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. 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. 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.
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).
^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.