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Evidence of oscillatory convection inside an evaporating multicomponent droplet in a closed chamber
Journal of Colloid and Interface Science 378 (2012) 260–262
Contents lists available at SciVerse ScienceDirect
Journal of Colloid and Interface Science www.elsevier.com/locate/jcis
Short Communication
Evidence of oscillatory convection inside an evaporating multicomponent droplet in a closed chamber Deepak Kumar Mandal, Shamit Bakshi ⇑ Department of Mechanical Engineering, Indian Institute of Technology – Madras, Chennai 600 036, India
a r t i c l e
i n f o
Article history: Received 14 January 2012 Accepted 16 April 2012 Available online 25 April 2012 Keywords: Multicomponent droplet evaporation Marangoni convection
a b s t r a c t Visualization of an evaporating binary (ethanol–water) droplet reveals presence of oscillatory internal circulation. The visualization is done by using a laser scattering technique. The oscillatory circulation possibly results from the opposing effect of solutal and thermal Marangoni convection as proposed in some earlier theoretical works. The frequency of this oscillation is measured and the variation of this frequency with the initial concentration of the volatile component (ethanol) is reported. Ó 2012 Elsevier Inc. All rights reserved.
1. Introduction Internal circulation in droplet has been observed in both levitated and suspended single-component droplets. The list includes acoustically levitated droplet by Yarin et al. [1], sessile droplet by Deegan et al. [2] suspended droplet by Hegseth et al. [3], Savino and Fico [4], Mandal and Bakshi [5] etc. In the present work the suspended droplet experiments are conducted for a multicomponent droplet and the observations provide evidence of occurrence of oscillatory convection as anticipated by theoretical analysis presented earlier [6]. The linear stability analysis by Pearson [7] clearly showed that circulation observed by Benard [8] in liquid layers can only be explained by forces resulting from surface tension variation with temperature. Nield [9] proposed a theory which showed that the buoyancy and surface tension driven instabilities reinforce each other. McTaggart [10] extended the approach of Pearson [7] to the case where the surface tension changes with both temperature and concentration. In these cases the thermal and solutal Marangoni numbers are positive or negative based on the gradient of temperature/concentration and the rate of change of surface tension with temperature/concentration. McTaggart [10] showed that a positive value of both solutal and thermal Marangoni number results in a strong coupling and both the effects are destabilizing. In this case stationary convection is preferred. When the solutal and thermal Marangoni numbers have opposite sign, then one effect is stabilizing and the other effect is destabilizing and under this condition oscillatory convection is preferred. Aharon and Shaw [6] presented a simplified analysis based on linear stability ⇑ Corresponding author. E-mail address: [email protected] (S. Bakshi). 0021-9797/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jcis.2012.04.046
approach on the evaporating bi-component droplet neglecting the effect of gravity. They reported that for mixtures with a negative value of rate of change of surface tension with temperature and concentration of the volatile component, the thermal and solutal effects oppose each other. The thermal effect is stabilizing and the solutal effect is destabilizing. This indicates the possibility of oscillatory convection in the system. A similar linear stability analysis was also conducted by Ha and Lai [11]. Considering a negative value of the rate of change of surface tension with temperature and concentration (of the volatile component) they predicted that the buoyancy and the solutal effects reinforce each other. However, they mention that there can be conditions under which the solutal and thermal effects can oppose each other. Armendariz and Matalon [12] also analyzed the stability of evaporating and subsequently burning liquid films. They also show in their study that the solutal and thermal Marangoni effects always oppose each other, which is similar to the case of Aharon and Shaw [6]. Recently, Machrafi et al. [13] presented a detailed stability analysis for a thin binary evaporating liquid layer. They show that for the thin layer solutal Marangoni will be most dominating at the instability threshold. In the present work we have made observations of oscillatory convection (internal circulation) as predicted from the literature based on stability analysis cited above. The frequency of this oscillatory motion with respect to the initial concentration of the droplet is also presented in this paper. 2. Oscillatory convection in evaporating ethanol–water droplet The suspended droplet experiments are conducted in a closed spherical chamber (inner diameter of around 18 cm) filled with nitrogen at atmospheric conditions. The liquid used is a mixture of pure ethanol and distilled water. Experiments were conducted
D.K. Mandal, S. Bakshi / Journal of Colloid and Interface Science 378 (2012) 260–262
with different initial concentration of the mixture. The sample after preparation is transferred to the syringe from where the liquid is supplied for forming the suspended droplet. The needle used for forming the suspended droplet had an outer diameter of 2.7 mm and produced droplets of a typical size of around 3 mm. The composition of the sample was obtained from infrared absorption spectroscopy (wavenumber range between 450 and 4000 cm 1) before and after the experiments to ensure that the sample concentration remains constant in the syringe. This spectroscopic method can be used for measurement of concentration down to hundred ppm and hence it gives a very accurate estimate of the mass fraction. The liquid was seeded with a small quantity of aluminium particles to visualize the internal flow. These types of particles are widely used for particle aided imaging techniques (Hegseth et al. [3]). The flow inside the droplet is visualized using a laser illumination. A continuous wave, 5 mW, 532 nm laser was used for the illumination. The beam diameter is around 3 mm. The beam was used to produce a volumetric illumination to visualize the internal flow. The streaking of the particle helps in clearly visualizing the flow pattern inside the droplet. The images were recorded in a CCD camera, the axis of which was kept perpendicular to the axis of the laser beam used for the illumination. A typical image sequence taken during the evaporation of an ethanol–water droplet (ethanol mass fraction of 0.119) is shown in Fig. 1. This figure clearly shows a single cycle of oscillation.
261
Starting from near-stationary state the convection roll speeds up and then decelerates to a similar initial state. The length of the path lines in the image sequence clearly depicts this process. This process repeats through several cycles before coming to a final near-stationary state again. Possibly this final state indicate the complete evaporation of the volatile component (ethanol) present in the droplet. It can be mentioned here that pure water does not exhibit any convection during evaporation at atmospheric conditions as above, whereas alcohols like ethanol exhibit a steady convection (Hegseth et al. [3], Savino and Fico [4], Mandal and Bakshi [5]). Addition of a small quantity of ethanol in water induces significant oscillatory convection in the mixture. The observation of oscillatory convection has also been confirmed from the measurement of velocity in a small region along the meridional plane of the pendant droplet. The velocity is measured using the method explained by Mandal and Bakshi [5] using a laser sheet instead of the volumetric illumination used for the visualization. This measurement clearly shows the oscillation in the temporal variation of velocity. The observation of oscillatory convection in an evaporating binary droplet probably confirms the theoretical conjecture of Aharon and Shaw [6] regarding the opposing effect of solutal and thermal Marangoni forces. The closest theoretical situation comparable to the present experiments is that of Aharon and Shaw [5] in terms of geometry and the choice of the sample liquids. An experimental evidence of this type of capillary instability is still not
Fig. 1. Snap shots at sequentially arranged time sequence of the oscillatory convection in an evaporating ethanol–water mixture (initial mass fraction of ethanol in the mixture is 0.119).
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D.K. Mandal, S. Bakshi / Journal of Colloid and Interface Science 378 (2012) 260–262
Fig. 2. Variation of frequency of oscillatory convection in an evaporating ethanol– water droplet with initial mass fraction of ethanol.
concentration of the volatile component (ethanol) of the binary mixture. The variation of the oscillation frequency is shown in Fig. 2. This show the oscillation is rather fast for the lower concentration of the volatile component. With the increase in the percentage of the volatile component in the initial mixture the oscillation becomes slower. However, it speeds up a little towards slightly higher initial concentration of the volatile component and finally oscillation stops for the pure liquid. The figure shows the spread in the data using error bars. The sample after preparation was transferred to a clean glass syringe and the spectroscopy was done to correctly estimate its composition. For a given composition, the evaporation experiments were repeated at least eight times to estimate the spread in the measured frequency in terms of the percentage deviation from the mean. Fig. 2 demonstrate the complex interaction between the solutal and thermal Marangoni forces in the evaporating binary droplet as the initial concentration of the volatile component is increased. 3. Conclusions
available. The present paper possibly strongly suggests the existence of this capillary instability from experimental observation. Apart from this, it can be also noticed that even the paper by Armendariz and Matalon [12] suggest that the thermo-capillary and solutal-capillary effects always oppose each other for a evaporating and a burning film. While the thermo-capillary effect is destabilizing for an evaporating film it becomes stabilizing for combustion with high heat transfer. The strong evidence of the opposing effect of the thermo and solutal capillary effect is the observation of oscillatory convection in the present experiments. It is also suggested from the value of critical radius by Aharon and Shaw [6] that a methanol–water system is more likely to exhibit the hydrodynamic instability as compared to alkane-alkane mixtures. The reason proposed is the more difference in the surface tension between methanol and water. This is also true for the ethanol–water system in the present work. The location with more concentration of the volatile component attains a lower temperature due to faster evaporation. Hence, the thermal and solutal gradients are opposite in sign. The capillary force due to surface tension variation resulting from concentration gradient opposes the same arising from the temperature gradient resulting in a hydrodynamic instability. Oscillatory convection was also observed by varying the initial percentage of ethanol in the mixture. The frequency of oscillation is measured for different initial
This paper presents the evidence of oscillatory convection in an evaporating binary mixture of ethanol in water. This probably results from the opposing effects of solutal and thermal Marangoni convection in the evaporating droplet. It is also observed that the oscillation slows down with increase in the volatile component in the mixture. References [1] A.L. Yarin, G. Brenn, O. Kastner, D. Rensink, C. Tropea, J. Fluid Mech. 399 (1999) 151. [2] R.D. Deegan, O. Bakajin, T.F. Dupont, G. Huber, S.R. Nagel, T.A. Witten, Nature 389 (1997) 827. [3] J.J. Hegseth, N. Rashidnia, A. Chai, Phys. Rev. E 54 (1996) 1640. [4] R. Savino, S. Fico, Phys. Fluids 16 (2004) 3738. [5] D.K. Mandal, S. Bakshi, Int. J. Multiphase Flow 42 (2012) 42. [6] I. Aharon, B.D. Shaw, Phys. Fluids 8 (1996) 1820. [7] J.R.A. Pearson, J. Fluid Mech. 4 (1958) 489. [8] H. Benard, Rev. Gn. Sci. Pures et Appl. 11 (1900) 1261. [9] D.A. Nield, J. Fluid Mech. 19 (1964) 341. [10] C.L. McTaggart, J. Fluid Mech. 134 (1983) 301. [11] V.M. Ha, C.L. Lai, Int. J. Heat Mass Transfer 45 (2002) 5143. [12] J. Armendariz, M. Matalon, Phys. Fluids 15 (2003) 1122. [13] H. Machrafi, A. Rednikov, P. Colinet, P.C. Dauby, J. Colloid Interface Sci. 349 (2010) 331.
Contents lists available at SciVerse ScienceDirect
Journal of Colloid and Interface Science www.elsevier.com/locate/jcis
Short Communication
Evidence of oscillatory convection inside an evaporating multicomponent droplet in a closed chamber Deepak Kumar Mandal, Shamit Bakshi ⇑ Department of Mechanical Engineering, Indian Institute of Technology – Madras, Chennai 600 036, India
a r t i c l e
i n f o
Article history: Received 14 January 2012 Accepted 16 April 2012 Available online 25 April 2012 Keywords: Multicomponent droplet evaporation Marangoni convection
a b s t r a c t Visualization of an evaporating binary (ethanol–water) droplet reveals presence of oscillatory internal circulation. The visualization is done by using a laser scattering technique. The oscillatory circulation possibly results from the opposing effect of solutal and thermal Marangoni convection as proposed in some earlier theoretical works. The frequency of this oscillation is measured and the variation of this frequency with the initial concentration of the volatile component (ethanol) is reported. Ó 2012 Elsevier Inc. All rights reserved.
1. Introduction Internal circulation in droplet has been observed in both levitated and suspended single-component droplets. The list includes acoustically levitated droplet by Yarin et al. [1], sessile droplet by Deegan et al. [2] suspended droplet by Hegseth et al. [3], Savino and Fico [4], Mandal and Bakshi [5] etc. In the present work the suspended droplet experiments are conducted for a multicomponent droplet and the observations provide evidence of occurrence of oscillatory convection as anticipated by theoretical analysis presented earlier [6]. The linear stability analysis by Pearson [7] clearly showed that circulation observed by Benard [8] in liquid layers can only be explained by forces resulting from surface tension variation with temperature. Nield [9] proposed a theory which showed that the buoyancy and surface tension driven instabilities reinforce each other. McTaggart [10] extended the approach of Pearson [7] to the case where the surface tension changes with both temperature and concentration. In these cases the thermal and solutal Marangoni numbers are positive or negative based on the gradient of temperature/concentration and the rate of change of surface tension with temperature/concentration. McTaggart [10] showed that a positive value of both solutal and thermal Marangoni number results in a strong coupling and both the effects are destabilizing. In this case stationary convection is preferred. When the solutal and thermal Marangoni numbers have opposite sign, then one effect is stabilizing and the other effect is destabilizing and under this condition oscillatory convection is preferred. Aharon and Shaw [6] presented a simplified analysis based on linear stability ⇑ Corresponding author. E-mail address: [email protected] (S. Bakshi). 0021-9797/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jcis.2012.04.046
approach on the evaporating bi-component droplet neglecting the effect of gravity. They reported that for mixtures with a negative value of rate of change of surface tension with temperature and concentration of the volatile component, the thermal and solutal effects oppose each other. The thermal effect is stabilizing and the solutal effect is destabilizing. This indicates the possibility of oscillatory convection in the system. A similar linear stability analysis was also conducted by Ha and Lai [11]. Considering a negative value of the rate of change of surface tension with temperature and concentration (of the volatile component) they predicted that the buoyancy and the solutal effects reinforce each other. However, they mention that there can be conditions under which the solutal and thermal effects can oppose each other. Armendariz and Matalon [12] also analyzed the stability of evaporating and subsequently burning liquid films. They also show in their study that the solutal and thermal Marangoni effects always oppose each other, which is similar to the case of Aharon and Shaw [6]. Recently, Machrafi et al. [13] presented a detailed stability analysis for a thin binary evaporating liquid layer. They show that for the thin layer solutal Marangoni will be most dominating at the instability threshold. In the present work we have made observations of oscillatory convection (internal circulation) as predicted from the literature based on stability analysis cited above. The frequency of this oscillatory motion with respect to the initial concentration of the droplet is also presented in this paper. 2. Oscillatory convection in evaporating ethanol–water droplet The suspended droplet experiments are conducted in a closed spherical chamber (inner diameter of around 18 cm) filled with nitrogen at atmospheric conditions. The liquid used is a mixture of pure ethanol and distilled water. Experiments were conducted
D.K. Mandal, S. Bakshi / Journal of Colloid and Interface Science 378 (2012) 260–262
with different initial concentration of the mixture. The sample after preparation is transferred to the syringe from where the liquid is supplied for forming the suspended droplet. The needle used for forming the suspended droplet had an outer diameter of 2.7 mm and produced droplets of a typical size of around 3 mm. The composition of the sample was obtained from infrared absorption spectroscopy (wavenumber range between 450 and 4000 cm 1) before and after the experiments to ensure that the sample concentration remains constant in the syringe. This spectroscopic method can be used for measurement of concentration down to hundred ppm and hence it gives a very accurate estimate of the mass fraction. The liquid was seeded with a small quantity of aluminium particles to visualize the internal flow. These types of particles are widely used for particle aided imaging techniques (Hegseth et al. [3]). The flow inside the droplet is visualized using a laser illumination. A continuous wave, 5 mW, 532 nm laser was used for the illumination. The beam diameter is around 3 mm. The beam was used to produce a volumetric illumination to visualize the internal flow. The streaking of the particle helps in clearly visualizing the flow pattern inside the droplet. The images were recorded in a CCD camera, the axis of which was kept perpendicular to the axis of the laser beam used for the illumination. A typical image sequence taken during the evaporation of an ethanol–water droplet (ethanol mass fraction of 0.119) is shown in Fig. 1. This figure clearly shows a single cycle of oscillation.
261
Starting from near-stationary state the convection roll speeds up and then decelerates to a similar initial state. The length of the path lines in the image sequence clearly depicts this process. This process repeats through several cycles before coming to a final near-stationary state again. Possibly this final state indicate the complete evaporation of the volatile component (ethanol) present in the droplet. It can be mentioned here that pure water does not exhibit any convection during evaporation at atmospheric conditions as above, whereas alcohols like ethanol exhibit a steady convection (Hegseth et al. [3], Savino and Fico [4], Mandal and Bakshi [5]). Addition of a small quantity of ethanol in water induces significant oscillatory convection in the mixture. The observation of oscillatory convection has also been confirmed from the measurement of velocity in a small region along the meridional plane of the pendant droplet. The velocity is measured using the method explained by Mandal and Bakshi [5] using a laser sheet instead of the volumetric illumination used for the visualization. This measurement clearly shows the oscillation in the temporal variation of velocity. The observation of oscillatory convection in an evaporating binary droplet probably confirms the theoretical conjecture of Aharon and Shaw [6] regarding the opposing effect of solutal and thermal Marangoni forces. The closest theoretical situation comparable to the present experiments is that of Aharon and Shaw [5] in terms of geometry and the choice of the sample liquids. An experimental evidence of this type of capillary instability is still not
Fig. 1. Snap shots at sequentially arranged time sequence of the oscillatory convection in an evaporating ethanol–water mixture (initial mass fraction of ethanol in the mixture is 0.119).
262
D.K. Mandal, S. Bakshi / Journal of Colloid and Interface Science 378 (2012) 260–262
Fig. 2. Variation of frequency of oscillatory convection in an evaporating ethanol– water droplet with initial mass fraction of ethanol.
concentration of the volatile component (ethanol) of the binary mixture. The variation of the oscillation frequency is shown in Fig. 2. This show the oscillation is rather fast for the lower concentration of the volatile component. With the increase in the percentage of the volatile component in the initial mixture the oscillation becomes slower. However, it speeds up a little towards slightly higher initial concentration of the volatile component and finally oscillation stops for the pure liquid. The figure shows the spread in the data using error bars. The sample after preparation was transferred to a clean glass syringe and the spectroscopy was done to correctly estimate its composition. For a given composition, the evaporation experiments were repeated at least eight times to estimate the spread in the measured frequency in terms of the percentage deviation from the mean. Fig. 2 demonstrate the complex interaction between the solutal and thermal Marangoni forces in the evaporating binary droplet as the initial concentration of the volatile component is increased. 3. Conclusions
available. The present paper possibly strongly suggests the existence of this capillary instability from experimental observation. Apart from this, it can be also noticed that even the paper by Armendariz and Matalon [12] suggest that the thermo-capillary and solutal-capillary effects always oppose each other for a evaporating and a burning film. While the thermo-capillary effect is destabilizing for an evaporating film it becomes stabilizing for combustion with high heat transfer. The strong evidence of the opposing effect of the thermo and solutal capillary effect is the observation of oscillatory convection in the present experiments. It is also suggested from the value of critical radius by Aharon and Shaw [6] that a methanol–water system is more likely to exhibit the hydrodynamic instability as compared to alkane-alkane mixtures. The reason proposed is the more difference in the surface tension between methanol and water. This is also true for the ethanol–water system in the present work. The location with more concentration of the volatile component attains a lower temperature due to faster evaporation. Hence, the thermal and solutal gradients are opposite in sign. The capillary force due to surface tension variation resulting from concentration gradient opposes the same arising from the temperature gradient resulting in a hydrodynamic instability. Oscillatory convection was also observed by varying the initial percentage of ethanol in the mixture. The frequency of oscillation is measured for different initial
This paper presents the evidence of oscillatory convection in an evaporating binary mixture of ethanol in water. This probably results from the opposing effects of solutal and thermal Marangoni convection in the evaporating droplet. It is also observed that the oscillation slows down with increase in the volatile component in the mixture. References [1] A.L. Yarin, G. Brenn, O. Kastner, D. Rensink, C. Tropea, J. Fluid Mech. 399 (1999) 151. [2] R.D. Deegan, O. Bakajin, T.F. Dupont, G. Huber, S.R. Nagel, T.A. Witten, Nature 389 (1997) 827. [3] J.J. Hegseth, N. Rashidnia, A. Chai, Phys. Rev. E 54 (1996) 1640. [4] R. Savino, S. Fico, Phys. Fluids 16 (2004) 3738. [5] D.K. Mandal, S. Bakshi, Int. J. Multiphase Flow 42 (2012) 42. [6] I. Aharon, B.D. Shaw, Phys. Fluids 8 (1996) 1820. [7] J.R.A. Pearson, J. Fluid Mech. 4 (1958) 489. [8] H. Benard, Rev. Gn. Sci. Pures et Appl. 11 (1900) 1261. [9] D.A. Nield, J. Fluid Mech. 19 (1964) 341. [10] C.L. McTaggart, J. Fluid Mech. 134 (1983) 301. [11] V.M. Ha, C.L. Lai, Int. J. Heat Mass Transfer 45 (2002) 5143. [12] J. Armendariz, M. Matalon, Phys. Fluids 15 (2003) 1122. [13] H. Machrafi, A. Rednikov, P. Colinet, P.C. Dauby, J. Colloid Interface Sci. 349 (2010) 331.