the addition of nanoparticles. In all cases, the final equilibrium states could be achieved after the droplet impacting the surface for 20000 ms. The visualization data indicate that the epoxy resin droplet has the largest deformation and the M 0.1 droplet has the lowest deformation. From Fig. 5, the differences of spreading and receding motions between the epoxy resin and P 0.1 droplets are larger than those between the epoxy resin and M 0.1. The detailed analysis of the spreading and receding behaviors of each droplet will be discussed in the following sections. No secondary droplets are observed in this work.
3.3. Effect of nanoparticle additives
In order to analyze the dynamic behaviors during the droplets impingement, the transient contacting factor D*= Dt/D0 (Dt is transient contacting diameter of droplet on surface and D0 is initial droplet diameter), transient dimen- sionless height H*= Ht/H0 (Ht is transient droplet height and H0 is initial droplet vertical diameter), and the dynamic contact angle (DCA) are introduced in this study.
Figures 6, 7, and 8 plot the transient variations of D*, H*, and DCA for the test liquids under on a hydro- philic surface (glass) respectively.
As demonstrated in Figs. 6 and 7, a liquid with a lower nanoparticle concentration or more spherical nanoparticle shape spreads out more extensively, but recedes more rap- idly. And larger variations of the contacting factor and dimensionless height could be found over the process.
This could be interpreted by that, despite the flow may
accelerate at low shear rates due to a faster decrease of the viscosity, it remains more viscous for the nanofluids with higher concentrations of the nanoparticles over entire We 800
Fig. 5. Impact sequence of droplet impact on hydrophilic surface at a velocity of 3.43 m/s ( ) (a) Resin, (b) P 0.1, and (c)
M 0.1. We 800
Fig. 6. (Color online) Transient contacting factor of droplets impact on hydrophilic surface with the velocity of 3.43 m/s ( ). (a) Epoxy resin, M 0.1, G 0.1, and P 0.1 and (b) epoxy resin, M 0.1 and M 0.2.We 800
shear region. In other words, fluids become shear-thinning but at the same time thicker. Consequently, the spreading diameter is smaller for the nanofluids with higher nanoparticle concentration (the maximum contacting fac- tor of M 0.1 droplet is 14% larger than M 0.2 droplet).
And a strong damping effect could be observed during the receding stage (nanofluid droplets exhibit minimal dimen- sionless height variations during the receding phase).
Among all nanofluid droplets, these consequences are most pronounced in CNT nanofluids whose disperse phase is tubular like. Previous studies on the non-Newto- nian droplets have shown that the maximum contacting factor of a shear-thinning droplet is less than bulk droplet.
Because once the droplet impacts on the substrate, the vis- cosity decreases suddenly towards the infinite shear vis- cosity. After that the shear viscosity increases back with the decreasing of shear rate and approximates the zero- shear viscosity at the maximum spread stage. However, the nanoparticle additives used in this study not only bring
shear-thinning property to the epoxy resin, they also increase the shear viscosity within the whole shear rate interval. Therefore, it is difficult to demonstrate whether shear-thinning property or thicker property causes the impacting dynamics of the droplets to change. According to the arguments of German and Bertola (2009), the thicker property seems to be more important during drop- let impacting and show good consent in case of nanofluid droplets in this study.
Figure 8a presents the variations in DCA along with the spreading time for different nanofluids, as well as the pure resin droplet. Minor difference of DCA between the epoxy resin and nanofluid droplets could be observed during spreading phase. However, one could notice the distinct variance during their receding phases. Those phenomena show the consistency with the rheological data in Fig. 4.
The infinite-shear viscosity , which might dominate the Fig. 7. (Color online) Transient dimensionless height of droplets
impact on hydrophilic surface with the velocity of 3.43 m/s ( ). (a) Epoxy resin, G 0.2, P 0.2, and M 0.2 and (b)
epoxy resin, P 0.1 and P 0.2.We 800 Fig. 8. (Color online) Dynamic contact angle of droplets impact on hydrophilic surface with the velocity of 3.43 m/s ( ).
(a) Epoxy resin, M 0.1, G 0.1, and P 0.1 and (b) epoxy resin, G 0.1 and G 0.2.
We 800
spreading process under higher shear rate region, does not have much difference among the test fluids (valued from about 2 Pa·s to 6 Pa·s). Nevertheless, the zero-shear vis- cosity 0 ranges from about 1 Pa·s to over 10 Pa·s, which may cause those dissimilar behaviors of test fluids during the receding phase. Figure 8b shows the DCA variations with increasing the mass fraction of graphene in nanoflu- ids. It indicates that the DCAs have similar trends in G 0.1 and G 0.2 nanofluids and those results could also be inter- preted by their similar rheological characteristics in a sim- ilar approach. It should be noted that the impact dynamics of the droplet may also be influenced by the friction between the droplet and the substrate. For droplet containing nano- particles, the friction force increases due to the nanoparticle aggregates with the surface. Furthermore, the increased viscosity may also enhance the contact line friction.
3.4. Effect of surface wettability
To investigate the effects of surface wettability on drop- let dynamics, the glass and teflon substrates have been selected to conduct a series of experiments. The measured equilibrium contact angles of epoxy resin droplets on glass and teflon substrate are 23 ± 1o and 143 ± 1o, respec- tively. Except for the type of substrate, other experimental conditions such as droplet impact velocity and fluid prop- erties are the same. Figures 9 and 10 present the results of contacting factor and dimensionless height for epoxy resin, M 0.2, G 0.2, and P 0.2 droplets impinging on hydrophilic (glass) and hydrophobic (teflon) surfaces, respectively. The comparison of contacting factor shows that, except epoxy resin droplet, nanofluid droplets reach their maximum diameters in shorter time on the hydro- philic substrate than those on the hydrophobic substrate.
Meanwhile, the value of transient contacting factor for epoxy resin droplet on the hydrophobic surface is smaller than it on the hydrophilic surface. Those results suggest an apparent variation of contacting factor and dimensionless height on the surface with different wettability, especially to the M 0.2 nanofluid droplet which has the largest shear viscosity over entire shear region.
3.5. Maximum spreading factor model for high-vis- cous shear-thinning droplet impacting
The previous analyses of maximum spreading models typically compare predictions with experimental results for droplet impacts at low Ohnesorge numbers. However, even the epoxy resin droplet which has the smallest Ohne- sorge number (Oh = 4.05) in the present study, the Ohne- sorge number is higher than most of the previous work and viscous force term plays a more important role during inertial impact. This led to the comparison of prior inves- tigation, the droplet morphology variation during impact- ing in this study is quite small and the droplet shape can differ significantly from a cylindrical lamella shape at the
end of inertial spreading. The models to predict max pro- posed by former researchers based on energy balance approach models show larger discrepancy. Furthermore, the dispersion of nanoparticles not only brings shear-thin- ning properties, but also increases the infinite shear vis- cosity of the fluid. Therefore, it is difficult to determine whether shear-thinning property or infinite shear viscosity changes the impacting dynamics of the droplets. However, the influence of the consistency coefficient appears to dominate. Clanet et al. (2004) established that the maxi- mum droplet spreading factor scales as max~ We1/4 for low-viscosity fluids (water) impacting on superhydropho- bic surfaces. Later, Attané et al. (2007) indicated that while the We1/4 power-law provides a reasonable predic- Fig. 9. (Color online) The transient contacting factor of droplets impact on hydrophilic (glass) and hydrophobic (teflon) surface with the velocity of 3.43 m/s (We 800 ).
Fig. 10. (Color online) The transient dimensionless height of droplets impact on hydrophilic (glass) and hydrophobic (teflon) surface with the velocity of 3.43 m/s (We 800 ).
tion of low Ohnesorge numbers (Oh < 102), this power- law changes to max~ We1/6 at higher Ohnesorge number.
Based on Clanet et al.’ model, using the adjustment parameter a to indicate the effect of viscous dissipation and making adequately scaling of inertial force and sur- face tension term, a new model was proposed to predict the maximum spreading factor of high-viscous droplet (Oh > 4).
(3) where the so called ‘‘adjustment parameter’’ is determined by experimental tests since it depends upon fluid rheology (in this study, it is numerically equal to the consistency coefficient). Nevertheless, the better models are still needed. However, the Fig. 9 shows that the predicted max
is always larger than the experimental value for droplets with smaller Weber numbers (We < 400, the deviation can be up to 4%), while it becomes minor for droplets with larger Weber numbers (We > 400, the maximum deviation is 1.5%), particularly for Newtonian droplet.
4. Conclusions
In conclusion, the impact dynamics of nanofluids drop- let on solid surfaces was studied by high-speed imaging with the analysis from the view of their rheological prop- erties. The homogenous nanofluids were first prepared by dispersing various nanoparticles to epoxy resin. The microscopy study has shown that the nanofluids are well dispersed and stable. The nanofluids with different nanoparticles display shear-thinning characteristics in dif- ferent degree which can be described with power-law model. With the increase of nanoparticles mass fraction, the nanofluids become more viscous and show more shear-thinning degree. The effects of the liquid shear vis-
cosity with shear-thinning characteristics, the surface wet- tability, and the inertial force on the impact behaviors of a droplet were investigated by analyzing the transient dynamics of impacting droplet. The results suggest that nanoparticle additives increase the viscous dissipation during droplet impact process, thus the spreading and receding behaviors of droplet were significantly sup- pressed. In addition, for droplet containing nanoparticles, the friction force increases due to the nanoparticle aggre- gates with the surface and viscosity enhancement also inhabits the impact dynamics. Comparing the distinction of droplet dynamics on hydrophilic (glass) and hydropho- bic (teflon) surfaces, we found that in addition to the New- tonian droplet, the contacting factor is larger when droplet impacts on a hydrophobic surface during receding phase.
Moreover, the surface wettability has a greater effect on dimensionless height of Newtonian droplet than nanoflu- ids droplet. A model to predict the maximum spreading factor for high-viscous droplet has been proposed and shows good agreement with experimental data.
Acknowledgments
This work was supported by National Natural Science Foundation of China (No. 51506078, No. 51876086, and No. 51706089) and the Doctoral Fund of Ministry of Edu- cation of China (2015M581732).
List of Symbols
a : Adjustment parameter Ca : Capillary number DCA : Dynamic contact angle D0 : Initial diameter
Dt : Transient contacting diameter Dv : Vertical diameter
Dh : Horizontal diameter D* : Contacting factor
G 0.05 : 0.05 wt.% Graphene nanofluid G 0.1 : 0.1 wt.% Graphene nanofluid G 0.2 : 0.2 wt.% Graphene nanofluid H0 : Initial droplet height
Ht : Transient droplet height H* : Dimensionless height K : Consistency coefficient
M 0.05 : 0.05 wt.% MWCNTs nanofluid M 0.1 : 0.1 wt.% MWCNTs nanofluid M 0.2 : 0.2 wt.% MWCNTs nanofluid n : Power-law index
Oh : Ohnesorge number
P 0.05 : 0.05 wt.% graphite particle nanofluid P 0.1 : 0.1 wt.% graphite particle nanofluid P 0.2 : 0.2 wt.% graphite particle nanofluid Re : Reynolds number
0.08 0.05
max a We
Fig. 11. (Color online) Comparison of measured max with pre- dictions using Eq. (4).
V : Impact velocity We : Weber number Greek Symbols
: Spreading factor
max : Maximum spreading factor
: Shear-viscosity : Infinite shear-viscosity
0 : Zero shear-viscosity
: Surface tension : Shear rate
: Density
: Contact angle
e : Equilibrium contact angle References
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