Kapitza number


The Kapitza number (Ka) is a dimensionless number named after the prominent Russian physicist Pyotr Kapitsa (Peter Kapitza). He provided the first extensive study of the ways in which a thin film of liquid flows down inclined surfaces.[1] Expressed as the ratio of surface tension forces to inertial forces, the Kapitza number acts as an indicator of the hydrodynamic wave regime in falling liquid films.[2] Liquid film behavior represents a subset of the more general class of free boundary problems. and is important in a wide range of engineering and technological applications such as evaporators, heat exchangers, absorbers, microreactors, small-scale electronics/microprocessor cooling schemes, air conditioning and gas turbine blade cooling.

After World War II Kapitza was removed from all his positions, including director of his Institute for Physical Problems, for refusing to work on nuclear weapons. He was at his country house and devised experiments to work on there, including his experiments on falling films of liquid.[3]

Unlike most dimensionless numbers used in the study of fluid mechanics, the Kapitza number represents a material property, as it is formed by combining powers of the surface tension, density, gravitational acceleration and kinematic viscosity.[4]

where σ is the surface tension (SI units: N/m), g is gravitational acceleration (m/s2), ρ is density (kg/m3), β is inclination angle (rad), and ν is kinematic viscosity (m2/s).


  1. ^ Kapitza, P. L. (1948). "Wave flow of thin layers of a viscous fluid: I. Free flow. II. Fluid flow in the presence of continuous gas flow and heat transfer". Zhurnal Eksperimental'noi i Teoreticheskoi Fiziki (in Russian). 18 (1): 1–28. Kapitza, P. L.; S. P. Kapitza (1949). "Wave flow of thin layers of a viscous fluid: III. Experimental study of undulatory flow conditions". Zhurnal Eksperimental'noi i Teoreticheskoi Fiziki (in Russian). 19 (2): 105–120. Bibcode:1949ZhETF..19..105K. Available in English in Kapitsa, Petr Leonidovich (1964). D. ter Haar (ed.). Collected Papers of P.L. Kapitza: 1938-1964. Macmillan.
  2. ^ Kalliadasis et al. 2011, p. 1.
  3. ^ Kalliandasis et al. 2011, pp. 357–360.
  4. ^ Kalliandasis et al. 2011, p. 31.


  • Kalliadasis, Serafim; Christian Ruyer-Quil; Benoit Scheid; Manuel García Velarde (2011). Falling Liquid Films (Volume 176 of Applied Mathematical Sciences). Springer. ISBN 978-1-84882-367-9.