Research Article

A Review on Hydrodynamical Stability of Thin Film Flowing Along an Inclined Plane

Volume: 2 Number: 2 August 30, 2019
Souradip Chattopadhyay *, Anandamoy Mukhopadhyay , Amlan Barua
EN

A Review on Hydrodynamical Stability of Thin Film Flowing Along an Inclined Plane

Abstract

The dynamics and stability of thin liquid films have fascinated scientists over many decades. Thin film flows occur over a wide range of length scales and are central to numerous areas of engineering, geophysics and biophysics. These include nanofluidics and microfluidics, lava flows, coating flows, tear-film rupture, dynamics of continental ice sheets and surfactant replacement therapy. Study of falling film instability has its wide applications in the practical field of industry and engineering. Practical applications in industrial processing motivate the recent research to investigate the factors which may affect the formation of waves on the surface of the coating layers and/or to determine the ways to overcome or to minimize the unwanted factors within the desired limit of tolerance. The dynamics of a liquid film flowing down a plane under the action of gravity is a problem which appears in many technological and natural systems, namely large scale geophysical environments such as lava flows or spillways, daily life scenarios such as water flowing down a window pane or a slippery road on a rainy day, chemical engineering processes such as evaporators, heat exchanges and falling film reactors or surface coating. The aim of this paper is to throw light on the studies conducted on hydrodynamical stability.

Keywords

Hydrodynamic stability, Thin film,Inclined plane

References

  1. [1] H. Schlichting, Boundary Layer Theory, McGraw-Hill Book Company Inc, New York., (1955), 308-337
  2. [2] C.C. Lin, Hydrodynamic Stability, Cambridge University Press, New York (1955)
  3. [3] D.Y. Hsieh, S.P. Ho, Wave and stability in fluids., World Scientific, Singapore (1994)
  4. [4] P.G. Drazin, W.H. Reid, Hydrodynamic Stability, Cambridge University Press, Cambridge(1981)
  5. [5] P.L. Kapitza, S.P. Kapitza, Wave flow of thin layers of a viscous fluid: III. Experimental study of undulatory flow conditions. Sov. Phys. J. Exp. Theor.Phys.,19 (1949), 105-120
  6. [6] T.B. Benjamin, Wave formation in laminar flow down an inclined plane. J. Fluid Mech. 2 (1957),554-574
  7. [7] C.S. Yih, Stability of liquid flow down an inclined plane. Phys. of Fluids 6(3) (1963), 321-334
  8. [8] D.J. Benny, Long waves on liquid films. J. Math. Phys. 45 (1966), 150-155
  9. [9] V.Ya. Shkadov, Wave models in the flow of a thin layer of a viscous liquid under the action of gravity. Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza 1 (1967), 43-50
  10. [10] V.Ya. Shkadov, Theory of wave flow of a thin layer of a viscous liquid. Izv. Akad. NaukSSSR, Mekh. Zhidk. Gaza 2 (1968), 20-25
APA
Chattopadhyay, S., Mukhopadhyay, A., & Barua, A. (2019). A Review on Hydrodynamical Stability of Thin Film Flowing Along an Inclined Plane. Journal of Mathematical Sciences and Modelling, 2(2), 133-142. https://doi.org/10.33187/jmsm.458359
AMA
1.Chattopadhyay S, Mukhopadhyay A, Barua A. A Review on Hydrodynamical Stability of Thin Film Flowing Along an Inclined Plane. Journal of Mathematical Sciences and Modelling. 2019;2(2):133-142. doi:10.33187/jmsm.458359
Chicago
Chattopadhyay, Souradip, Anandamoy Mukhopadhyay, and Amlan Barua. 2019. “A Review on Hydrodynamical Stability of Thin Film Flowing Along an Inclined Plane”. Journal of Mathematical Sciences and Modelling 2 (2): 133-42. https://doi.org/10.33187/jmsm.458359.
EndNote
Chattopadhyay S, Mukhopadhyay A, Barua A (August 1, 2019) A Review on Hydrodynamical Stability of Thin Film Flowing Along an Inclined Plane. Journal of Mathematical Sciences and Modelling 2 2 133–142.
IEEE
[1]S. Chattopadhyay, A. Mukhopadhyay, and A. Barua, “A Review on Hydrodynamical Stability of Thin Film Flowing Along an Inclined Plane”, Journal of Mathematical Sciences and Modelling, vol. 2, no. 2, pp. 133–142, Aug. 2019, doi: 10.33187/jmsm.458359.
ISNAD
Chattopadhyay, Souradip - Mukhopadhyay, Anandamoy - Barua, Amlan. “A Review on Hydrodynamical Stability of Thin Film Flowing Along an Inclined Plane”. Journal of Mathematical Sciences and Modelling 2/2 (August 1, 2019): 133-142. https://doi.org/10.33187/jmsm.458359.
JAMA
1.Chattopadhyay S, Mukhopadhyay A, Barua A. A Review on Hydrodynamical Stability of Thin Film Flowing Along an Inclined Plane. Journal of Mathematical Sciences and Modelling. 2019;2:133–142.
MLA
Chattopadhyay, Souradip, et al. “A Review on Hydrodynamical Stability of Thin Film Flowing Along an Inclined Plane”. Journal of Mathematical Sciences and Modelling, vol. 2, no. 2, Aug. 2019, pp. 133-42, doi:10.33187/jmsm.458359.
Vancouver
1.Souradip Chattopadhyay, Anandamoy Mukhopadhyay, Amlan Barua. A Review on Hydrodynamical Stability of Thin Film Flowing Along an Inclined Plane. Journal of Mathematical Sciences and Modelling. 2019 Aug. 1;2(2):133-42. doi:10.33187/jmsm.458359