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G. Biswas and K. C. Sahu
which increases the evaporation rate in the wake region. A ‘fore-aft’ asymmetric in
the vapour envelope is seen at later time as the vapour produced at the bottom part
of the drop moves towards the wake region due to buoyancy. It can also be seen that
as the drop moves in the downward direction, it has deformed slightly to an oblate
shape.
7 Concluding Remarks
In the present chapter, some specific problems under the broad area of free-surface
flows are analysed and discussed. Multiphase flows are characterized by the contrast
in fluid properties and the surface tension acting at the interface separating the fluids.
Due to the associated complex interfacial dynamics, free-surface flows are challenging to handle both computationally and experimentally. The review presented in this
chapter is an attempt to highlight the non-intuitive phenomena and complex flow
physics observed in some free-surface flows. In spite of the long history, this subject
has been attracting the attention of many researchers due to its relevance in many
industrial applications and heretofore unexplained natural phenomena. Few examples
are ink-jet printing, particle sorting, atomization, mixing, combustion, separation and
spraying technologies, carbon sequestration, bubble-column reactors, microfluidics,
seepage of groundwater, ice melting, gravity waves, clouds and raindrops. Understanding of multiphase flows involving fluids with phase change, non-Newtonian
rheology and external forcing has been the current trend due to its usefulness in the
emerging areas of microfluidics and bioengineering in last two decades.
References
1. Yeung, R.W.: Numerical methods in free-surface flows. Annu. Rev. Fluid Mech. 14, 395
(1982)
2. White, F.M., Corfield, I.: Viscous Fluid Flow, vol. 3. McGraw-Hill, New York, Boston (2006)
3. Som, S.K., Biswas, G., Chakraborty, S.: Introduction to Fluid Mechanics and Fluid Machines.
McGraw-Hill, New Delhi (2017)
4. Govindarajan, R., Sahu, K.C.: Instabilities in viscosity-stratified flow. Annu. Rev. Fluid Mech.
46, 331 (2014)
5. Biswas, G., Som, S.K., Gupta, A.S.: Instability of a moving cylindrical liquid sheet. J. Fluids
Eng. 107, 451 (1985)
6. Leal, L.G.: Advanced Transport Phenomena: fluid Mechanics and Convective Transport Processes, vol. 7. Cambridge University Press, Cambridge (2007)
7. Stokes, G.G.: On the effect of internal friction of fluids on the motion of pendulums. Trans.
Camb. Philos. Soc. 9, 8 (1851)
8. Hadamard, J.S.: Mouvement permanent lent d’une sphère liquid et visqueuse dans un liquide
visqueux. CR Hebd. Seances Acad. Sci. Paris 152, 1735 (1911)
9. Rybczynski, W.: Uber die fortschreitende Bewegung einer flussigen Kugel in einem zahen
Medium. Bull. Acad. Sci. Crac. A 1, 40 (1911)
G. Biswas and K. C. Sahu
which increases the evaporation rate in the wake region. A ‘fore-aft’ asymmetric in
the vapour envelope is seen at later time as the vapour produced at the bottom part
of the drop moves towards the wake region due to buoyancy. It can also be seen that
as the drop moves in the downward direction, it has deformed slightly to an oblate
shape.
7 Concluding Remarks
In the present chapter, some specific problems under the broad area of free-surface
flows are analysed and discussed. Multiphase flows are characterized by the contrast
in fluid properties and the surface tension acting at the interface separating the fluids.
Due to the associated complex interfacial dynamics, free-surface flows are challenging to handle both computationally and experimentally. The review presented in this
chapter is an attempt to highlight the non-intuitive phenomena and complex flow
physics observed in some free-surface flows. In spite of the long history, this subject
has been attracting the attention of many researchers due to its relevance in many
industrial applications and heretofore unexplained natural phenomena. Few examples
are ink-jet printing, particle sorting, atomization, mixing, combustion, separation and
spraying technologies, carbon sequestration, bubble-column reactors, microfluidics,
seepage of groundwater, ice melting, gravity waves, clouds and raindrops. Understanding of multiphase flows involving fluids with phase change, non-Newtonian
rheology and external forcing has been the current trend due to its usefulness in the
emerging areas of microfluidics and bioengineering in last two decades.
References
1. Yeung, R.W.: Numerical methods in free-surface flows. Annu. Rev. Fluid Mech. 14, 395
(1982)
2. White, F.M., Corfield, I.: Viscous Fluid Flow, vol. 3. McGraw-Hill, New York, Boston (2006)
3. Som, S.K., Biswas, G., Chakraborty, S.: Introduction to Fluid Mechanics and Fluid Machines.
McGraw-Hill, New Delhi (2017)
4. Govindarajan, R., Sahu, K.C.: Instabilities in viscosity-stratified flow. Annu. Rev. Fluid Mech.
46, 331 (2014)
5. Biswas, G., Som, S.K., Gupta, A.S.: Instability of a moving cylindrical liquid sheet. J. Fluids
Eng. 107, 451 (1985)
6. Leal, L.G.: Advanced Transport Phenomena: fluid Mechanics and Convective Transport Processes, vol. 7. Cambridge University Press, Cambridge (2007)
7. Stokes, G.G.: On the effect of internal friction of fluids on the motion of pendulums. Trans.
Camb. Philos. Soc. 9, 8 (1851)
8. Hadamard, J.S.: Mouvement permanent lent d’une sphère liquid et visqueuse dans un liquide
visqueux. CR Hebd. Seances Acad. Sci. Paris 152, 1735 (1911)
9. Rybczynski, W.: Uber die fortschreitende Bewegung einer flussigen Kugel in einem zahen
Medium. Bull. Acad. Sci. Crac. A 1, 40 (1911)