- Email: [email protected]
Evaporation of a sessile oil drop in the Wenzel-like regime
International Journal of Thermal Sciences 151 (2020) 106236
Contents lists available at ScienceDirect
International Journal of Thermal Sciences journal homepage: http://www.elsevier.com/locate/ijts
Evaporation of a sessile oil drop in the Wenzel-like regime Dorra Khilifi a, d, *, Walid Foudhil a, c, Souad Harmand b, Sadok Ben Jabrallah a, c a
Laboratory of Energetics and Thermal and Mass Transfer (LETTM), Science Faculty of Tunis, University of Tunis El Manar, 1060, Tunis, Tunisia Polytechnic University of Hauts-de-France, LAMIH, UMR CNRS - 8201, F-59313, Valenciennes, France c University of Carthage, Science Faculty of Bizerte, 7021, Bizerte, Tunisia d University of Tunis El Manar, Science Faculty of Tunis, 1060, Tunis, Tunisia b
A R T I C L E I N F O
A B S T R A C T
Keywords: Wenzel-like regime Sessile drop Evaporation Micro-textures Oil
In this work, we present an experimental study of the evaporation of oil drops deposited on both textured and smooth silicon substrates at two different temperatures (20 � C and 270 � C). We show that the sessile drops take a hexagonal form and are linked by an oil film (a droplet sitting on a mixture of solid and liquid). This wetting regime represents the Wenzel-like regime. We are particularly interested in the propagation of the oil film on the textured surface over time. The effect of the surface fraction of the micro-textures ∅ and the temperature of the substrate Th on the film propagation were also studied. We reveal that the spreading length of the oil drops increases as ∅ decreases and Th increases. We also demonstrate that the textured surface favors oil drop evaporation.
1. Introduction Drop evaporation has been intensively studied due to its utility in many applications such as spray drying, DNA mapping [1,2], Inkjet printing [3,4], combustion engineering [5,6], electronic cooling [7], etc., and, the wetting regimes can be classified into three main types: Wenzel-like regime, Wenzel regime, and Cassie–Baxter regime. For instance, Hisler et al. [8] examined the wettability behavior of a sessile drop in the Wenzel-like regime. The drop was deposited on a textured silicon substrate with micro-pillars of diameter d and height H. The micro-pillars were distributed over a hexagonal network such that l represented the shortest distance between two units (Fig. 1). The authors revealed that the liquid spontaneously filled the voids of the micro-pillars, forming a film surrounding the drop. They also showed that the wettability behavior could be obtained only if the equilibrium contact angle, on a smooth surface, had the same chemical composition as the textured substrate, θeq < 90� . Based on energetic arguments, Bico et al. [9] defined the critical contact angle θc below which a liquid was spontaneously imbibed in the roughness voids. This critical contact angle was obtained by considering the interfacial energy variation dE corresponding to a displacement dx of a liquid with surface tension σ [9]. dE ¼ ðσsl
σ sv Þðr
∅Þdx þ σð1
∅Þdx
(1)
Considering that the liquid wets the substrate if dE is negative and introducing Young’s relation (σcosθeq ¼ σsv σsl ) in Eq. (1), we can define a condition for the spontaneous 2D imbibition to occur as θeq < θc
with
cosθc ¼
1 r
∅ ∅
(2)
A droplet with a wetting contact angle θeq < θc on such a substrate should spontaneously fill the roughness to form at equilibrium a film connected to the droplet (droplet sitting on a mixture of solid and liquid)), i.e., a Wenzel-like regime [Fig. 2 (c)] [10]. If the Young contact angle θeq exceeds the critical angle θc (θeq > θc ), the rough surface is dry ahead of the contact line, i.e., a Wenzel regime [Fig. 2 (a)] [10]. According to the Cassie–Baxter regime, air can be trapped below the drop forming “air pockets.” Thus, hydrophobicity is strengthened, because the drop “sits” partially on the air (Fig. 2 (b)) [10]. Researchers have endeavored to understand the causes of the extremely low contact-angle hysteresis characterizing superhydrophobic surfaces for this regime. Hasimoto et al. have reported the pinning/depinning of the contact line at the origin of the contact-angle hysteresis as a function of the morphology and surface density of posts, holes or stripes pinning the contact line [11]. Hasimoto et al. [12] investigated the flow of a liquid film through a porous medium. The employed textures were cylindrical micro-pillars of diameter d and height H. This configuration is the simple representation
* Corresponding author. Laboratory of Energetics and Thermal and Mass Transfer (LETTM), Science Faculty of Tunis, University of Tunis El Manar, 1060, Tunis, Tunisia. E-mail address: [email protected] (D. Khilifi). https://doi.org/10.1016/j.ijthermalsci.2019.106236 Received 30 March 2019; Received in revised form 7 October 2019; Accepted 16 December 2019 Available online 6 January 2020 1290-0729/© 2019 Elsevier Masson SAS. All rights reserved.
D. Khilifi et al.
International Journal of Thermal Sciences 151 (2020) 106236
Nomenclatures D d e G H K K L l mev Pc Pv S T Th
t V Δv
drop diameter hole diameter hole depth propagation coefficient relative humidity permeability viscous resistance spreading length of the liquid film distance separating the two closest holes evaporation rate capillary pressure viscous pressure drop surface temperature temperature of the substrate
time drop volume volume between the states before and after the liquid fills a unit cell
Greek symbols θ contact angle ∅ surface fraction of the holes δ height of the holes edges ρ density ν kinematic viscosity μ dynamic viscosity σ surface tension Subscripts amb environmental condition
f :Re ¼
d2 K
(6)
Hasimoto et al. expressed the product (f⋅Re) as a function of the solid volume fraction ∅V . This product was obtained by the following solution [12]: f :Re ¼
of a fibrous porous medium. In their theoretical study, the authors showed that the flow resistance increased as the permeability K decreased, which in an increase in the solid volume fraction ∅V . They determined the flow resistance by the product (f⋅Re) where f corresponds to the friction factor and Re represents the Reynolds number defined by the following relation: ΔP d L ρU 2
(3)
Re ¼
ρUd μ
(4)
f :Re ¼
(7)
ln∅V
1:476 þ 2∅V
32∅V 1:774∅2V þ 4:076∅3V þ 0ð∅4V Þ
(8)
The subsequent solutions developed by Sangani and Acrivos [14], Drummond and Tahir [15], and Skartsis et al. [16] using analytical and numerical methods were in good agreement with the previously Table 1 Previous experimental research on the flow of Newtonian fluids through square arrays of cylinders, for Re≪1.
Here, d denotes the diameter of the pattern, U stands for the flow ve locity in the porous medium, and L is the spreading length of the film. According to Darcy’s law, ΔP μ ¼ U L K
32∅V 1:476 þ 2∅V þ 0ð∅2V Þ
It is worth noting that Hasimoto’s solution can be applied only in square networks of cylindrical patterns. This approach was improved by Sangani and Acrivos [13] to obtain more precise solutions for square and hexagonal networks given by:
Fig. 1. Cylindrical micro-pillars with diameter d, period l, and height H.
f ¼
ln∅V
(5)
where K represents the permeability. Thus,
Authors
Fiber material and diameter, in mm
Solid volume fraction ∅V
f⋅Re
Kirsch and Fuch [17]
Kapron fibers 0.15; 0.225 & 0.4
0.0055; 0.01 0.018; 0.045 0.065; 0.11; 0.15
Chmielewski and Jayaraman [18] Khomami and Moreno [19]
Acrylic rods 4.76
0.3
0.048; 0.10 0.23; 0.91 1.54; 4.0; 6.67 37.6
Acrylic rods 12.7 & 6.35
0.55 0.14
210 7.8
Fig. 2. (a) Wenzel regime, (b) Cassie–Baxter regime and (c) Wenzel-like regime [10]. 2
D. Khilifi et al.
International Journal of Thermal Sciences 151 (2020) 106236
obtained solutions. Table 1 presents the results of some experimental studies on the measurement of flow resistance to Newtonian fluid flow through square networks with cylindrical patterns. The above-cited works showed that such resistance increases by augmenting the solid volume fraction ∅V . The experimental data of the flow resistance are clearly in good agree ment with the theoretical values provided by applying Hamisto’s solution. Xiao et al. [20] studied the propagation of a water film on a textured surface with micro-pillars of diameter d and height H. The micro-pillars were distributed on a square network in which l represents the distance separating the micro-pillars. They proved experimentally that the spreading length of the water film L increased with increasing l. Darcy’s law was used to assimilate the propagation of the oil film on the textured substrate to flow in a porous medium: ΔP μ ¼ U x K
ΔE: The net change in surface energies associated with the imbibition of liquid into a unit cell Δv: Volume between the states before and after the liquid fills a unit cell. ΔE ¼ ½bð2ab þ bÞ þ 4ah�rng ðσls ðσ ls
L
x dx ¼ 0
L¼
Z
�1 � 2Pc :K 2
μ
t
dt
μ
0
1
: ½t�2
(11)
Pv ¼
where G¼
� �1 2Pc :K 2
μ
¼
� �12 2Pc μ and K ¼ K K
μUL K
(18)
This equilibrium is translated by Darcy’s law (Eq. (9)). Many authors also investigated the evaporation of fuels in the form of oil drops and showed the presence of a residue at the end of the evaporation process. This residue is generally transformed into a particle of coal [22,23]. Haletta et al. [24] studied the evaporation of oil drops from biomass pyrolysis at an initial temperature T0 ¼ 26.7 � C and initial diameters of 1.6 mm and 1.7 mm. These drops were heated to high temperatures between 299.7 � C and 749.7 � C. The used fuel was composed of organic acids, aldehydes/ketone, water and pyrolytic lignin. The authors also examined the evaporation of each component over time. They reported that all volatile components were totally evaporated, except pyrolytic lignin (a non-volatile component), where one part evaporated, and the other was transformed into coal. Brett et al. [25] focused on the evaporation of a drop of bio-oil whose diameter ranged from 1.6 mm to 1.7 mm at an initial temperature T0 ¼ 26.7 � C. The heating temperature was varied between 299.7 � C and 499.7 � C. The authors also developed a numerical model to study the effect of internal diffusion rate on evaporation. They proved that the internal diffusion improved the bio-oil drop evaporation. Other works, such as [26], revealed the occurrence of a micro-explosion during the evaporation of a drop of kerosene mixed with bio-oil. Because the water content of the bio-oil in the aqueous phase was high and the light substances in the oil evaporated easily, the drop boiled quickly and generated small bubbles during the initial combustion phase. The combustion of the highly volatile substances in the drop reached a threshold temperature, causing the drop micro-explosion. Many authors [27,28] confirmed the existence of a micro-explosion during the evaporation of a mixture of oil and water under certain conditions. For example, Fu et al. [29] studied the evaporation of oil–water mixed drops having initial diameters between 0.2 mm and 0.4 mm. They applied a physical model to describe the appearance of a micro-explosion of emulsions (drops dispersed in liquid) in two cases: oil
(12) (13)
1
L ¼ G:½t�2
(17)
The process of liquid imbibition into surface textures is dictated by the balance between capillary and viscous forces [20,21]. The rate of imbibition into the micro-pillars of a textured surface is governed by the balance between the capillary pressure (Pc) (Eq. (15)) that develops across the advancing liquid–vapor front of the micro-imbibition layer and the viscous pressure (Pv) associated with the flow of liquid between micro-pillars [21].
(10)
Pc :K
σ:cosθeq
(16)
a: represents the width of micro-pillar h: denotes height of micro-pillar b: designates the distance between two micro-pillars rng : is the nanograss, equal to 1 in case of micro-textures
ΔP ¼ Pc : presents the capillary pressure U ¼ dx dt : denotes the velocity of propagation μ : corresponds to the dynamic viscosity K : is the permeability
Z
σsv Þ ¼
σ sv Þ þ bð2a þ bÞσ
where
(9)
Pc :K 1 μ U
(15)
Note that the liquid continues to flow into the micro-textures as long as Pc > 0.
where
x¼
ΔE Δv
Pc ¼
(14)
Here, G stands for the propagation coefficient. They defined the capillary pressure responsible for the propagation of the liquid between the micro-pillars by the following relation [9,20, and21]]:
Fig. 3. Schematic of the experimental setup. 3
D. Khilifi et al.
International Journal of Thermal Sciences 151 (2020) 106236
Technologies, 15 fps, 780 � 580 pixels) was used to record the evapo ration process of the droplets for profile analysis by using a Kruss® drop shape analyzer (DSA) to measure the contact angle, volume, surface, diameter, and height of the sessile droplets during evaporation. The uncertainties of the measurements are provided in Table 2.
Table 2 Experimental uncertainties. Parameters
Uncertainty
Ambient temperature
� 0:5 � C
Relative humidity
� 2%
Surface temperature of drop
� 1%
Contact angle
� 0:1 �
3. Materials The substrate used in this experiment was textured silicon (1.33 � 1.77 mm) with spherical holes with diameter d ¼ 100 μm and depth e ¼ 50 μm (see Fig. 4). The holes were distributed over a hexagonal network where l denotes the distance between two holes. This distance is also called the period. The hole machining of the utilized substrate caused stresses on the machined material. As demonstrated in Fig. 5, analysis of the surface condition showed roughness at the hole edges, creating a “lip”, noted δ � 12 nm high. This height represents the average value of the asperities on the surface related to the manufacture of the substrates. Physical properties of the oil: The characteristics of the oil (SilOil M40) used in this experiment are provided in Table 3. From the SilOil M40 data sheet, we established how the viscosity and density varied as a function of temperature. This information allowed us to determine these values at each temperature, particularly Tamb ¼ 20 � C and Th ¼ 270 � C (see Fig. 6). The surface tension of the oil was measured at different temperatures
in water and water in oil. In the present work, we focus on the behavior of a drop of SilOil M40 deposited on smooth and textured substrates at room and high tem peratures equal to 20 � C and 270 � C, respectively. Special attention is given to the propagation of the oil film appearing around the drop, on the textured substrate. The analysis of the experimental results con centrates essentially on the effects of substrate nature and temperature on the evaporation kinetics. 2. Experimental process and materials A silicon substrate was placed in a vapor chamber (14 � 12.4 � 7.5 cm) in which the ambient temperature and relative humidity were controlled and set to 20 � C and 50%, respectively (Fig. 3). A droplet of oil (3.4 μL) was deposited on a heated silicon substrate (Th ranging from 20 � C to 270 � C) by means of a programmable syringe (KD Scientific Legato 100). The air inside of the chamber was at rest. The top of the vapor chamber had a sapphire window for the infrared camera and a hole for passing the syringe. The infrared camera (FLIR X6580SC, 640 � 512 pixels, 15 μm detector pitch) was installed at the top for infrared thermal mapping and visualization of thermal instabilities on the surfaces of the droplets. A side-view charge-coupled device (CCD) camera (Allied Vision
Table 3 Characteristic of SilOil M40 at different temperatures. 1
σ (mN.m ) ρ (g.cm 3)
ν (mm2.s 1)
T amb ¼ 20 � C
Th ¼ 270 � C
20.73
6.2
0.94
0.71
11.24
1.2
Fig. 4. Spherical micro-patterns of diameter d, period l, and depth e: (a) schematic diagram, (b) 2D view, and (c) 3D view.
Fig. 5. (a) Microscopic snapshots of a hole in 3D and (b) a section of the substrate. 4
D. Khilifi et al.
International Journal of Thermal Sciences 151 (2020) 106236
Fig. 6. Variations of the kinematic viscosity and the density of oil as a function of temperature.
Fig. 7. Variations of the surface tension of oil as a function of temperature.
Fig. 8. Photo of the oil drop deposited on textured silicon at ∅ ¼ 44% and T ¼ 20 � C: (a) oil drop and (b) oil film (in blue). . (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
5
D. Khilifi et al.
International Journal of Thermal Sciences 151 (2020) 106236
Fig. 9. Photo of the oil drop deposited on textured silicon at ∅ ¼ 25% and T ¼ 20 � C: (a) oil drop and (b) oil film (in blue). (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
Fig. 10. Measurement of the spreading length of the liquid film at t ¼ 1300 s: (a) ∅ ¼ 44% and (b) ∅ ¼ 25%.
by the pendant drop method with the Kruss® DSA system (see Fig. 7). We considered two series of substrates where we made holes of equal size (d ¼ 100 μm and e ¼ 50 μm) by varying the period l:
drops have hexagonal shapes. A very thin oil film spreads between the holes, which proves that the wetting regime is Wenzel-like. These results are in agreement with those presented in Refs. [8,9], where the morphology of water drops deposited on substrates textured by micro-pillars are described. During its propagation around the drop, the oil film bypassed the holes, as observed in the case of micro-pillars in the configurations studied by Bico et al. and Hisler et al. [8,9]. The “lip” at the hole edge (height δ � 12 nm) prevented the oil film from invading the holes during its propagation. These holes behaved on the edges as micro-pillars of diameter d. Therefore, the fraction of the holes’ surface can be defined by the following relation [8,9]:
➢ Series 1: l ¼ 50 μm ➢ Series 2: l ¼ 100 μm 4. Results and discussion 4.1. Tests at room temperature In this section, we examine the wettability behavior of an oil drop (3.4 μL) deposited on a textured substrate at room temperature Tamb ¼ 20 � C.
∅¼
4.1.1. Wenzel-like regime
d2 ðl þ dÞ2
(19)
4.1.1.2. Effect of ∅ on the oil film propagation. In this section, we focus on the influence of the propagation of the oil film, appearing around the drops on the two textured substrates over time. The purpose of our study is to examine the effect of the surface fraction of the holes ∅ on this phenomenon. Fig. 10 shows how the spreading length was measured based on continuity of the film propagated on the two textured substrates. For instance, at t ¼ 1300 s, the measurement of the spreading length L of the oil film gave the following results:
4.1.1.1. Experimental observation. The morphology of an oil drop was observed and recorded using a high speed camera (Keyence, VW600C) mounted on an optical microscopic lens (Keyence, VH-Z100R, magni fication zoom from 100 � to 1000 � ). Video editing/analysis software (Keyence, VW-9000 Motion Analyzer) was used to visually observe oil propagation over time. Figs. 8 and 9 show the morphologies of SilOil M40 drops deposited on the textured substrates (series 1 and 2). As shown in the figures, the 6
D. Khilifi et al.
International Journal of Thermal Sciences 151 (2020) 106236
Fig. 11. Variation of the spreading length of the oil film on different textured substrates ∅ ¼ 44% and ∅ ¼ 25% over time.
➢ Series 1 (∅¼ 44%): L ¼ 1.06 mm ➢ Series 2 (∅¼ 25%): L ¼ 2.1 mm
The formation of the oil film around the drop was due to a negative energy difference [9,10], which resulted in a small displacement dx of the liquid front for a short time dt, generating an initial velocity and causing the propagation of the oil film on the textured surface. This velocity diminished over time until it vanished and the film stabilized. Fig. 11 also reveals that the spreading length of the oil film, propa gated on a textured surface of ∅ ¼ 25% increased more rapidly than that of the film propagated on a textured surface of ∅ ¼ 44%. This result was proven experimentally by Xiao [20] in the case of a textured surface
This method was used to measure the spreading length at any time. Fig. 11 represents the variation of the spreading length of the dispersed oil film as a function of time on the different textured surfaces. The length of the oil film increases significantly during the first few seconds. Then, this increase slows down over time and eventually stabilizes at a constant value.
Fig. 12. Snapshots from infrared video camera of the evaporation process of oil drop deposited on textured surface silicon: ∅ ¼ 44%, Th ¼ 270 � C and V ¼ 3.4 μL (see the Information for visualization section). with ➢ ➢ ➢ ➢
(1): (2): (3): (4):
liquid–gas interface of the oil drop. the area of the substrate on which the oil spreads and propagates as a function of time. the substrate (textured silicon) heated at 270 � C. the trace of the drop after evaporation. 7
D. Khilifi et al.
International Journal of Thermal Sciences 151 (2020) 106236
Fig. 13. Variation of the spreading length of the oil film over time at different temperatures for ∅ ¼ 44% and V ¼ 3.4 μL.
with cylindrical micro-pillars. Indeed, the increase in the permeability K after the ∅ decrease of 43.18% significantly minimized the viscous resistance, K ¼ Kμ [20], which facilitated the film propagation. Moreover, it is clear from Fig. 11 that the spreading length L of the oil film stabilized at around 1300 s.
4.2. Behavior of the drop of sessile oil in the Wenzel-like regime at high temperature 4.2.1. Effect of temperature on the propagation of the oil film Another oil drop (3.4 μL) was deposited on the textured silicon of ∅ ¼ 44% heated to Th ¼ 270 � C. To deeply study the effect of temperature on the behavior of this drop, we compared the results with those ob tained at room temperature. Fig. 12 demonstrates that the drop deposited on the textured has a hexagonal form connected by a thin film, thus representing a Wenzellike regime. This result is also visible in Fig. 8. The series of images presented in Fig. 12 reveals that the oil film initially propagates rapidly at a high temperature, and then disappears, highlighting the effect of intensive evaporation. In order to study the influence of temperature on the propagation of the oil film, we represent the variation of the spreading length L of the oil film as a function of time for different temperatures (Fig. 13). This figure reveals that the film spreading length L increased considerably as the temperature increased. This decreased the liquid viscosity by 87% (Fig. 6), which reduced the viscous resistance and facilitated the oil film propagation.
➢ Lmax ¼ 1.06 mm: ∅ ¼ 44% ➢ Lmax ¼ 2.1 mm: ∅ ¼ 25% From the previously presented findings, it can be deduced that the 43.18% increase of ∅ decreases the maximum spreading length Lmax of the oil film by 50%. 4.1.1.3. Theoretical study. Considering that the propagation of the oil film on the textured substrate with holes was identical to that of the micro-pillars, the spreading length can be calculated applying equations 13–17. If Δv represents the difference in volume between two halfspherical–shaped holes of diameter (d þ l) and d, we obtain: Δv ¼
π�
ðd þ lÞ3
12
d3
�
� Pc ¼ σ
12lð2d þ lÞ � � cosθeq π ðd þ lÞ3 d3
(20) � 48dδ 1 þ � π ðd þ lÞ3
d3
� �
(21)
4.2.1.1. Theoretical study. Because the surface tension and the viscosity of the oil depend on the temperature, we can write
where θeq ¼ 0. Then, we get: 48dδ Pc ¼ σ � π ðd þ lÞ3
d3
�
GðTÞ ¼
(22)
� �1 2Pc :K 2
μ �
(25)
�12
Note that the liquid imbibes into the micro-textures as long as Pc > 0. For a substrate textured with spherical-holes of diameter d, the permeability K is given by the Ergün equation.
GðTh Þ ¼ GðTamb Þ �σðT
d2 ð1 ∅Þ3 K¼ 150 ð∅Þ2
GðTh Þ � 1:92 GðTamb Þ
(27)
LðTh Þ � 1:92 LðTamb Þ
(28)
σðTh Þ μðTh Þ
�12 � 1:92
(26)
amb Þ
μðTamb Þ
(23)
Therefore, we obtain sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 96 d3 δ ð1 ∅Þ3 σ pffi LðtÞ ¼ t � � 3 μ 150 π ðd þ lÞ d3 ð∅Þ2
Fig. 13 compares the experimental and theoretical L (t) results for different temperatures, and it demonstrates good quantitative agreement.
Fig. 11 compares the experimental and theoretical L (t) for the two values of ∅, showing good quantitative agreement.
4.2.1.2. Information for visualization. According to the Ste fan Boltzmann law, the radiant existence of a gray body j is determined 8
D. Khilifi et al.
International Journal of Thermal Sciences 151 (2020) 106236
Fig. 14. Variation of the drop volume over time: Th ¼ 270 � C, Tamb ¼ 20 � C, ∅ ¼ 44%, and V ¼ 3.4 μL.
Fig. 15. Variations of the drop contact angle and diameter over time: Th ¼ 270 � C, Tamb ¼ 20 � C, ∅ ¼ 44%, and V ¼ 3.4 μL.
Fig. 16. Variation of the drop evaporation rate over time: Th ¼ 270 � C, Tamb ¼ 20 � C, ∅ ¼ 44%, and V ¼ 3.4 μL.
as j ¼ εγT 4
thermal mapping represents the level of thermal radiation l received by 0 the infrared camera. In fact, the l level is proportional to the radiant j. The various colors denote different temperatures or emissivities related to several substances. After a few seconds of evaporation, the oil drop became homogeneous and its temperature equaled that of the silicon 0
(29)
where γ is the Stefan Boltzmann constant and ε and T are the emissivity and temperature of the substance, respectively. The scale in the infrared 9
D. Khilifi et al.
International Journal of Thermal Sciences 151 (2020) 106236
angle, and diameter of the drop over time. Obviously, the volume of the drop decreases over time, and it vanishes at almost 70 s. The oil drop evaporating on textured silicon substrate had a constant diameter for almost 20 s, whereas the contact angle decreased linearly over time, which represents the constant line mode (stage 1). This mode is justified by Fig. 17. Stage (2): During this stage, the drop deposited on the textured sil icon exhibited different behavior, in which the diameter and the contact angle decreased simultaneously over time, which indicates the stick slip mode. Fig. 16 depicts the evolution of the evaporation rate over time. The evaporation rate is defined by mev ¼
dV dt
S
(30)
Fig. 16 also shows that this rate had a maximum value at t ¼ 0 s due to the important concentration gradient between the liquid–gas inter face and the surrounding air. As evaporation started, air in the imme diate vicinity of the drop became more saturated with oil vapor, which resulted in a considerable decrease of the concentration gradient and consequently a decrease in the evaporation rate over time. 4.2.2.2. Thermal study. Fig. 12 represents a series of images taken by an infrared camera. These images describe the lifetime of the oil drop deposited on the textured silicon (∅ ¼ 44%) heated at 270 � C. This figure shows that the total evaporation of the oil film whose lifetime was around 266 s took longer to evaporate than the drop whose lifetime was about 70 s (Fig. 17). In fact, at the base of the drop, the liquid spontaneously filled the holes (Wenzel-like regime), which increased the liquid–solid contact surface, increasing the temperature of the drop and consequently intensifying evaporation. The oil film appearing around the drop spread across the substrate avoiding holes, which explains the delay of oil film evaporation compared to that of the drop.
Fig. 17. CCD snapshots at different instants: Th ¼ 270 � C, Tamb ¼ 20 � C, ∅ ¼ 44%, and V ¼ 3.4 μL.
substrate, Th ¼ 270 � C, whereas the emissivity of the oil remained higher than that of the silicon substrate. Therefore, we observed a color contrast between the oil drop and the silicon substrate. This contrast was visu alized by the infrared camera. The normal temperature profile of a sil icon substrate was constant at Th ¼ 270 � C. According to the infrared images presented in Fig. 8, the color consistency at the substrate surface until the end of evaporation indicated a temperature less than 270 � C.
4.3. Behavior of oil drop deposited on a smooth surface In this part, the evaporation of a drop of SilOil M40 deposited on a smooth-surface silicon substrate is considered. The surface had the same chemical composition and the same dimensions as the textured silicon surface. The purpose here is to study the effect of surface nature on the evaporation kinetics. The images presented in Fig. 18 shows that the oil drop, deposited on
4.2.2. Study of the oil drop evaporation at high temperature 4.2.2.1. Dynamic study. In this section, we focus on the dynamic study of the oil drop presented in Fig. 12 (zone 1). Fig. 14 and15 show respectively the variations of the volume, contact
Fig. 18. Snapshots from infrared video camera of evaporation process of oil drop deposited on smooth-surface silicon: Th ¼ 270 � C and V ¼ 3.4 μL (see the In formation for visualization section). 10
D. Khilifi et al.
International Journal of Thermal Sciences 151 (2020) 106236
the smooth-surface silicon substrate, spread across the whole surface of the substrate, forming a thin film. As demonstrated, the life of the oil film was around 2400 s. Comparing these results with those illustrated in Fig. 12, we note that the evaporation of a drop deposited on a textured surface was more intense than that of a drop deposited on a smooth surface. In fact, the micro-texture reduced the drop lifetime by 89% and increased the heat exchange surface between the drop and the substrate, which improved the heat transfer at the liquid–solid interface, thus fa voring evaporation. This phenomenon explains the delay of the oil film evaporation compared to that of the drop, as observed in Fig. 12.
References [1] W. Wang, J. Lin, D.C. Schwartz, Scanning force microscopy of 665 DNA molecules elongated by convective fluid flow in an evaporating 666 droplet, Biophys. J. 667 (75) (1998) 513–520. [2] M. Chopra, L. Li, H. Hu, M.A. Burns, R.G. Larson, DNA 668 molecular configurations in an evaporating droplet near a glass surface, J. Rheol. 669 (47) (2003) 1111. [3] T. Kawase, H. Sirringhaus, R.H. Friend, T. Shimoda, Inkjet 659 printed via-hole interconnections and resistors for all-polymer 660 transistor circuits, Adv. Mater. 13 (2001) 1601–1605, 661. [4] B.J. de Gans, P.C. Duineveld, U.S. Schubert, Inkjet printing 662 of polymers: state of the art and future developments, Adv. Mater. 663 (16) (2004) 203–213. [5] M. Sato Saito, M. Suzuki, I. Evaporation and combustion of a 671 single fuel droplet in acoustic fields, Fuel 73 (1994) 349–353, 672. [6] C.W. Park, M. Kaviany, Evaporation-combustion affected by 673 in-cylinder, reciprocating porous regenerator, J. Heat Transf. 674 124 (2002) 184–194. [7] A. Bar-Cohen, M. Arik, M. Ohadi, Direct liquid cooling of high flux micro and nano electronic components, Proc. IEEE 94 (8) (2006) 1549–1570. [8] Valentin Hisler, Laurent Vonna, Vincent Le Houerou, Stephan Knopf, Christian Gauthier, Michel Nardin, Hamidou Haidara, Model experimental study of scale invariant wetting behaviors in Cassie Baxter and Wenzel regimes, Langmuir 30 (2014) 9378–9383. [9] J. Bico, C. Tordeux, D. Qu�er� e, Rough wetting, Europhys. Lett. 55 (2) (2001) 214–220. [10] C. Ishino, K. Okumura, D. Quere, Wetting transitions on rough surfaces, Europhys. Lett. 68 (3) (2004) 419–425. [11] Christian Dorrer, Jurgen Ruhe, Advancing and receding motion of droplets on ultrahydrophobic post surfaces, Langmuir 22 (2006) 7652–7657. [12] H. Hasimoto, On the periodic fundamental solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres, J. Fluid Mech. 5 (1959) 317–328. [13] A.S. Sangani, A. Acrivos, Slow flow through a periodic array of spheres, Int. J. Multiph. Flow 8 (1982) 343–360. [14] A.S. Sangani, A. Acrivos, Slow flow past periodic arrays of cylinders with application to heat transfer, Int. J. Multiph. Flow 8 (1982) 193–206. [15] J.E. Drummond, M.I. Tahir, Laminar viscous flow through regular arrays of parallel solid cylinders, Int. J. Multiph. Flow 10 (5) (1984) 515–540. [16] L. Skartsis, B. Khomami, J.K. Kardos, Resin flow through fiber beds during composite manufacturing processes, Part IINumerical and experimental studies of Newtonian flow through ideal and actual fiber beds, Polym. Eng. Sci. 32 (1992) 231–239. [17] A.A. Kirsch, N.A. Fuchs, Studies on fibrous aerosol filters—II Pressure drops in systems of parallel cylinders, Ann. Occup. Hyg. 10 (1967) 23–30. [18] C. Chmielewski, K. Jayaraman, The effect of polymer extensibility on cross flow of polymer solutions through cylinder arrays, J. Rheol. 36 (1992) 1105–1126. [19] B. Khomami, Moreno, LD Stability of viscoelastic flow around periodic arrays of cylinders, Rheol. Acta 36 (1997) 367–383. [20] Rong Xiao, Enright Ryan, N. Evelyn, Wang, Prediction and optimization of liquid propagation in micropillar arrays, Langmuir 26 (19) (2010) 15070–15075. [21] Navdeep Singh Dhillon, Jacopo Buongiorno, Kripa K. Varanasi, Critical heat flux maxima during boiling crisis on textured surfaces, Nat. Commun. 6 (2015) 8247. [22] C.R. Shaddix, P.R. Tennison, in: Effects of Char Content and Simple Additives on Biomass Pyrolysis Oil Droplet Combustion 27th Symposium (International) on Combustion, The Combustion Institute, 1998, 1907–14. [23] J. D’Alessio, M. Lazzaro, P. Massoli, V. Moccia, in: Thermo-optical Investigation of Burning Biomass Pyrolysis Oil Droplets 27th Symposium (International) on Combustion, The Combustion Institute, 1998, 1915–22. [24] W.L.H. Halletta, N.A. Clarkb, A model for the evaporation of biomass pyrolysis oil droplets, Fuel 85 (2006) 532–544. [25] James Brett, Andrew Ooi, Julio Soria, The effect of internal diffusion on an evaporating bio-oil droplet, the chemistry free case, biomass and bioenergy 34 (2010), e1140, 1134. [26] M.S. Wu, S.I. Yang, Combustion characteristics of multi-component cedar bio-oil/ kerosene droplet, Energy 113 (2016) 788e795. [27] G. Greeves, I.M. Khan, G. Onion, in: 16th Symposium (International) on Combustion, 1976, pp. 321–336. [28] Z. Zhang, J. Yang, X. Chen, Trans. CSICE (Chin. Soc. Intern. Combust. Engines) 3 (1985) 321–332. [29] Wei Biao Fu, Ling Yun Hou, Lipo Wang, Fan Hua Ma, A unified model for the micro-explosion of emulsified droplets of oil and water, Fuel Process. Technol. 79 (2002) 107–119.
5. Conclusion In this research work, we carried out an experimental study on the propagation of a SilOil M40 film as a function of the textures of a sub strate. We also examined the effect of solid fraction ∅ and temperature on the propagation of the film. We showed that the film propagation increased � by decreasing the surface fraction of the holes ∅ � by increasing the substrate temperature Theoretical studies were carried out to confirm the experimental results. We determined an expression of the propagation coefficient G using the Darcy equation. This coefficient depended on the surface tension σ , the dynamic viscosity μ, and the surface fraction of the holes ∅. From this relationship, we proved that the propagation coefficient G increases by decreasing the surface fraction of the holes ∅ and increasing temperature T. Then, we highlighted of the effect of the nature of the substrate surface on the evaporation of SilOil M40 oil drop at high temperature. � Smooth-surfaced substrate: The sessile drop of initial volume V0 ¼ 3.4 μL spread across the whole surface of the substrate, forming a thin film. It evaporated over 2400 s. � Textured-surfaced substrate (∅ ¼ 44%): The sessile drop evaporated in the Wenzel-like regime over 266 s. The experimental results showed that the micro-texture accelerated the evaporation of the oil drop. The obtained findings provide a better understanding of the effect of substrate surface on the kinetics of the evaporation of an oil drop and the importance of choosing an appro priate surface to reduce the energy needed during the evaporation process. Declaration of competing interest The authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.ijthermalsci.2019.106236.
11
Contents lists available at ScienceDirect
International Journal of Thermal Sciences journal homepage: http://www.elsevier.com/locate/ijts
Evaporation of a sessile oil drop in the Wenzel-like regime Dorra Khilifi a, d, *, Walid Foudhil a, c, Souad Harmand b, Sadok Ben Jabrallah a, c a
Laboratory of Energetics and Thermal and Mass Transfer (LETTM), Science Faculty of Tunis, University of Tunis El Manar, 1060, Tunis, Tunisia Polytechnic University of Hauts-de-France, LAMIH, UMR CNRS - 8201, F-59313, Valenciennes, France c University of Carthage, Science Faculty of Bizerte, 7021, Bizerte, Tunisia d University of Tunis El Manar, Science Faculty of Tunis, 1060, Tunis, Tunisia b
A R T I C L E I N F O
A B S T R A C T
Keywords: Wenzel-like regime Sessile drop Evaporation Micro-textures Oil
In this work, we present an experimental study of the evaporation of oil drops deposited on both textured and smooth silicon substrates at two different temperatures (20 � C and 270 � C). We show that the sessile drops take a hexagonal form and are linked by an oil film (a droplet sitting on a mixture of solid and liquid). This wetting regime represents the Wenzel-like regime. We are particularly interested in the propagation of the oil film on the textured surface over time. The effect of the surface fraction of the micro-textures ∅ and the temperature of the substrate Th on the film propagation were also studied. We reveal that the spreading length of the oil drops increases as ∅ decreases and Th increases. We also demonstrate that the textured surface favors oil drop evaporation.
1. Introduction Drop evaporation has been intensively studied due to its utility in many applications such as spray drying, DNA mapping [1,2], Inkjet printing [3,4], combustion engineering [5,6], electronic cooling [7], etc., and, the wetting regimes can be classified into three main types: Wenzel-like regime, Wenzel regime, and Cassie–Baxter regime. For instance, Hisler et al. [8] examined the wettability behavior of a sessile drop in the Wenzel-like regime. The drop was deposited on a textured silicon substrate with micro-pillars of diameter d and height H. The micro-pillars were distributed over a hexagonal network such that l represented the shortest distance between two units (Fig. 1). The authors revealed that the liquid spontaneously filled the voids of the micro-pillars, forming a film surrounding the drop. They also showed that the wettability behavior could be obtained only if the equilibrium contact angle, on a smooth surface, had the same chemical composition as the textured substrate, θeq < 90� . Based on energetic arguments, Bico et al. [9] defined the critical contact angle θc below which a liquid was spontaneously imbibed in the roughness voids. This critical contact angle was obtained by considering the interfacial energy variation dE corresponding to a displacement dx of a liquid with surface tension σ [9]. dE ¼ ðσsl
σ sv Þðr
∅Þdx þ σð1
∅Þdx
(1)
Considering that the liquid wets the substrate if dE is negative and introducing Young’s relation (σcosθeq ¼ σsv σsl ) in Eq. (1), we can define a condition for the spontaneous 2D imbibition to occur as θeq < θc
with
cosθc ¼
1 r
∅ ∅
(2)
A droplet with a wetting contact angle θeq < θc on such a substrate should spontaneously fill the roughness to form at equilibrium a film connected to the droplet (droplet sitting on a mixture of solid and liquid)), i.e., a Wenzel-like regime [Fig. 2 (c)] [10]. If the Young contact angle θeq exceeds the critical angle θc (θeq > θc ), the rough surface is dry ahead of the contact line, i.e., a Wenzel regime [Fig. 2 (a)] [10]. According to the Cassie–Baxter regime, air can be trapped below the drop forming “air pockets.” Thus, hydrophobicity is strengthened, because the drop “sits” partially on the air (Fig. 2 (b)) [10]. Researchers have endeavored to understand the causes of the extremely low contact-angle hysteresis characterizing superhydrophobic surfaces for this regime. Hasimoto et al. have reported the pinning/depinning of the contact line at the origin of the contact-angle hysteresis as a function of the morphology and surface density of posts, holes or stripes pinning the contact line [11]. Hasimoto et al. [12] investigated the flow of a liquid film through a porous medium. The employed textures were cylindrical micro-pillars of diameter d and height H. This configuration is the simple representation
* Corresponding author. Laboratory of Energetics and Thermal and Mass Transfer (LETTM), Science Faculty of Tunis, University of Tunis El Manar, 1060, Tunis, Tunisia. E-mail address: [email protected] (D. Khilifi). https://doi.org/10.1016/j.ijthermalsci.2019.106236 Received 30 March 2019; Received in revised form 7 October 2019; Accepted 16 December 2019 Available online 6 January 2020 1290-0729/© 2019 Elsevier Masson SAS. All rights reserved.
D. Khilifi et al.
International Journal of Thermal Sciences 151 (2020) 106236
Nomenclatures D d e G H K K L l mev Pc Pv S T Th
t V Δv
drop diameter hole diameter hole depth propagation coefficient relative humidity permeability viscous resistance spreading length of the liquid film distance separating the two closest holes evaporation rate capillary pressure viscous pressure drop surface temperature temperature of the substrate
time drop volume volume between the states before and after the liquid fills a unit cell
Greek symbols θ contact angle ∅ surface fraction of the holes δ height of the holes edges ρ density ν kinematic viscosity μ dynamic viscosity σ surface tension Subscripts amb environmental condition
f :Re ¼
d2 K
(6)
Hasimoto et al. expressed the product (f⋅Re) as a function of the solid volume fraction ∅V . This product was obtained by the following solution [12]: f :Re ¼
of a fibrous porous medium. In their theoretical study, the authors showed that the flow resistance increased as the permeability K decreased, which in an increase in the solid volume fraction ∅V . They determined the flow resistance by the product (f⋅Re) where f corresponds to the friction factor and Re represents the Reynolds number defined by the following relation: ΔP d L ρU 2
(3)
Re ¼
ρUd μ
(4)
f :Re ¼
(7)
ln∅V
1:476 þ 2∅V
32∅V 1:774∅2V þ 4:076∅3V þ 0ð∅4V Þ
(8)
The subsequent solutions developed by Sangani and Acrivos [14], Drummond and Tahir [15], and Skartsis et al. [16] using analytical and numerical methods were in good agreement with the previously Table 1 Previous experimental research on the flow of Newtonian fluids through square arrays of cylinders, for Re≪1.
Here, d denotes the diameter of the pattern, U stands for the flow ve locity in the porous medium, and L is the spreading length of the film. According to Darcy’s law, ΔP μ ¼ U L K
32∅V 1:476 þ 2∅V þ 0ð∅2V Þ
It is worth noting that Hasimoto’s solution can be applied only in square networks of cylindrical patterns. This approach was improved by Sangani and Acrivos [13] to obtain more precise solutions for square and hexagonal networks given by:
Fig. 1. Cylindrical micro-pillars with diameter d, period l, and height H.
f ¼
ln∅V
(5)
where K represents the permeability. Thus,
Authors
Fiber material and diameter, in mm
Solid volume fraction ∅V
f⋅Re
Kirsch and Fuch [17]
Kapron fibers 0.15; 0.225 & 0.4
0.0055; 0.01 0.018; 0.045 0.065; 0.11; 0.15
Chmielewski and Jayaraman [18] Khomami and Moreno [19]
Acrylic rods 4.76
0.3
0.048; 0.10 0.23; 0.91 1.54; 4.0; 6.67 37.6
Acrylic rods 12.7 & 6.35
0.55 0.14
210 7.8
Fig. 2. (a) Wenzel regime, (b) Cassie–Baxter regime and (c) Wenzel-like regime [10]. 2
D. Khilifi et al.
International Journal of Thermal Sciences 151 (2020) 106236
obtained solutions. Table 1 presents the results of some experimental studies on the measurement of flow resistance to Newtonian fluid flow through square networks with cylindrical patterns. The above-cited works showed that such resistance increases by augmenting the solid volume fraction ∅V . The experimental data of the flow resistance are clearly in good agree ment with the theoretical values provided by applying Hamisto’s solution. Xiao et al. [20] studied the propagation of a water film on a textured surface with micro-pillars of diameter d and height H. The micro-pillars were distributed on a square network in which l represents the distance separating the micro-pillars. They proved experimentally that the spreading length of the water film L increased with increasing l. Darcy’s law was used to assimilate the propagation of the oil film on the textured substrate to flow in a porous medium: ΔP μ ¼ U x K
ΔE: The net change in surface energies associated with the imbibition of liquid into a unit cell Δv: Volume between the states before and after the liquid fills a unit cell. ΔE ¼ ½bð2ab þ bÞ þ 4ah�rng ðσls ðσ ls
L
x dx ¼ 0
L¼
Z
�1 � 2Pc :K 2
μ
t
dt
μ
0
1
: ½t�2
(11)
Pv ¼
where G¼
� �1 2Pc :K 2
μ
¼
� �12 2Pc μ and K ¼ K K
μUL K
(18)
This equilibrium is translated by Darcy’s law (Eq. (9)). Many authors also investigated the evaporation of fuels in the form of oil drops and showed the presence of a residue at the end of the evaporation process. This residue is generally transformed into a particle of coal [22,23]. Haletta et al. [24] studied the evaporation of oil drops from biomass pyrolysis at an initial temperature T0 ¼ 26.7 � C and initial diameters of 1.6 mm and 1.7 mm. These drops were heated to high temperatures between 299.7 � C and 749.7 � C. The used fuel was composed of organic acids, aldehydes/ketone, water and pyrolytic lignin. The authors also examined the evaporation of each component over time. They reported that all volatile components were totally evaporated, except pyrolytic lignin (a non-volatile component), where one part evaporated, and the other was transformed into coal. Brett et al. [25] focused on the evaporation of a drop of bio-oil whose diameter ranged from 1.6 mm to 1.7 mm at an initial temperature T0 ¼ 26.7 � C. The heating temperature was varied between 299.7 � C and 499.7 � C. The authors also developed a numerical model to study the effect of internal diffusion rate on evaporation. They proved that the internal diffusion improved the bio-oil drop evaporation. Other works, such as [26], revealed the occurrence of a micro-explosion during the evaporation of a drop of kerosene mixed with bio-oil. Because the water content of the bio-oil in the aqueous phase was high and the light substances in the oil evaporated easily, the drop boiled quickly and generated small bubbles during the initial combustion phase. The combustion of the highly volatile substances in the drop reached a threshold temperature, causing the drop micro-explosion. Many authors [27,28] confirmed the existence of a micro-explosion during the evaporation of a mixture of oil and water under certain conditions. For example, Fu et al. [29] studied the evaporation of oil–water mixed drops having initial diameters between 0.2 mm and 0.4 mm. They applied a physical model to describe the appearance of a micro-explosion of emulsions (drops dispersed in liquid) in two cases: oil
(12) (13)
1
L ¼ G:½t�2
(17)
The process of liquid imbibition into surface textures is dictated by the balance between capillary and viscous forces [20,21]. The rate of imbibition into the micro-pillars of a textured surface is governed by the balance between the capillary pressure (Pc) (Eq. (15)) that develops across the advancing liquid–vapor front of the micro-imbibition layer and the viscous pressure (Pv) associated with the flow of liquid between micro-pillars [21].
(10)
Pc :K
σ:cosθeq
(16)
a: represents the width of micro-pillar h: denotes height of micro-pillar b: designates the distance between two micro-pillars rng : is the nanograss, equal to 1 in case of micro-textures
ΔP ¼ Pc : presents the capillary pressure U ¼ dx dt : denotes the velocity of propagation μ : corresponds to the dynamic viscosity K : is the permeability
Z
σsv Þ ¼
σ sv Þ þ bð2a þ bÞσ
where
(9)
Pc :K 1 μ U
(15)
Note that the liquid continues to flow into the micro-textures as long as Pc > 0.
where
x¼
ΔE Δv
Pc ¼
(14)
Here, G stands for the propagation coefficient. They defined the capillary pressure responsible for the propagation of the liquid between the micro-pillars by the following relation [9,20, and21]]:
Fig. 3. Schematic of the experimental setup. 3
D. Khilifi et al.
International Journal of Thermal Sciences 151 (2020) 106236
Technologies, 15 fps, 780 � 580 pixels) was used to record the evapo ration process of the droplets for profile analysis by using a Kruss® drop shape analyzer (DSA) to measure the contact angle, volume, surface, diameter, and height of the sessile droplets during evaporation. The uncertainties of the measurements are provided in Table 2.
Table 2 Experimental uncertainties. Parameters
Uncertainty
Ambient temperature
� 0:5 � C
Relative humidity
� 2%
Surface temperature of drop
� 1%
Contact angle
� 0:1 �
3. Materials The substrate used in this experiment was textured silicon (1.33 � 1.77 mm) with spherical holes with diameter d ¼ 100 μm and depth e ¼ 50 μm (see Fig. 4). The holes were distributed over a hexagonal network where l denotes the distance between two holes. This distance is also called the period. The hole machining of the utilized substrate caused stresses on the machined material. As demonstrated in Fig. 5, analysis of the surface condition showed roughness at the hole edges, creating a “lip”, noted δ � 12 nm high. This height represents the average value of the asperities on the surface related to the manufacture of the substrates. Physical properties of the oil: The characteristics of the oil (SilOil M40) used in this experiment are provided in Table 3. From the SilOil M40 data sheet, we established how the viscosity and density varied as a function of temperature. This information allowed us to determine these values at each temperature, particularly Tamb ¼ 20 � C and Th ¼ 270 � C (see Fig. 6). The surface tension of the oil was measured at different temperatures
in water and water in oil. In the present work, we focus on the behavior of a drop of SilOil M40 deposited on smooth and textured substrates at room and high tem peratures equal to 20 � C and 270 � C, respectively. Special attention is given to the propagation of the oil film appearing around the drop, on the textured substrate. The analysis of the experimental results con centrates essentially on the effects of substrate nature and temperature on the evaporation kinetics. 2. Experimental process and materials A silicon substrate was placed in a vapor chamber (14 � 12.4 � 7.5 cm) in which the ambient temperature and relative humidity were controlled and set to 20 � C and 50%, respectively (Fig. 3). A droplet of oil (3.4 μL) was deposited on a heated silicon substrate (Th ranging from 20 � C to 270 � C) by means of a programmable syringe (KD Scientific Legato 100). The air inside of the chamber was at rest. The top of the vapor chamber had a sapphire window for the infrared camera and a hole for passing the syringe. The infrared camera (FLIR X6580SC, 640 � 512 pixels, 15 μm detector pitch) was installed at the top for infrared thermal mapping and visualization of thermal instabilities on the surfaces of the droplets. A side-view charge-coupled device (CCD) camera (Allied Vision
Table 3 Characteristic of SilOil M40 at different temperatures. 1
σ (mN.m ) ρ (g.cm 3)
ν (mm2.s 1)
T amb ¼ 20 � C
Th ¼ 270 � C
20.73
6.2
0.94
0.71
11.24
1.2
Fig. 4. Spherical micro-patterns of diameter d, period l, and depth e: (a) schematic diagram, (b) 2D view, and (c) 3D view.
Fig. 5. (a) Microscopic snapshots of a hole in 3D and (b) a section of the substrate. 4
D. Khilifi et al.
International Journal of Thermal Sciences 151 (2020) 106236
Fig. 6. Variations of the kinematic viscosity and the density of oil as a function of temperature.
Fig. 7. Variations of the surface tension of oil as a function of temperature.
Fig. 8. Photo of the oil drop deposited on textured silicon at ∅ ¼ 44% and T ¼ 20 � C: (a) oil drop and (b) oil film (in blue). . (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
5
D. Khilifi et al.
International Journal of Thermal Sciences 151 (2020) 106236
Fig. 9. Photo of the oil drop deposited on textured silicon at ∅ ¼ 25% and T ¼ 20 � C: (a) oil drop and (b) oil film (in blue). (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
Fig. 10. Measurement of the spreading length of the liquid film at t ¼ 1300 s: (a) ∅ ¼ 44% and (b) ∅ ¼ 25%.
by the pendant drop method with the Kruss® DSA system (see Fig. 7). We considered two series of substrates where we made holes of equal size (d ¼ 100 μm and e ¼ 50 μm) by varying the period l:
drops have hexagonal shapes. A very thin oil film spreads between the holes, which proves that the wetting regime is Wenzel-like. These results are in agreement with those presented in Refs. [8,9], where the morphology of water drops deposited on substrates textured by micro-pillars are described. During its propagation around the drop, the oil film bypassed the holes, as observed in the case of micro-pillars in the configurations studied by Bico et al. and Hisler et al. [8,9]. The “lip” at the hole edge (height δ � 12 nm) prevented the oil film from invading the holes during its propagation. These holes behaved on the edges as micro-pillars of diameter d. Therefore, the fraction of the holes’ surface can be defined by the following relation [8,9]:
➢ Series 1: l ¼ 50 μm ➢ Series 2: l ¼ 100 μm 4. Results and discussion 4.1. Tests at room temperature In this section, we examine the wettability behavior of an oil drop (3.4 μL) deposited on a textured substrate at room temperature Tamb ¼ 20 � C.
∅¼
4.1.1. Wenzel-like regime
d2 ðl þ dÞ2
(19)
4.1.1.2. Effect of ∅ on the oil film propagation. In this section, we focus on the influence of the propagation of the oil film, appearing around the drops on the two textured substrates over time. The purpose of our study is to examine the effect of the surface fraction of the holes ∅ on this phenomenon. Fig. 10 shows how the spreading length was measured based on continuity of the film propagated on the two textured substrates. For instance, at t ¼ 1300 s, the measurement of the spreading length L of the oil film gave the following results:
4.1.1.1. Experimental observation. The morphology of an oil drop was observed and recorded using a high speed camera (Keyence, VW600C) mounted on an optical microscopic lens (Keyence, VH-Z100R, magni fication zoom from 100 � to 1000 � ). Video editing/analysis software (Keyence, VW-9000 Motion Analyzer) was used to visually observe oil propagation over time. Figs. 8 and 9 show the morphologies of SilOil M40 drops deposited on the textured substrates (series 1 and 2). As shown in the figures, the 6
D. Khilifi et al.
International Journal of Thermal Sciences 151 (2020) 106236
Fig. 11. Variation of the spreading length of the oil film on different textured substrates ∅ ¼ 44% and ∅ ¼ 25% over time.
➢ Series 1 (∅¼ 44%): L ¼ 1.06 mm ➢ Series 2 (∅¼ 25%): L ¼ 2.1 mm
The formation of the oil film around the drop was due to a negative energy difference [9,10], which resulted in a small displacement dx of the liquid front for a short time dt, generating an initial velocity and causing the propagation of the oil film on the textured surface. This velocity diminished over time until it vanished and the film stabilized. Fig. 11 also reveals that the spreading length of the oil film, propa gated on a textured surface of ∅ ¼ 25% increased more rapidly than that of the film propagated on a textured surface of ∅ ¼ 44%. This result was proven experimentally by Xiao [20] in the case of a textured surface
This method was used to measure the spreading length at any time. Fig. 11 represents the variation of the spreading length of the dispersed oil film as a function of time on the different textured surfaces. The length of the oil film increases significantly during the first few seconds. Then, this increase slows down over time and eventually stabilizes at a constant value.
Fig. 12. Snapshots from infrared video camera of the evaporation process of oil drop deposited on textured surface silicon: ∅ ¼ 44%, Th ¼ 270 � C and V ¼ 3.4 μL (see the Information for visualization section). with ➢ ➢ ➢ ➢
(1): (2): (3): (4):
liquid–gas interface of the oil drop. the area of the substrate on which the oil spreads and propagates as a function of time. the substrate (textured silicon) heated at 270 � C. the trace of the drop after evaporation. 7
D. Khilifi et al.
International Journal of Thermal Sciences 151 (2020) 106236
Fig. 13. Variation of the spreading length of the oil film over time at different temperatures for ∅ ¼ 44% and V ¼ 3.4 μL.
with cylindrical micro-pillars. Indeed, the increase in the permeability K after the ∅ decrease of 43.18% significantly minimized the viscous resistance, K ¼ Kμ [20], which facilitated the film propagation. Moreover, it is clear from Fig. 11 that the spreading length L of the oil film stabilized at around 1300 s.
4.2. Behavior of the drop of sessile oil in the Wenzel-like regime at high temperature 4.2.1. Effect of temperature on the propagation of the oil film Another oil drop (3.4 μL) was deposited on the textured silicon of ∅ ¼ 44% heated to Th ¼ 270 � C. To deeply study the effect of temperature on the behavior of this drop, we compared the results with those ob tained at room temperature. Fig. 12 demonstrates that the drop deposited on the textured has a hexagonal form connected by a thin film, thus representing a Wenzellike regime. This result is also visible in Fig. 8. The series of images presented in Fig. 12 reveals that the oil film initially propagates rapidly at a high temperature, and then disappears, highlighting the effect of intensive evaporation. In order to study the influence of temperature on the propagation of the oil film, we represent the variation of the spreading length L of the oil film as a function of time for different temperatures (Fig. 13). This figure reveals that the film spreading length L increased considerably as the temperature increased. This decreased the liquid viscosity by 87% (Fig. 6), which reduced the viscous resistance and facilitated the oil film propagation.
➢ Lmax ¼ 1.06 mm: ∅ ¼ 44% ➢ Lmax ¼ 2.1 mm: ∅ ¼ 25% From the previously presented findings, it can be deduced that the 43.18% increase of ∅ decreases the maximum spreading length Lmax of the oil film by 50%. 4.1.1.3. Theoretical study. Considering that the propagation of the oil film on the textured substrate with holes was identical to that of the micro-pillars, the spreading length can be calculated applying equations 13–17. If Δv represents the difference in volume between two halfspherical–shaped holes of diameter (d þ l) and d, we obtain: Δv ¼
π�
ðd þ lÞ3
12
d3
�
� Pc ¼ σ
12lð2d þ lÞ � � cosθeq π ðd þ lÞ3 d3
(20) � 48dδ 1 þ � π ðd þ lÞ3
d3
� �
(21)
4.2.1.1. Theoretical study. Because the surface tension and the viscosity of the oil depend on the temperature, we can write
where θeq ¼ 0. Then, we get: 48dδ Pc ¼ σ � π ðd þ lÞ3
d3
�
GðTÞ ¼
(22)
� �1 2Pc :K 2
μ �
(25)
�12
Note that the liquid imbibes into the micro-textures as long as Pc > 0. For a substrate textured with spherical-holes of diameter d, the permeability K is given by the Ergün equation.
GðTh Þ ¼ GðTamb Þ �σðT
d2 ð1 ∅Þ3 K¼ 150 ð∅Þ2
GðTh Þ � 1:92 GðTamb Þ
(27)
LðTh Þ � 1:92 LðTamb Þ
(28)
σðTh Þ μðTh Þ
�12 � 1:92
(26)
amb Þ
μðTamb Þ
(23)
Therefore, we obtain sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 96 d3 δ ð1 ∅Þ3 σ pffi LðtÞ ¼ t � � 3 μ 150 π ðd þ lÞ d3 ð∅Þ2
Fig. 13 compares the experimental and theoretical L (t) results for different temperatures, and it demonstrates good quantitative agreement.
Fig. 11 compares the experimental and theoretical L (t) for the two values of ∅, showing good quantitative agreement.
4.2.1.2. Information for visualization. According to the Ste fan Boltzmann law, the radiant existence of a gray body j is determined 8
D. Khilifi et al.
International Journal of Thermal Sciences 151 (2020) 106236
Fig. 14. Variation of the drop volume over time: Th ¼ 270 � C, Tamb ¼ 20 � C, ∅ ¼ 44%, and V ¼ 3.4 μL.
Fig. 15. Variations of the drop contact angle and diameter over time: Th ¼ 270 � C, Tamb ¼ 20 � C, ∅ ¼ 44%, and V ¼ 3.4 μL.
Fig. 16. Variation of the drop evaporation rate over time: Th ¼ 270 � C, Tamb ¼ 20 � C, ∅ ¼ 44%, and V ¼ 3.4 μL.
as j ¼ εγT 4
thermal mapping represents the level of thermal radiation l received by 0 the infrared camera. In fact, the l level is proportional to the radiant j. The various colors denote different temperatures or emissivities related to several substances. After a few seconds of evaporation, the oil drop became homogeneous and its temperature equaled that of the silicon 0
(29)
where γ is the Stefan Boltzmann constant and ε and T are the emissivity and temperature of the substance, respectively. The scale in the infrared 9
D. Khilifi et al.
International Journal of Thermal Sciences 151 (2020) 106236
angle, and diameter of the drop over time. Obviously, the volume of the drop decreases over time, and it vanishes at almost 70 s. The oil drop evaporating on textured silicon substrate had a constant diameter for almost 20 s, whereas the contact angle decreased linearly over time, which represents the constant line mode (stage 1). This mode is justified by Fig. 17. Stage (2): During this stage, the drop deposited on the textured sil icon exhibited different behavior, in which the diameter and the contact angle decreased simultaneously over time, which indicates the stick slip mode. Fig. 16 depicts the evolution of the evaporation rate over time. The evaporation rate is defined by mev ¼
dV dt
S
(30)
Fig. 16 also shows that this rate had a maximum value at t ¼ 0 s due to the important concentration gradient between the liquid–gas inter face and the surrounding air. As evaporation started, air in the imme diate vicinity of the drop became more saturated with oil vapor, which resulted in a considerable decrease of the concentration gradient and consequently a decrease in the evaporation rate over time. 4.2.2.2. Thermal study. Fig. 12 represents a series of images taken by an infrared camera. These images describe the lifetime of the oil drop deposited on the textured silicon (∅ ¼ 44%) heated at 270 � C. This figure shows that the total evaporation of the oil film whose lifetime was around 266 s took longer to evaporate than the drop whose lifetime was about 70 s (Fig. 17). In fact, at the base of the drop, the liquid spontaneously filled the holes (Wenzel-like regime), which increased the liquid–solid contact surface, increasing the temperature of the drop and consequently intensifying evaporation. The oil film appearing around the drop spread across the substrate avoiding holes, which explains the delay of oil film evaporation compared to that of the drop.
Fig. 17. CCD snapshots at different instants: Th ¼ 270 � C, Tamb ¼ 20 � C, ∅ ¼ 44%, and V ¼ 3.4 μL.
substrate, Th ¼ 270 � C, whereas the emissivity of the oil remained higher than that of the silicon substrate. Therefore, we observed a color contrast between the oil drop and the silicon substrate. This contrast was visu alized by the infrared camera. The normal temperature profile of a sil icon substrate was constant at Th ¼ 270 � C. According to the infrared images presented in Fig. 8, the color consistency at the substrate surface until the end of evaporation indicated a temperature less than 270 � C.
4.3. Behavior of oil drop deposited on a smooth surface In this part, the evaporation of a drop of SilOil M40 deposited on a smooth-surface silicon substrate is considered. The surface had the same chemical composition and the same dimensions as the textured silicon surface. The purpose here is to study the effect of surface nature on the evaporation kinetics. The images presented in Fig. 18 shows that the oil drop, deposited on
4.2.2. Study of the oil drop evaporation at high temperature 4.2.2.1. Dynamic study. In this section, we focus on the dynamic study of the oil drop presented in Fig. 12 (zone 1). Fig. 14 and15 show respectively the variations of the volume, contact
Fig. 18. Snapshots from infrared video camera of evaporation process of oil drop deposited on smooth-surface silicon: Th ¼ 270 � C and V ¼ 3.4 μL (see the In formation for visualization section). 10
D. Khilifi et al.
International Journal of Thermal Sciences 151 (2020) 106236
the smooth-surface silicon substrate, spread across the whole surface of the substrate, forming a thin film. As demonstrated, the life of the oil film was around 2400 s. Comparing these results with those illustrated in Fig. 12, we note that the evaporation of a drop deposited on a textured surface was more intense than that of a drop deposited on a smooth surface. In fact, the micro-texture reduced the drop lifetime by 89% and increased the heat exchange surface between the drop and the substrate, which improved the heat transfer at the liquid–solid interface, thus fa voring evaporation. This phenomenon explains the delay of the oil film evaporation compared to that of the drop, as observed in Fig. 12.
References [1] W. Wang, J. Lin, D.C. Schwartz, Scanning force microscopy of 665 DNA molecules elongated by convective fluid flow in an evaporating 666 droplet, Biophys. J. 667 (75) (1998) 513–520. [2] M. Chopra, L. Li, H. Hu, M.A. Burns, R.G. Larson, DNA 668 molecular configurations in an evaporating droplet near a glass surface, J. Rheol. 669 (47) (2003) 1111. [3] T. Kawase, H. Sirringhaus, R.H. Friend, T. Shimoda, Inkjet 659 printed via-hole interconnections and resistors for all-polymer 660 transistor circuits, Adv. Mater. 13 (2001) 1601–1605, 661. [4] B.J. de Gans, P.C. Duineveld, U.S. Schubert, Inkjet printing 662 of polymers: state of the art and future developments, Adv. Mater. 663 (16) (2004) 203–213. [5] M. Sato Saito, M. Suzuki, I. Evaporation and combustion of a 671 single fuel droplet in acoustic fields, Fuel 73 (1994) 349–353, 672. [6] C.W. Park, M. Kaviany, Evaporation-combustion affected by 673 in-cylinder, reciprocating porous regenerator, J. Heat Transf. 674 124 (2002) 184–194. [7] A. Bar-Cohen, M. Arik, M. Ohadi, Direct liquid cooling of high flux micro and nano electronic components, Proc. IEEE 94 (8) (2006) 1549–1570. [8] Valentin Hisler, Laurent Vonna, Vincent Le Houerou, Stephan Knopf, Christian Gauthier, Michel Nardin, Hamidou Haidara, Model experimental study of scale invariant wetting behaviors in Cassie Baxter and Wenzel regimes, Langmuir 30 (2014) 9378–9383. [9] J. Bico, C. Tordeux, D. Qu�er� e, Rough wetting, Europhys. Lett. 55 (2) (2001) 214–220. [10] C. Ishino, K. Okumura, D. Quere, Wetting transitions on rough surfaces, Europhys. Lett. 68 (3) (2004) 419–425. [11] Christian Dorrer, Jurgen Ruhe, Advancing and receding motion of droplets on ultrahydrophobic post surfaces, Langmuir 22 (2006) 7652–7657. [12] H. Hasimoto, On the periodic fundamental solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres, J. Fluid Mech. 5 (1959) 317–328. [13] A.S. Sangani, A. Acrivos, Slow flow through a periodic array of spheres, Int. J. Multiph. Flow 8 (1982) 343–360. [14] A.S. Sangani, A. Acrivos, Slow flow past periodic arrays of cylinders with application to heat transfer, Int. J. Multiph. Flow 8 (1982) 193–206. [15] J.E. Drummond, M.I. Tahir, Laminar viscous flow through regular arrays of parallel solid cylinders, Int. J. Multiph. Flow 10 (5) (1984) 515–540. [16] L. Skartsis, B. Khomami, J.K. Kardos, Resin flow through fiber beds during composite manufacturing processes, Part IINumerical and experimental studies of Newtonian flow through ideal and actual fiber beds, Polym. Eng. Sci. 32 (1992) 231–239. [17] A.A. Kirsch, N.A. Fuchs, Studies on fibrous aerosol filters—II Pressure drops in systems of parallel cylinders, Ann. Occup. Hyg. 10 (1967) 23–30. [18] C. Chmielewski, K. Jayaraman, The effect of polymer extensibility on cross flow of polymer solutions through cylinder arrays, J. Rheol. 36 (1992) 1105–1126. [19] B. Khomami, Moreno, LD Stability of viscoelastic flow around periodic arrays of cylinders, Rheol. Acta 36 (1997) 367–383. [20] Rong Xiao, Enright Ryan, N. Evelyn, Wang, Prediction and optimization of liquid propagation in micropillar arrays, Langmuir 26 (19) (2010) 15070–15075. [21] Navdeep Singh Dhillon, Jacopo Buongiorno, Kripa K. Varanasi, Critical heat flux maxima during boiling crisis on textured surfaces, Nat. Commun. 6 (2015) 8247. [22] C.R. Shaddix, P.R. Tennison, in: Effects of Char Content and Simple Additives on Biomass Pyrolysis Oil Droplet Combustion 27th Symposium (International) on Combustion, The Combustion Institute, 1998, 1907–14. [23] J. D’Alessio, M. Lazzaro, P. Massoli, V. Moccia, in: Thermo-optical Investigation of Burning Biomass Pyrolysis Oil Droplets 27th Symposium (International) on Combustion, The Combustion Institute, 1998, 1915–22. [24] W.L.H. Halletta, N.A. Clarkb, A model for the evaporation of biomass pyrolysis oil droplets, Fuel 85 (2006) 532–544. [25] James Brett, Andrew Ooi, Julio Soria, The effect of internal diffusion on an evaporating bio-oil droplet, the chemistry free case, biomass and bioenergy 34 (2010), e1140, 1134. [26] M.S. Wu, S.I. Yang, Combustion characteristics of multi-component cedar bio-oil/ kerosene droplet, Energy 113 (2016) 788e795. [27] G. Greeves, I.M. Khan, G. Onion, in: 16th Symposium (International) on Combustion, 1976, pp. 321–336. [28] Z. Zhang, J. Yang, X. Chen, Trans. CSICE (Chin. Soc. Intern. Combust. Engines) 3 (1985) 321–332. [29] Wei Biao Fu, Ling Yun Hou, Lipo Wang, Fan Hua Ma, A unified model for the micro-explosion of emulsified droplets of oil and water, Fuel Process. Technol. 79 (2002) 107–119.
5. Conclusion In this research work, we carried out an experimental study on the propagation of a SilOil M40 film as a function of the textures of a sub strate. We also examined the effect of solid fraction ∅ and temperature on the propagation of the film. We showed that the film propagation increased � by decreasing the surface fraction of the holes ∅ � by increasing the substrate temperature Theoretical studies were carried out to confirm the experimental results. We determined an expression of the propagation coefficient G using the Darcy equation. This coefficient depended on the surface tension σ , the dynamic viscosity μ, and the surface fraction of the holes ∅. From this relationship, we proved that the propagation coefficient G increases by decreasing the surface fraction of the holes ∅ and increasing temperature T. Then, we highlighted of the effect of the nature of the substrate surface on the evaporation of SilOil M40 oil drop at high temperature. � Smooth-surfaced substrate: The sessile drop of initial volume V0 ¼ 3.4 μL spread across the whole surface of the substrate, forming a thin film. It evaporated over 2400 s. � Textured-surfaced substrate (∅ ¼ 44%): The sessile drop evaporated in the Wenzel-like regime over 266 s. The experimental results showed that the micro-texture accelerated the evaporation of the oil drop. The obtained findings provide a better understanding of the effect of substrate surface on the kinetics of the evaporation of an oil drop and the importance of choosing an appro priate surface to reduce the energy needed during the evaporation process. Declaration of competing interest The authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.ijthermalsci.2019.106236.
11