The Influence of Gravity on Contact Angle and Circumference of

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The Influence of Gravity on Contact Angle and Circumference of Sessile and Pendant Drops has a Crucial Historic Aspect Semih Gulec, Sakshi B. Yadav, RATUL DAS, Vaibhav Bhave, and Rafael Tadmor Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b03861 • Publication Date (Web): 06 Mar 2019 Downloaded from http://pubs.acs.org on March 12, 2019

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The Influence of Gravity on Contact Angle and Circumference of Sessile and Pendant Drops has a Crucial Historic Aspect Semih Gulec1,#, Sakshi Yadav1,#, Ratul Das1, Vaibhav Bhave1 and Rafael Tadmor*,1,2 * Corresponding Author. Email: [email protected] and [email protected] # These authors contributed equally 1. Dan F. Smith Department of Chemical Engineering, Lamar University, Beaumont, TX 77710. 2. Department of Mechanical Engineering, Ben Gurion University, Beer Sheva, Israel Keywords: Contact Angle Hysteresis, Drop Shape, Drop Contact Angle, Varying Effective Gravity, Interfacial Modulus, Work of Adhesion, Centrifugal Adhesion Balance

Abstract Normally, pendant drops adapt contact angles that are closer to 90o than their sessile analogues. This is due to the drop’s weight that pulls on the pendant drop and straightens its contact angles. In this paper, we show a case in which the opposite happens: sessile drops which adapt contact angles that are closer to 90o than their pendant analogues. To achieve these peculiar states, one needs to increase the effective gravity on the drops and then relax it again to 1 𝑔. Apparently, this and other phenomena, depend not only on the direction of the gravitational force, but also on the drop’s history. We show that the drop’s contact angle (and resultant area) is affected by two types of histories: shortterm history, and long-term history. For example, if we gradually increase the effective gravity on the drop and then decrease it back to 1 𝑔, and repeat this cycle again and again, we see that the first cycle is drastically different, while other cycles approach a plateau in their behavior. In addition to drop’s history, we explain these observations in terms of volume conservation, drop contact area, and pinning effect. This study can be generalized for other body forces such as electrical, magnetic or accelerating systems.

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Introduction To describe the effect of gravity on wetting properties1–6 often, Bond number (or capillary length) is used. The Bond number (𝐵𝑜)7 describes the ratio between the gravitational and surface tension forces and is defined as: 𝐵𝑜≅

𝐿2𝜌𝑔 𝛾𝐿𝑉

(1)

,

where, 𝐿 is a characteristic length scale (in drops, this would be the drop’s radius), 𝜌 is the difference between the density of the drop’s liquid and that of the surrounding, 𝑔 is the gravitational acceleration and 𝛾𝐿𝑉 is the liquid’s surface tension. A generalized form of 𝐵𝑜 which considers other body forces, such as those used in the Centrifugal Adhesion Balance (CAB) experiments, is 8–11:

(

)

𝐵𝑜 = 𝜌𝐿2 𝑓 ⊥ 𝑚 𝛾𝐿𝑉,

(2)

where, 𝑓 ⊥ is the normal force acting on the drop and 𝑚 is the mass of the drop. Equations 1 and 2 are useful for describing various phenomena that relate to the interplay between surface tension and other forces (gravity, static pressure, and inertia)7. At the same time, they lack subtleties such as the role of history on the drop’s shape at different gravities. In this paper, a controlled set-up is used to change the effective gravity with time. We study the influence of effective gravity on a drop’s contact angle and circumference by periodically changing the gravity from 1 𝑔 to 4.8 𝑔 for a pushed drops (sessile) and a pulled drops (pendant), at constant drop volume. The contact angles considered here are the apparent ones and not the equilibrium contact angles which do not depend on body forces, such as gravity, magnetic field or electric, inertia, etc12–14. According to the studies by Shanahan, de Gennes and Tadmor11,16–18,21–23, the solid-liquid interaction results in a deformation of the solid’s outmost layer at the solid-liquid triple contact line. This deformation is usually topographically negligible, but it is significant from an intermolecular forces point of view as it causes molecular reorientation of the outmost solid surface. The liquid induces this reorientation in a way that increases the solid-liquid interaction. The system prefers this reorientation as it lowers the interfacial energy, i.e. increase the intermolecular interaction. As time progresses, the


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resultant pinning of the drop to the surface increases. The drop retention force, according to this model, is11,16–18,21–23: 𝑓∥ =

4 𝛾2𝐿𝑉sin 𝜃 𝐺𝑠

(cos 𝜃𝑅 ― cos 𝜃𝐴) ,

(3)

where, 𝑓 ∥ is the lateral force required to slide the drop along the surface, 𝜃 is the contact angle that the drop adopted when it was resting on the surface before the onset of motion, 𝜃𝑅 and 𝜃𝐴 are the drop receding and advancing contact angles and 𝐺𝑠 (Interfacial Modulus)16,17,22,24. 𝐺𝑆, quantifies the resistance of the solid surface’s molecules to interact with liquid’s molecules. Thus, if the outmost molecular layer of the solid is completely rigid, namely no functional groups within molecules can budge, then 𝐺𝑆 will be infinite. The surface potential of the solid under the drop and under the air will be the same, and no force will be required to move the drop. On the other hand, if solid functional groups can easily reorient on the surface as a result of a liquid contact, then 𝐺𝑆 will be small, and the surface potential of the solid under the drop and under the air will be different, and force will be required to move the drop. In our experimental setup we increase or decrease the effective gravity on a drop in a closed chamber. This setup mimics a practical case wherein a fluid in a closed box is accelerated or decelerated as can be done using magnetic or electric forces, or by accelerating the system.

Materials and Method The controlled setup used in this paper is obtained by a Centrifugal Adhesion Balance (CAB)8– 10,16,17,25,26(see

fig. 1). The CAB is a desktop device used to conduct studies pertaining to liquid–solid

interactions. The normal force applied on the drops is periodically varied while the lateral force is maintained at zero. This force variation is achieved by a combination of centrifugal and gravitational forces to allow decoupling between normal and lateral forces. Fig. 1 shows some parts of the CAB. It consists of a rotating arm which moves perpendicular to the gravitational field (fig. 1c). One end of the arm has a chamber which houses a goniometer (sample holder, light source and a camera) (fig. 1a and 1b) and the other end has a tablet computer that also acts as a counter balance (fig. 1c). The chamber can be tilted perpendicular to the rotation.


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(b)

(a) 4 1

2 3

1

3 4 2

(c)

3

1

2

4

Figure 1: (a) Side view of the goniometer assembly of the CAB – (1) CCD Camera (2) Sample holder and optic dome (3) Light source (4) Syringe Holder. (b) Top view of the goniometer (1) CCD Camera (2) Syringe Holder (3) Sample holder and optic dome (4) Light source (4). (c) Picture of the rotating arm of the CAB with the counterbalance – (1) Goniometer (2) DC motor (inside the cylinder) (3) Tablet computer (which also acts as a counter balance) (4) PID controller.


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Fig.2 shows a schematic of the forces acting on a drop placed in the CAB’s goniometer. The drop experiences two kinds of forces – gravity (𝑚𝑔), due to the earth’s mass and centrifugal (𝜔2𝑅), due to the rotation of the CAB’s arm. Both of these forces are controlled and changed by the tilt angle (𝛼) of the goniometer and the angular velocity (𝜔) of the arm, respectively. The vectorial summation of the forces give the equations for the normal and lateral forces: eq. 4 for the lateral and eq. 5 for the normal forces. In this study, as the angular velocity changes, the goniometer tilt changes as well to maintain 𝑓 ∥ = 0. Thus, the lateral components of the gravitational and centrifugal forces cancel each other, and their normal components are added as shown in fig. 2. To obtain this, as the centrifugal force increases, the automated tilt of the goniometer is synchronized with the centrifugal rotation using a PID controller (shown in fig. 1c) to ensure that the goniometer tilt angle (𝛼) and the angular velocity (𝜔) of the CAB arm change such as that the lateral force (eq. 4) is zero.

Figure 2: Schematics for the CAB alignment for drop sliding at zero normal force.

The CAB manipulates normal and lateral forces according to following equations: 𝑓 ∥ = 𝑚(𝜔2𝑅 𝑐𝑜𝑠𝛼 ― 𝑔 𝑠𝑖𝑛𝛼) ,

(4)

𝑓 ⊥ = 𝑚(𝜔2 𝑅 𝑠𝑖𝑛𝛼 + 𝑔cos 𝛼) ,

(5)

where 𝑓 ⊥ and 𝑓 ∥ are the normal and lateral force acting on the drop, respectively, 𝑚 is the drop’s mass, 𝜔 is the CAB angular velocity, 𝑅 is the drop’s distance from the CAB’s center of rotation, 𝑔 is the gravitational acceleration, and 𝛼 is the tilt angle with respect to the horizon.


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Material: We used silicon wafers which were silanized8,27–30 (silicon wafers covered with self-assembled monolayer of silane). Silicon wafers were obtained from Virginia Semi- conductor, VA (diameter: 76.2 mm ± 0.3 mm, center thickness: 381 μm ± 25 μm) and cut into rectangular slides of 2 cm × 1.5 cm. Hydrogen peroxide (50 wt% in water) was obtained from Acros Organics. Ethanol (99.5%, 200 proof absolute), deionized water, ammonium hydroxide (99.99%), hydrochloric acid (37%), toluene (99.5%), and octadecyltrimethoxysilane (90% technical grade, CAS No. 3069-42-9) all obtained from Sigma Aldrich and used for the self-assembly silanization process. Method: The experiments are conducted when the lab environment was at 23 ± 1 °C and the humidity inside the CAB optic dome was close to saturation31. The silanized silicon surface was placed in the CAB sample holder, the main water drop was placed at the center of the silicon surface and, near it, a few satellite droplets are added. The sample was then covered with an optic, glass dome to bring the system to near saturation condition30–32.

Result and Discussion The nanoscopic roughness of the silanized silica surface, used to conduct the experiments, was measured using Anton Paar Tosca 400 Atomic Force Microscope (AFM). The topographic measurements of a 10X10 μm region within the sample are shown in fig. 3 which corresponds to a Root Mean Square (RMS) roughness of 1.5 nm.

(a)

(c)

(b)


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Figure 3: AFM images of the silanized silica surface. (a) A three-dimensional image of surface topography. (b) A two-dimensional image of surface topography. (c) A topographic profile of the horizontal line marked by “1” in fig. 3b.

Fig. 4a shows images of a 6 μl pendant (pulled) water drop under a periodically varying normal acceleration. The length of the blue arrows is proportional to the normal acceleration which increases gradually from -1 𝑔 to -4.8 𝑔 and back to -1 𝑔. The negative sign represents a pulling direction. The red arrows indicate the direction of change of the drop’s circumference, corresponding to the history or change of the applied force.

Circumference Contact Angle Normal (mm) (deg) Acceleration (g)

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-6 -3

(b)

0 96 92

5 1

3-4

6

1

2 Time (min)

7

2

88

8.5 8.0 7.5 0


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Figure 4: (a) Images of a 6 μl pendant (pulled) water drop on silanized (C18) silicon surface, under a periodically varying normal acceleration. The vertical blue arrows show the direction of the applied normal force. The horizontal, red arrows show the change in circumference with the change in normal force. (b) Circumference and contact angle of the 6 μl pendant water drop, shown in fig. 4a, over 2 cycles, as a function of the time from the moment that the surface was flipped. (c) Illustration showing a qualitative zone-wise change in the pendant water drop circumference and contact angle, shown in fig. 4b, with the applied normal force.

The change in contact angle and circumference of the pendant drop shown in fig. 4a is due to the variation of the normal acceleration from -1 𝑔 to -4.8 𝑔. The first two cycles of this experimental run are shown in fig. 4b versus the time. Fig. 4b shows the changes in the normal force, drop contact angle and drop circumference together with a zone division which is numbered in accordance with an exaggerated illustration in fig. 4c. Below, we describe the zones chronologically: Zone 1 in fig. 4b (illustrated in fig. 4c.1): In this zone, with the increase in the applied normal force, the drop is pulled. This pulling decreases the contact angle as the drop tends towards a bell shape. The drop circumference remains the same because of the strong pinning at the triple line while the contact angle decreases. Zone 2 in fig. 4b (fig. 4c.2): As the force keeps increasing, eventually drop depinning occurs and the circumference decreases sharply. As this happens, the contact angle increases to conserve its volume. The variation of the contact angle compared with the natural state for a droplet under the gravitational effect also agrees with the triple contact line (TCL) model by Liu et al33,34 according to which, the TCL will remain fixed with the increase in the drop volume until the volume exceeds a critical value. In analogy to this model, in our setup, the drop circumference remains constant with the increase in the applied normal force until the force reaches a critical value. Zone 3-4 in fig. 4b (fig. 4c.3 and 4c.4): In this zone, the force changes the sign of its time derivative but not the sign of the function (the orange dashed lines in fig 4b marks the change in the derivative), i.e. the force is still very high. Right as the force derivative changes its sign, the circumference stops decreasing and after a short plateau, it starts to decrease slowly in pursuit of its new equilibrium. This plateau is more pronounced in subsequent cycles. At the same time the contact angle steadily increases. 8 ACS Paragon Plus Environment

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This is because the drop still tends more towards a bell shape w.r.t. its equilibrium position, and therefore, relaxes its contact angle to fit a rounder drop shape, i.e. higher contact angle (fig. 4c.4). This is enabled because the pinning of the triple line is weak at this stage. Zone 5 in fig. 4b (fig. 4c.5): As the force continues to decrease, the drop finally reaches a rounder shape. The circumference continues to increase and therefore the contact angle needs to go down to conserve the drop’s volume. Zone 6 in fig. 4b (fig. 4c.6): The triple line (i.e. circumference) remains roughly steady and allows pinning to intensify. At the same time, the contact angle adjusts itself to the forces at a fixed triple line. Zone 7 in fig. 4b: Here, unlike in zone 2 in fig. 4b, the drop depinning occurs a bit later (at -3.6 g instead at -3.2 g) because the circumference is smaller than that in zone 1 and is closer to its drop's equilibrium shape under this force, i.e. the one in zone 6. Hence the change in the circumference fits the pulling force better. The change in drop circumference, contact angle and the drop shape are similar to those illustrated in fig. 4c.2. For the same system shown in fig. 4; fig. 5 shows the changes in the drop’s contact angle and circumference due to the variation of the normal acceleration from -1 𝑔 to -4.8 𝑔, periodically, over 8 cycles. We see that the changes in the contact angles, past the first cycle, are smaller. The circumference, on the other hand, seems to change more pronouncedly on later cycles as well. The lower extreme of the circumference increases and the upper extreme decreases, though less significantly. these curves represent a single experimental run. We discuss these later on, on the basis of the average of several such runs. Circumference Contact Angle Normal (mm) (deg) Acceleration (g)

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Figure 5: Circumference and contact angle of a 6 μl pendant water drop under a periodically varying normal acceleration versus time from the moment the surface was flipped. So far, we described drops that are pulled from the surface (pendant drops). We now move on to describing the opposite situation, namely drops that are pushed against the surface (sessile drops). Fig. 6 shows the image of a 6 μl sessile (pushed) water drop under a periodically varying normal acceleration. The length of the blue arrows is proportional to the normal acceleration which increases gradually from 1 𝑔 to 4.8 𝑔 and back to 1 𝑔. The red arrows indicate the direction of change of the drop’s circumference, corresponding to the applied force.

Circumference Contact Angle Normal (deg) Acceleration (g) (mm)

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(b)

0 96 92

5 1

3

2

6

4

88 9.9 9.6 9.3 9.0 0

1

2 Time (min)


3

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Figure 6: (a) Images of a 6 μl sessile (pushed) water drop on silanized (C18) silicon surface, under a periodically varying normal acceleration. The vertical blue arrows show the direction of the applied normal force. The horizontal, red arrows show the change in circumference with the change in normal force. (b) Circumference and contact angle of the 6 μl sessile water drop, as shown in fig. 6a, under periodically varying normal acceleration, over 2 cycles. (c) Illustration showing the zone-wise changes in the sessile water drop’s circumference and contact angle, shown in fig. 6b, with the applied normal force.

The change in contact angle and circumference of the sessile drop shown in fig. 6 is due to the variation of the normal acceleration from 1 𝑔 to 4.8 𝑔. The first two cycles of this experimental run are shown in fig. 6b versus the time from the onset of the CAB’s rotation. Fig. 6a shows the changes in the normal force, drop contact angle and drop circumference together with a zone division which is numbered in accordance with an exaggerated illustration in fig. 6c. Below, we describe the zones chronologically:

Zone 1 in fig. 6b (illustrated in fig. 6c.1): In this zone, the changes in the drop circumference and contact angle are minor because the change in the force is small. Initially, the changes are within the experimental scatter. Later, the triple line (circumference) remains pinned and the contact angle rises a little to maintain the volume of the drop at the higher effective gravity. Towards the end of this zone, the force is finally sufficient to push the triple line to a wider circumference and the contact angle remains

roughly

constant,

namely

it

maintains

a

similar

(towards

pancake)

curvature.

Generally, the increase in the gravity increases the pressure on the drop and reduces the drop’s height, giving it a shape that deviates from a spherical one towards a pancake shape. Zone 2 in fig. 6b (fig. 6c.2): As the force keeps increasing, the circumference continues to increase. As this happens, the contact angle seems to reach its highest possible value as it increases very little (enhancing the curvature of the pancake shape a little) and then decreases (relieving the pancake shape a little) at constant volume. Towards the end of this zone, the pressure that builds up due to the increase in the force field reaches a maximum, and the contact angle decreases continuously, relieving the high curvature of the pancake shape. The decrease in the contact angle merges with the next zone 11 ACS Paragon Plus Environment

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33,34.

We reiterate, that the variation of the contact angle compared with the natural state for a droplet

under the gravitational effect also agrees with the triple contact line (TCL) model by Liu et al33,34. Zone 3 in fig. 6b (fig. 6c.3): As the force changes direction (shown by green dashed lines in fig. 6b), and starts decreasing, the circumference stops increasing, and after a short plateau, decreases as well, but slowly. This slowness has two reasons: (i) the force reduction allows a rounder drop shape, i.e. reduction in the contact angle, for which volume conservation requires smaller change in the circumference; and (ii) due to the depinning of the triple line the drop relaxes from a pancake shape to a rounder shape, i.e. lower contact angle. Zone 4 in fig. 6b (fig. 6c.4): The force returns to its starting point, but the drop now has a different shape. Specifically, it has a more extreme pancake shape than it had in the beginning of the zeroth cycle. The triple line remains roughly steady, as the force hardly changes, and allows the pinning to intensify. As the force grows, the pinned triple line remains roughly constant, which forces the contact angle to increase and intensify the pancake shape (the drop’s height reduces). Zone 5 in fig. 6b (fig. 6c.5): As the force continues to increase, the triple line finally de-pins and the circumference increases. The height of the drop is pushed down, which also intensifies the pancake shape, i.e. the contact angle increases. This is enabled due to the pinning of the triple line which resists a fast motion of the triple line. Zone 6 in fig. 6b (fig. 6c.6): This zone corresponds to the end of zone 2 and the first half of zone 3 with similar features as described before, with the exception that at the time that the force changes direction, the plateau is longer because the contact angle happens to be slightly smaller at the force’s peak. Smaller contact angle corresponds to a more circular, i.e. milder, drop curvature. For the same system shown in fig. 6; fig. 7 shows the changes in the drop’s contact angle and circumference due to the variation of the normal acceleration from 1 𝑔 to 4.8 𝑔, periodically, over 8 cycles. Again, we see that the changes in the contact angles, past the first cycle, change much less while the circumference changes more pronouncedly. Again, we note that these curves represent one single experimental run and discuss these below on the basis of the average of several such runs.

Contact Angle Normal (deg) Acceleration (g)

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Figure 7: Circumference and contact angle of a 6 μl sessile water drop under a periodically varying normal acceleration as a function of time from the moment the CAB started rotating.

The experimental result shown in fig. 5 and 7 were repeated several times and the corresponding averaged drop parameters are plotted in fig. 8.

Circumference at -1 g (mm)

100

96

8.5

Pendant

8.0

92

88

104

9.0

7.5

0

4

8

12

7.0 16

(b)

9.6

Circumference at 1 g (mm)

(a)

o Contact Angle at 1 g ( )

104

o Contact Angle at -1 g ( )

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9.2

100

Sessile 96

8.8

92

8.4

88

0

Time (min)

4

8

12

8.0 16

Time (min)

Figure 8: (a) Average of circumference and contact angle of a 6 μl water drop from different experimental runs taken at the time in which the acceleration cycle reaches (a) 𝑔 = ― 9.8 m/s2 (pendant). and (b) 𝑔 = + 9.8 m/s2 (sessile). The zeroth cycle represents a gravitational history that is non-existent in subsequent cycles (drops that never experienced a gravity of 4.8 𝑔 before).

Figure 8 demonstrates the common features to fig.s 5 and 7. It show that the drops behave in a different manner in the initial cycle as compared to the subsequent cycles. It appears that drop behavior is influenced by the short-term history, during the initial cycle and the long-term history, during the 13 ACS Paragon Plus Environment

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subsequent cycles. The anomalous drop behavior in the first cycle is because the first cycle is characterized by a stronger drop pinning to the surface due to the fact that the region outside the drop has never been wetted. This results in a higher drop resistance to the change in the effective gravity. In the duration between the placement of the drop on the surface and the beginning of the experiment, when the liquid drop is stable, the solid molecules, at and around the triple line, have time to reorient to the fluids above them: the solid-liquid and solid-air interfaces, which are clearly defined and stable at that time. In turn, this results in a stronger pinning. In the subsequent cycles, the drop pinning is weaker than the initial cycle. As the effective gravity changes, the drop retracts or expands, depending on the drop orientation (sessile or pendant). The movement of the triple line does not allow sufficient time for the solid surface molecules, at and near the triple line, to fully reorient to the air above them. There is also a possibility that the solid surface gets coated by a monolayer of liquid as the drop retracts and this influences its adhesion to the liquid drop. As seen in fig. 8, the drop parameters show a significant change at the end of the first cycle and approach a stable value in the subsequent cycles. Fig. 8a (pendant drop) shows that the value of the contact angle at 𝑔 = ― 9.8 m/s2 jumps following the end of the first cycle and during the subsequent cycles it remains at a closely constant value (about 95o). At the same time, the drop’s circumference reduces from its initial value and then, as the cycles progress, it approaches a stable value (about 8.4 mm, which slowly decrease possibly due to evaporation). For the case of sessile drop, fig. 8b shows that the contact angle at 𝑔 = 9.8 m/s2 decreases at the end of the first cycle and during the subsequent cycles it attains an average value (about 90o). The drop circumference, at the same time, increases from its initial value and then, as the cycles progresses it closely approaches a stable value (around 9.6 mm, which slowly decrease possibly due to evaporation). Fig. 8b shows that after several cycles the contact angle of the sessile drops stabilizes at ≈ 90o, and it is closer to the pendant drop contact angle at t= 0 min before it experienced a change in the effective gravity (≈ 89.5o). Similarly, Fig. 8a shows that after several cycles the contact angle of the pendant drop stabilizes at ≈ 95o, and it is closer to the sessile drop contact angle at t = 0 min before it experienced a change in the effective gravity (≈ 96.5o). This behavior is emphasized in fig. 9a where we see 𝜃𝑆𝑒𝑠𝑠𝑖𝑙𝑒 > 𝜃𝑃𝑒𝑛𝑑𝑎𝑛𝑡, at the zeroth cycle, where both drops have a former historical sessile 14 ACS Paragon Plus Environment

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orientation, while in the following cycles, 𝜃𝑆𝑒𝑠𝑠𝑖𝑙𝑒 < 𝜃𝑃𝑒𝑛𝑑𝑎𝑛𝑡 because now their historical orientation doesn’t change the direction of their effective gravity. Their histories fluctuate from extreme pendant to less extreme pendant and from extreme sessile to less extreme sessile, respectively. Figure 9b shows that at the 4.8 𝑔 side of the cycles, the pendant drop is slower to relax to its steady state value than the sessile drop. This may be due to the more drastic change that the pendant drop underwent when the surface was flipped. Unlike the contact angles, whose curved crossed at fig. 9a, the two circumferences at fig 9c only get further away from each other. In fig. 9d, however, they get slightly closer as a result of

9.6

(c)

o (mm) ContactCircumference Angle ( )

Circumference (mm) o

their respective histories as explained in figures 4 and 6.

9.6

Sessile

(d) Sessile

9.0

9.2 98

(a)

96 8.4

8.8 96

Contact Angle ( )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Pendant Pendant

8.4 94 8.0 920

2

4

Cycle

90 0

2

4

Cycle

6

8

Sessile

6

(b) Pendant Sessile

93 7.8 90 7.2

8

0

2

84 0

2

87

4

Pendant 6 8

4

6

Cycle

Cycle

8

Figure 9: Average of circumference and contact angle of a 6 μl water drop from different experimental runs (a) pendant and sessile contact angles at ±1 𝑔 (b) pendant and sessile contact angle at ±4.8 𝑔 (c) pendant and sessile circumferences at ±1 𝑔 (d) pendant and sessile circumferences at ±4.8 𝑔. The zeroth 15 ACS Paragon Plus Environment

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cycle represents a gravitational history that is non-existent in subsequent cycles (drops that never experienced a gravity of 4.8 𝑔 before). Therefore, only (a) and (c) have a zeroth cycle.

The change in effective gravity from ±1 𝑔 to ±4.8 𝑔 causes a significant difference in the drop geometrical parameters, as shown in fig. 10. The absolute difference between the contact angles for a pendant drop at -4.8 𝑔 and -1 𝑔 increasing while their circumference difference decreases. The same trend is observed for the two parameters of a sessile drop. Irrespective of the change, the difference in the parameters does approach plateau. Change in Δ(Contact Angle) and Δ(Circumference), from the first cycle8to the last is higher for the pendant drop than the sessile drop.

(a)

o

0.6

(a)

Sessile

04

Pendant

0

2 2

4

Cycle 4

Cycle

Pendant

-0.6 -1.2

Pendant 6 8

6

Sessile

0.0 -0.6

-40

-8 0

Sessile

(b)

0.6 0.0

Sessile

-8-4

(b)

 Circumference (mm)  Circumference (mm)

48

o  Contact Angle ()  Contact Angle ( )

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Pendant

-1.2 -1.8 0

8

-1.8

2 0

4

Cycle 2

4

Cycle

6

8 6

Figure 10: The average of difference between the values at 1 𝑔 and 4.8 𝑔 for (a) contact angles and (b) circumferences for 6 μl pendant and sessile DI water drops.

It is interesting to note that the contact angle difference in the zeroth cycle has an opposite sign to the subsequent cycles, as expected from the different history of that cycle. We also see that the pendant case is slower to reach a steady state both for the contact angles and for the circumferences. This is probably due to the more drastic change that the pendant drop underwent as it was flipped.

Conclusion 16 ACS Paragon Plus Environment

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We performed experiments in which the effective gravity on sessile and pendant drops was gradually increased and then decreased back to 1 𝑔 in a cycle that was repeated. This enabled us to observe a hysteresis that is induced by gravitational changes. This hysteresis was characterized according to the drop’s contact angle and circumference. It was observed that the first cycle was drastically different, while subsequent cycles approached a plateau in their behavior. The arrival at plateau was slower for pendant drops than for sessile drops. This is explained in terms of the different histories of the two drops, the pendant one having a history of a sessile drop that was flipped. Thus, when the effective gravity is increased and then relaxed again to 1 𝑔, the sessile drops adapt contact angles that are closer to 90o than the pendant drops of the same system, which is opposite to the trends normally seen when gravity isn’t varied. We show that the drop’s contact angle (and resultant area) is affected by two types of histories: short-term history, and long-term history. In addition to drop’s history, we explained these observations in terms of volume conservation, drop contact area, and pinning effect.

Acknowledgement This study was supported by NSF grants CMMI-1405109, CBET-1428398 and CBET-0960229. SG and SY acknowledge the support from the Houston chapter of the STLE.

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The Influence of Gravity on Contact Angle and Circumference of

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