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Local heating at convection fronts and moving contact lines on hygroscopic fluids
Colloids and Surfaces A: Physicochem. Eng. Aspects 393 (2012) 42–45
Contents lists available at SciVerse ScienceDirect
Colloids and Surfaces A: Physicochemical and Engineering Aspects journal homepage: www.elsevier.com/locate/colsurfa
Local heating at convection fronts and moving contact lines on hygroscopic fluids R.T. Cerbus a,∗ , S. Garoff b , W.I. Goldburg a , E.R. Peterson c a
Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260, USA Department of Physics and Center for Complex Fluids Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA c Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA b
a r t i c l e
i n f o
Article history: Received 7 September 2011 Received in revised form 15 October 2011 Accepted 20 October 2011 Available online 31 October 2011 Keywords: Local heat of mixing Convection front Moving contact line Hygroscopic Spreading
a b s t r a c t A temperature rise on the order of tenths of a degree is observed as one fluid spreads over a hygroscopic fluid. While this behavior is only exhibited with hygroscopic fluids, it is independent of the properties of the spreading fluid. The spreading induces a ‘rolling’ motion in the subphase which brings ‘fresh’ fluid to the surface, exposing it to the water vapor in the air. As water is absorbed into the hygroscopic liquid, heat is released. The same behavior is observed whether the spreading fluid has a spreading monolayer that drives a convection front or is a spreading lens with a moving three-phase contact line. © 2011 Elsevier B.V. All rights reserved.
1. Introduction
2. Materials and methods
The spreading of one liquid on top of another causes motion in the underlying fluid substrate. For example, a drop spreading on a deep layer of volatile fluid exhibits a cooling behavior at the leading edge of the spreading fluid [1,2]. The spreading fluid drives the motion of the underlying fluid which causes a convective roll to develop, thus exposing new fluid to the surface [1]. This ‘rolling’ motion is also observed in the velocity profiles of a thin liquid film driven by a spreading monolayer of insoluble surfactant [3]. The motion of the underlying fluid enables an exothermic chemical process, which causes the release of a local heat of mixing, at the moving contact line or convection front.1 Using a simple experimental arrangement and an infrared camera, we are able to observe the resulting temperature rise, T. The particular chemical process we observe is the absorption of water into a hygroscopic fluid subphase. The mixing of water from the vapor phase with a hygroscopic material necessarily releases energy in the form of heat [4], and it is the temperature rise from this heating that we are able to observe.
Fig. 1 shows the experimental setup of the spreading experiments. A Petri dish is filled with the subphase liquid to a height of 1 cm. The dish is inside a cardboard box that is painted black so as to minimize IR reflections. A 1 l drop of liquid is formed at the end of either a pipette or a metallic needle. A servo mechanism lowers the coated needle onto the liquid subphase surface at its lateral center. The camera (FLIR A320) that captures the temperature image of the spreading liquid is located outside and above the box, viewing at an angle relative to the surface. It records the subsequent temperature T(x, y, t) from which we calculate the change T(x, y, t) from the temperature before deposition (at t = 0) across the top face (x, y) of the substrate. The camera is sensitive to radiation in the wavelength range 3–15 m, with a sensitivity maximum near 10 m. It has a temperature range from −20 ◦ C to 120 ◦ C, with a sensitivity of 0.1 ◦ C and captures images at a rate of 30 Hz. We performed experiments in Petri dishes of diameter 9 cm or 14 cm. The results are equivalent in the sense that if we observed spreading to the edge of the dish for 9 cm we saw the same behavior in the 14 cm dish. The humidity, or water content of the atmosphere, was not controlled but lay in the range of 40–60% relative humidity and the temperature of the air in the room was 23 ◦ C. It is, of course, necessary for the temperature of the subphase, the spreading liquid, the Petri dish, and all mechanical devices to equilibrate to the ambient temperature inside the box before the experiment commences (at t = 0). As seen in Table 1, we used several different fluids and obtained qualitatively similar results. However, the results described in most
∗ Corresponding author. Tel.: +1 412 624 9385. E-mail addresses: [email protected] (R.T. Cerbus), [email protected] (S. Garoff), [email protected] (W.I. Goldburg), [email protected] (E.R. Peterson). 1 We define a contact line as the junction where the three phases meet and a convection front as the fluid motion driven by a spreading monolayer. 0927-7757/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.colsurfa.2011.10.022
R.T. Cerbus et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 393 (2012) 42–45
43
Table 1 Systems examined. Substrate
Hygroscopic?
Spreading fluid
Max T
Glycerol Glycerol Glycerol Glycerol Ethylene glycol Ethylene glycol Ethylene glycol Water Bromododecane
Yes Yes Yes Yes Yes Yes Yes No No
Oleic acid 10 cSt PDMS 100 cSt PDMS Hexadecane Oleic acid 10 cSt PDMS 100 cSt PDMS Oleic acid 10 cSt PDMS
0.4 K 0.3 K 0.3 K 0.2 K 0.2 K 0.2 K 0.2 K N/A N/A
detail here are for oleic acid, a surfactant, spreading on glycerol. This system is chosen because it gives the largest magnitude of temperature rise, and so it is easier to see details of the temperature evolution. Water concentration in the ‘fresh’ glycerol is less than 0.1% when poured into the dish and several minutes before the spreading experiments begin. The attenuation length of 10 m radiation in glycerol is 23 m (it is 10 m in water) [5], so we are only observing effects that occur at the surface. 3. Results and discussion The time evolution of the temperature change associated with the spreading of oleic acid on glycerol is shown at three values of t in Fig. 2. A temperature-color scale is to the right of each image. Fig. 2a, at t = 0, shows T(x, y, 0) a fraction of a second before the drop is deposited on the glycerol. At t = 4.1 s, the radius of the ring of higher temperature rise reaches roughly halfway across the Petri dish. One sees that at this time, T = 0.3 K near the rim of the expanding disk (ring in yellow). The third panel shows T(x, y) at t = 27 s, the time at which the ring of higher temperature has just reached the edge of the dish. The magnitude of T is roughly the same as at t = 4.1 s. For time t greater than these, a T(x, y) appears to rise uniformly across the entire dish and persists for several hours. This temperature rise is not connected with the spreading and may be seen even when a dish of glycerol is simply placed in the open air and nothing is added. We also observe a temperature rise at the periphery of a very small nonspreading, static droplet of water placed on a glycerol subphase, despite the fact that the temperature at the center of the droplet is lower due to evaporation (see Fig. 3). Finally, if we allow the glycerol to sit out for longer times before the spreading takes place, thus allowing for a better equilibration with atmospheric water vapor, the temperature rise from the spreading of oleic acid still occurs but is smaller.
Fig. 1. Apparatus for imaging spreading.
Fig. 2. Image from infrared camera. The shading identifies the temperature increase. The solid circle shows the dish diameter. (a) is at t = 0 s, or just when the wire touches the surface. The second image is t = 4.1 s later, and the last image is at t = 27 s, when the temperature increase reaches the edge of the dish.
Fig. 3. Water droplet on glycerol. The image is magnified.
44
R.T. Cerbus et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 393 (2012) 42–45
While the T behavior is qualitatively the same for spreading liquids of varying character, temperature changes are only observed for fluid substrates that are hygroscopic, as shown in Table 1. When such a fluid is brought into contact with the atmosphere, moisture in the air will begin diffusing into the fluid and heat will be released. However, this mass diffusion process is extremely slow (D 10−7 cm2 /s [6]), so when the hygroscopic fluid is poured into the dish, the surface temperature rises and then falls quickly as the heat from the initial mixing conducts away. In fact, since the thermal diffusivity is large ( = 9.22 × 10−4 cm2 /s [7]) compared with the molecular diffusivity, no temperature rise should be seen unless the heat is being continually generated. Thus, after the glycerol surface equilibrates with the water vapor after being poured in the Petri dish, no further temperature rise is seen unless fresh (undersaturated) glycerol is brought to the surface. Gaver and Grotberg examined the spreading of a monolayer of insoluble surfactant on a thin fluid film both analytically and experimentally [3,8]. Their experimental work is described in [8], where they observe the surface and bulk fluid flows induced by the spreading of oleic acid on glycerol. They also developed a mathematical model for the spreading of a monolayer of insoluble surfactant on a thin liquid film [3]. This model is then used to calculate the velocity fields of the fluid in the film. Near the convection front, the velocity fields suggest a rolling motion of the underlying fluid as the surfactant spreads, as in Fig. 3 in [3]. These results are within the lubrication approximation, while our experiments cannot be described in this limit because the ratio of the liquid subphase depth H to the radius of the spreading oleic acid R is not small (H/L ≈ 1). However, for deeper layers we expect that the rolling motion should be more pronounced as the vertical velocity within the fluid is allowed to be larger than in the case of the thin film limit. This rolling motion explains the temperature rise that we observe. As fresh hygroscopic liquid is brought to the surface, it mixes with the water in the air and releases energy in the form of heat [4], and the accompanying temperature rise can readily be observed with an infrared camera. One alternative hypothesis is that the temperature rise we observe is due to the heat generated by viscous shear in the film. However, this cannot be the source of the heat because the rise is only observed for hygroscopic subphases. This rolling behavior in the subphase is also similar to the results of the experiment described in Dussaud and Troian [1]. This effect may be observed for other spreading fluids besides oleic acid, as shown in Table 1. The spreading of monolayers such as in the oleic acid case is driven by solutal Marangoni stresses whereas the spreading of the drops of the other fluids is driven by gravitational forces capillary forces. These results suggest that the observation of a T is related to the properties of the subphase. Both PDMS and oleic acid spread to the edge of the dish and show a comparable temperature rise. Hexadecane does not spread to the edge of the dish, if the volume of the drop is very small,2 but shows a temperature rise of the same order of magnitude as PDMS and oleic acid while it spreads. While the temperature rise is similar for all spreading liquids, the origins of the rolling motion needed to drive undersaturated glycerol to the surface is different. For the oleic acid, the temperature rise is caused by rolling motion in the subphase associated with the convection front driven by the spreading monolayer of oleic acid which extends out to the edge of the dish. From their experiments, Fraaije and Cazabat [9] conclude that there is a monolayer of PDMS in front of the spreading drop. From our experiments, we cannot tell whether this monolayer is present or not. Thus we cannot say whether the observed temperature rise is located at the
2
By ‘very small’ is meant the amount of hexadecane that wets a small metal pin.
Fig. 4. Spreading rates for several fluids on glycerol and ethylene glycol. The straight line is a power law of t1/2 . The error bars are no larger than the marker size for all but oleic acid–ethylene glycol and are due to the uncertainty from the camera resolution. The larger error bars for this system are due to the difficulty in discerning the ring location, because the magnitude of the temperature rise is smaller on ethylene glycol.
moving contact line or at the front of a monolayer for PDMS. However, in the case of hexadecane, where the spreading terminates in a lens with nonzero contact angle and there is no monolayer, the temperature rise we observe must be occurring at a moving contact line. To our knowledge, rolling motion in the subphase under a spreading drop or lens has not been previously discussed in the literature. Using video taken with the infrared camera, we were able to measure the rate of spreading for the ring of temperature rise. As can be seen in Fig. 4, both the convection front and the moving contact line move as power laws. In the fitting, we have omitted one or two initial points (which are influenced by inertia) and the long time behavior of the hexadecane, which spreads until it forms a static lens. We find that our exponents range from 0.43 to 0.58 with a weighted mean of 0.48 ± 0.01. This result fits within the context of prior literature. A surfactant on a deep sublayer is expected to spread like t3/8 [10]. However, surface contamination often times increases that spreading behavior to as much as t3/4 [10]. Experimentally, spreading rates have been observed throughout this range [1,11,12]. We find it surprising that despite their differences, the temperature rise from all of the spreading liquids spreads out as t1/2 . Also, the hexadecane plot becomes flat at t∼ 200 s, which shows that it stops spreading. 4. Conclusion We observe an exothermic chemical process as one fluid spreads on a hygroscopic liquid. The presence of this chemical reaction is independent of whether the spreading is driven by a convection front (molecular monolayer) or a three phase contact line (liquid lens). In both cases, the spreading behavior induces a rolling motion in the subphase which brings fresh liquid to the surface. Water from the atmosphere then mixes with the subphase which causes heat to be generated. This rolling motion has been observed previously where a decrease in temperature of a volatile fluid corresponded to the spreading of a convection front [1,2]. Surprisingly, for a hygroscopic fluid a temperature increase was observed to be independent of the properties of the spreading fluid (convection front or contact line). The spreading rate in both cases are similar and agree with the range of power law behavior previously observed in the literature. Since temperature gradients are known to induce
R.T. Cerbus et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 393 (2012) 42–45
Marangoni stresses, the temperature rise at the edge of the spreading fluid may effect the spreading behavior. These thermal Marangoni stresses arise due to temperature gradients, whereas any surfactant will spread due to solutal Marangoni stresses. This influence of the thermal Marangoni stress might be important when interpreting the results of experiments performed on a glycerol subphase such as power laws for spreading.
References
Acknowledgments
[6] [7] [8] [9] [10] [11]
We wish to thank Stefanus, Christina McDonald, and Pinaki Chakraborti for their help. We also thank Roomi Kalita and Ramankur Sharma for their determination that there is no monolayer in the case of hexadecane. R.T.C. and W.I.G. were supported by NSF Grant No. DMR0604477. S.G. was supported by NSF Grant No. CBET-0931057, and E.R.P. was supported by NSF Grant No. DMS-0635983.
[1] [2] [3] [4] [5]
[12]
45
A.D. Dussaud, S.M. Troian, Phys. Fluids 10 (1998) 23. J.R. Saylor, G.B. Smith, K.A. Flack, Phys. Fluids 12 (2000) 597. D.P. Gaver, J.B. Grotberg, J. Fluid Mech. 213 (1990) 127. Y. Marcus, Phys. Chem. Chem. Phys. 2 (2000) 4891. P.J. Linstrom, W.J. Mallard (Eds.), NIST Chemistry WebBook, NIST Standard Reference Database Number 69, National Institute of Standards and Technology, Gaithersburg, MD 20899, http://webbook.nist.gov (retrieved February 17, 2011). C.S. Miner, Glycerol, Reinhold Pub. Corp., New York, 1953. J.A. Balderas-Lopez, A. Mandelis, J.A. Garcia, Anal. Sci. 17 (2001) 519. D.P. Gaver, J.B. Grotberg, J. Fluid Mech. 235 (1992) 399. J.G.E.M. Fraaije, A.M. Cazabat, J. Colloid Interface Sci. 133 (1989) 452. O.E. Jensen, J. Fluid Mech. 293 (1995) 349. J.A. Fay, in: D.P. Hoult (Ed.), Oil on the Sea, Plenum Press, New York, 1969, p. 53. D.P. Hoult, Annu. Rev. Fluid Mech. 4 (1972) 341.
Contents lists available at SciVerse ScienceDirect
Colloids and Surfaces A: Physicochemical and Engineering Aspects journal homepage: www.elsevier.com/locate/colsurfa
Local heating at convection fronts and moving contact lines on hygroscopic fluids R.T. Cerbus a,∗ , S. Garoff b , W.I. Goldburg a , E.R. Peterson c a
Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260, USA Department of Physics and Center for Complex Fluids Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA c Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA b
a r t i c l e
i n f o
Article history: Received 7 September 2011 Received in revised form 15 October 2011 Accepted 20 October 2011 Available online 31 October 2011 Keywords: Local heat of mixing Convection front Moving contact line Hygroscopic Spreading
a b s t r a c t A temperature rise on the order of tenths of a degree is observed as one fluid spreads over a hygroscopic fluid. While this behavior is only exhibited with hygroscopic fluids, it is independent of the properties of the spreading fluid. The spreading induces a ‘rolling’ motion in the subphase which brings ‘fresh’ fluid to the surface, exposing it to the water vapor in the air. As water is absorbed into the hygroscopic liquid, heat is released. The same behavior is observed whether the spreading fluid has a spreading monolayer that drives a convection front or is a spreading lens with a moving three-phase contact line. © 2011 Elsevier B.V. All rights reserved.
1. Introduction
2. Materials and methods
The spreading of one liquid on top of another causes motion in the underlying fluid substrate. For example, a drop spreading on a deep layer of volatile fluid exhibits a cooling behavior at the leading edge of the spreading fluid [1,2]. The spreading fluid drives the motion of the underlying fluid which causes a convective roll to develop, thus exposing new fluid to the surface [1]. This ‘rolling’ motion is also observed in the velocity profiles of a thin liquid film driven by a spreading monolayer of insoluble surfactant [3]. The motion of the underlying fluid enables an exothermic chemical process, which causes the release of a local heat of mixing, at the moving contact line or convection front.1 Using a simple experimental arrangement and an infrared camera, we are able to observe the resulting temperature rise, T. The particular chemical process we observe is the absorption of water into a hygroscopic fluid subphase. The mixing of water from the vapor phase with a hygroscopic material necessarily releases energy in the form of heat [4], and it is the temperature rise from this heating that we are able to observe.
Fig. 1 shows the experimental setup of the spreading experiments. A Petri dish is filled with the subphase liquid to a height of 1 cm. The dish is inside a cardboard box that is painted black so as to minimize IR reflections. A 1 l drop of liquid is formed at the end of either a pipette or a metallic needle. A servo mechanism lowers the coated needle onto the liquid subphase surface at its lateral center. The camera (FLIR A320) that captures the temperature image of the spreading liquid is located outside and above the box, viewing at an angle relative to the surface. It records the subsequent temperature T(x, y, t) from which we calculate the change T(x, y, t) from the temperature before deposition (at t = 0) across the top face (x, y) of the substrate. The camera is sensitive to radiation in the wavelength range 3–15 m, with a sensitivity maximum near 10 m. It has a temperature range from −20 ◦ C to 120 ◦ C, with a sensitivity of 0.1 ◦ C and captures images at a rate of 30 Hz. We performed experiments in Petri dishes of diameter 9 cm or 14 cm. The results are equivalent in the sense that if we observed spreading to the edge of the dish for 9 cm we saw the same behavior in the 14 cm dish. The humidity, or water content of the atmosphere, was not controlled but lay in the range of 40–60% relative humidity and the temperature of the air in the room was 23 ◦ C. It is, of course, necessary for the temperature of the subphase, the spreading liquid, the Petri dish, and all mechanical devices to equilibrate to the ambient temperature inside the box before the experiment commences (at t = 0). As seen in Table 1, we used several different fluids and obtained qualitatively similar results. However, the results described in most
∗ Corresponding author. Tel.: +1 412 624 9385. E-mail addresses: [email protected] (R.T. Cerbus), [email protected] (S. Garoff), [email protected] (W.I. Goldburg), [email protected] (E.R. Peterson). 1 We define a contact line as the junction where the three phases meet and a convection front as the fluid motion driven by a spreading monolayer. 0927-7757/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.colsurfa.2011.10.022
R.T. Cerbus et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 393 (2012) 42–45
43
Table 1 Systems examined. Substrate
Hygroscopic?
Spreading fluid
Max T
Glycerol Glycerol Glycerol Glycerol Ethylene glycol Ethylene glycol Ethylene glycol Water Bromododecane
Yes Yes Yes Yes Yes Yes Yes No No
Oleic acid 10 cSt PDMS 100 cSt PDMS Hexadecane Oleic acid 10 cSt PDMS 100 cSt PDMS Oleic acid 10 cSt PDMS
0.4 K 0.3 K 0.3 K 0.2 K 0.2 K 0.2 K 0.2 K N/A N/A
detail here are for oleic acid, a surfactant, spreading on glycerol. This system is chosen because it gives the largest magnitude of temperature rise, and so it is easier to see details of the temperature evolution. Water concentration in the ‘fresh’ glycerol is less than 0.1% when poured into the dish and several minutes before the spreading experiments begin. The attenuation length of 10 m radiation in glycerol is 23 m (it is 10 m in water) [5], so we are only observing effects that occur at the surface. 3. Results and discussion The time evolution of the temperature change associated with the spreading of oleic acid on glycerol is shown at three values of t in Fig. 2. A temperature-color scale is to the right of each image. Fig. 2a, at t = 0, shows T(x, y, 0) a fraction of a second before the drop is deposited on the glycerol. At t = 4.1 s, the radius of the ring of higher temperature rise reaches roughly halfway across the Petri dish. One sees that at this time, T = 0.3 K near the rim of the expanding disk (ring in yellow). The third panel shows T(x, y) at t = 27 s, the time at which the ring of higher temperature has just reached the edge of the dish. The magnitude of T is roughly the same as at t = 4.1 s. For time t greater than these, a T(x, y) appears to rise uniformly across the entire dish and persists for several hours. This temperature rise is not connected with the spreading and may be seen even when a dish of glycerol is simply placed in the open air and nothing is added. We also observe a temperature rise at the periphery of a very small nonspreading, static droplet of water placed on a glycerol subphase, despite the fact that the temperature at the center of the droplet is lower due to evaporation (see Fig. 3). Finally, if we allow the glycerol to sit out for longer times before the spreading takes place, thus allowing for a better equilibration with atmospheric water vapor, the temperature rise from the spreading of oleic acid still occurs but is smaller.
Fig. 1. Apparatus for imaging spreading.
Fig. 2. Image from infrared camera. The shading identifies the temperature increase. The solid circle shows the dish diameter. (a) is at t = 0 s, or just when the wire touches the surface. The second image is t = 4.1 s later, and the last image is at t = 27 s, when the temperature increase reaches the edge of the dish.
Fig. 3. Water droplet on glycerol. The image is magnified.
44
R.T. Cerbus et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 393 (2012) 42–45
While the T behavior is qualitatively the same for spreading liquids of varying character, temperature changes are only observed for fluid substrates that are hygroscopic, as shown in Table 1. When such a fluid is brought into contact with the atmosphere, moisture in the air will begin diffusing into the fluid and heat will be released. However, this mass diffusion process is extremely slow (D 10−7 cm2 /s [6]), so when the hygroscopic fluid is poured into the dish, the surface temperature rises and then falls quickly as the heat from the initial mixing conducts away. In fact, since the thermal diffusivity is large ( = 9.22 × 10−4 cm2 /s [7]) compared with the molecular diffusivity, no temperature rise should be seen unless the heat is being continually generated. Thus, after the glycerol surface equilibrates with the water vapor after being poured in the Petri dish, no further temperature rise is seen unless fresh (undersaturated) glycerol is brought to the surface. Gaver and Grotberg examined the spreading of a monolayer of insoluble surfactant on a thin fluid film both analytically and experimentally [3,8]. Their experimental work is described in [8], where they observe the surface and bulk fluid flows induced by the spreading of oleic acid on glycerol. They also developed a mathematical model for the spreading of a monolayer of insoluble surfactant on a thin liquid film [3]. This model is then used to calculate the velocity fields of the fluid in the film. Near the convection front, the velocity fields suggest a rolling motion of the underlying fluid as the surfactant spreads, as in Fig. 3 in [3]. These results are within the lubrication approximation, while our experiments cannot be described in this limit because the ratio of the liquid subphase depth H to the radius of the spreading oleic acid R is not small (H/L ≈ 1). However, for deeper layers we expect that the rolling motion should be more pronounced as the vertical velocity within the fluid is allowed to be larger than in the case of the thin film limit. This rolling motion explains the temperature rise that we observe. As fresh hygroscopic liquid is brought to the surface, it mixes with the water in the air and releases energy in the form of heat [4], and the accompanying temperature rise can readily be observed with an infrared camera. One alternative hypothesis is that the temperature rise we observe is due to the heat generated by viscous shear in the film. However, this cannot be the source of the heat because the rise is only observed for hygroscopic subphases. This rolling behavior in the subphase is also similar to the results of the experiment described in Dussaud and Troian [1]. This effect may be observed for other spreading fluids besides oleic acid, as shown in Table 1. The spreading of monolayers such as in the oleic acid case is driven by solutal Marangoni stresses whereas the spreading of the drops of the other fluids is driven by gravitational forces capillary forces. These results suggest that the observation of a T is related to the properties of the subphase. Both PDMS and oleic acid spread to the edge of the dish and show a comparable temperature rise. Hexadecane does not spread to the edge of the dish, if the volume of the drop is very small,2 but shows a temperature rise of the same order of magnitude as PDMS and oleic acid while it spreads. While the temperature rise is similar for all spreading liquids, the origins of the rolling motion needed to drive undersaturated glycerol to the surface is different. For the oleic acid, the temperature rise is caused by rolling motion in the subphase associated with the convection front driven by the spreading monolayer of oleic acid which extends out to the edge of the dish. From their experiments, Fraaije and Cazabat [9] conclude that there is a monolayer of PDMS in front of the spreading drop. From our experiments, we cannot tell whether this monolayer is present or not. Thus we cannot say whether the observed temperature rise is located at the
2
By ‘very small’ is meant the amount of hexadecane that wets a small metal pin.
Fig. 4. Spreading rates for several fluids on glycerol and ethylene glycol. The straight line is a power law of t1/2 . The error bars are no larger than the marker size for all but oleic acid–ethylene glycol and are due to the uncertainty from the camera resolution. The larger error bars for this system are due to the difficulty in discerning the ring location, because the magnitude of the temperature rise is smaller on ethylene glycol.
moving contact line or at the front of a monolayer for PDMS. However, in the case of hexadecane, where the spreading terminates in a lens with nonzero contact angle and there is no monolayer, the temperature rise we observe must be occurring at a moving contact line. To our knowledge, rolling motion in the subphase under a spreading drop or lens has not been previously discussed in the literature. Using video taken with the infrared camera, we were able to measure the rate of spreading for the ring of temperature rise. As can be seen in Fig. 4, both the convection front and the moving contact line move as power laws. In the fitting, we have omitted one or two initial points (which are influenced by inertia) and the long time behavior of the hexadecane, which spreads until it forms a static lens. We find that our exponents range from 0.43 to 0.58 with a weighted mean of 0.48 ± 0.01. This result fits within the context of prior literature. A surfactant on a deep sublayer is expected to spread like t3/8 [10]. However, surface contamination often times increases that spreading behavior to as much as t3/4 [10]. Experimentally, spreading rates have been observed throughout this range [1,11,12]. We find it surprising that despite their differences, the temperature rise from all of the spreading liquids spreads out as t1/2 . Also, the hexadecane plot becomes flat at t∼ 200 s, which shows that it stops spreading. 4. Conclusion We observe an exothermic chemical process as one fluid spreads on a hygroscopic liquid. The presence of this chemical reaction is independent of whether the spreading is driven by a convection front (molecular monolayer) or a three phase contact line (liquid lens). In both cases, the spreading behavior induces a rolling motion in the subphase which brings fresh liquid to the surface. Water from the atmosphere then mixes with the subphase which causes heat to be generated. This rolling motion has been observed previously where a decrease in temperature of a volatile fluid corresponded to the spreading of a convection front [1,2]. Surprisingly, for a hygroscopic fluid a temperature increase was observed to be independent of the properties of the spreading fluid (convection front or contact line). The spreading rate in both cases are similar and agree with the range of power law behavior previously observed in the literature. Since temperature gradients are known to induce
R.T. Cerbus et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 393 (2012) 42–45
Marangoni stresses, the temperature rise at the edge of the spreading fluid may effect the spreading behavior. These thermal Marangoni stresses arise due to temperature gradients, whereas any surfactant will spread due to solutal Marangoni stresses. This influence of the thermal Marangoni stress might be important when interpreting the results of experiments performed on a glycerol subphase such as power laws for spreading.
References
Acknowledgments
[6] [7] [8] [9] [10] [11]
We wish to thank Stefanus, Christina McDonald, and Pinaki Chakraborti for their help. We also thank Roomi Kalita and Ramankur Sharma for their determination that there is no monolayer in the case of hexadecane. R.T.C. and W.I.G. were supported by NSF Grant No. DMR0604477. S.G. was supported by NSF Grant No. CBET-0931057, and E.R.P. was supported by NSF Grant No. DMS-0635983.
[1] [2] [3] [4] [5]
[12]
45
A.D. Dussaud, S.M. Troian, Phys. Fluids 10 (1998) 23. J.R. Saylor, G.B. Smith, K.A. Flack, Phys. Fluids 12 (2000) 597. D.P. Gaver, J.B. Grotberg, J. Fluid Mech. 213 (1990) 127. Y. Marcus, Phys. Chem. Chem. Phys. 2 (2000) 4891. P.J. Linstrom, W.J. Mallard (Eds.), NIST Chemistry WebBook, NIST Standard Reference Database Number 69, National Institute of Standards and Technology, Gaithersburg, MD 20899, http://webbook.nist.gov (retrieved February 17, 2011). C.S. Miner, Glycerol, Reinhold Pub. Corp., New York, 1953. J.A. Balderas-Lopez, A. Mandelis, J.A. Garcia, Anal. Sci. 17 (2001) 519. D.P. Gaver, J.B. Grotberg, J. Fluid Mech. 235 (1992) 399. J.G.E.M. Fraaije, A.M. Cazabat, J. Colloid Interface Sci. 133 (1989) 452. O.E. Jensen, J. Fluid Mech. 293 (1995) 349. J.A. Fay, in: D.P. Hoult (Ed.), Oil on the Sea, Plenum Press, New York, 1969, p. 53. D.P. Hoult, Annu. Rev. Fluid Mech. 4 (1972) 341.