Diffusion, viscosity, convection and the boundary layer

Jolanta Wołowicz



Ryszard Wojnar




Abstract

We analyze the formation of the boundary layer and point to its affinity for diffusion. Based on Prandl's work, we discuss the properties of the boundary layer and its transition to the vortex state. We also describe the ways to reduce the unfavorable effects of the boundary layer encountered in nature.


Keywords:

viscosity, parabolicity, laminar flow, capillary flow, Albert Einstein's formula


ANDERSON E.J., MCGILLIS W.R., GROSENBAUGH M.A. 2001. The boundary layer of swimming fish. The Journal of Experimental Biology, 204: 81-102.   Google Scholar

BLASIUS H. 1908. Grenzschichten in Flǖssigkeiten mit kleiner Reibung. Zeitschrift fǖr Mathematik und Physik, 56:1-37.   Google Scholar

Boundary value control. Retrieved from https://en.wikipedia.org/wiki/Boundary_layer_control (1.12.2025).   Google Scholar

BULLOUGH R.K., CAUDREY P.J. 1980. The Soliton and Its History. In: R.K. Bullough & P.J. Caudrey, eds. Solitons. Part of the book series: Topics in Current Physics, 17:1-64.   Google Scholar

CAI J., JIN T., KOU J., ZOU S., XIAO J., MENG Q. 2021. Lucas–Washburn Equation-Based Modeling of Capillary-Driven Flow in Porous Systems. Langmuir, 9;37(5):1623-1636. https://doi.org/10.1021/acs.langmuir.0c03134   Google Scholar

COLE J.D. 1951. On a quasi-linear parabolic equation occurring in aerodynamics. Quarterly of Applied Mathematics. Vol. IX(3): 225-236.   Google Scholar

DOU Z., WANG J., CHEN D. 2012. Bionic Research on Fish Scales for Drag Reduction. Journal of Bionic Engineering, 9:457- 464.   Google Scholar

EINSTEIN A. 1905. Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen [On the Movement of Small Particles Suspended in Stationary Liquids Required by the Molecular-Kinetic Theory of Heat]. Annalen der Physik (in German), 322(8): 549-560.   Google Scholar

FISHER L.R., LARK P.D. 1979. An Experimental Study of the Washburn Equation for Liquid Flow in Very Fine Capillaries. Journal of Colloid and Interface Science, 69(3): 486-492.   Google Scholar

Flow separation. Retrieved from https://en.wikipedia.org/wiki/Flow_separation (1.12.2025).   Google Scholar

KIANOOSH Y., REZA S. 2015. Three-dimensional suction flow control and suction jet length optimization of NACA 0012 wing. Meccanica, 50(6): 1481-1494. https://doi.org/10.1007/s11012-015-0100-9   Google Scholar

LANDAU L.D., LIFSHITZ E.M. 1987. Fluid Mechanics, Course of Theoretical Physics, Volume 6. 2nd English ed., translated from the Russian by J.B. Sykes & W.H. Reid. Oxford – New York – Beijing – Frankfurt – São Paulo – Sydney – Tokyo – Toronto: Pergamon Press; 1987: 539.   Google Scholar

MUTHURAMALINGAM M., PUCKERT D.K., RIST U., BRUECKER C. 2020. Transition delay using biomimetic fish scale arrays. https://doi.org/10.1038/141598-020-71434-8   Google Scholar

MUTHURAMALINGAM M., VILLEMIN L.S., BRUECKER C. 2019. Streak formation in flow over biomimetic fish scale arrays. Journal of Experimental Biology, 222(16): 205963. https://doi.org/10.1242/jeb.205963   Google Scholar

PIAU J.M., BREMOND M., COUETTE J.M., PIAU M. 1994. Maurice Couette, one of the founders of rheology. Rheologica Acta, 33:357-368.   Google Scholar

POHL R.W. 1955. Mechanik-Akustik und Wärmelehre, Dreizehnte Verbesserte Auflage, Springer Verlags, Berlin-Göttingen-Heidelberg, p. 345.   Google Scholar

PRANDTL L. 1905. Űber Flüssigkeitsbewegung bei sehr kleiner Reibung. Verhandlungen des dritten internationalen Mathematiker-Kongresses in Heidelberg 1904, A. Krazer ed., Teubner, Leipzig, p. 484-491.   Google Scholar

SCHLICHTIN, H., GERSTEN K. 2017. Boundary-layer theory (Ninth ed.). Berlin Heidelberg: Springer.   Google Scholar

WASHBURN E.W. 1921. The dynamics of capillary flow. The Physical Review, XVII(3): 273-283.   Google Scholar

WEYBURNE D. 2023. Aspects of Boundary Layer Theory. Publisher: Basic Science. 2nd Edition. November 2023. ISBN: 979-8-218-22091-4.   Google Scholar

YANASE K. 2016. Pentti Saarenrinne Boundary layer control by a fish: Unsteady laminar boundary layers of rainbow trout swimming in turbulent flows. Open Access. Biology Open, 5(12):1853-1863. https://doi.org/10.1242/bio.020008   Google Scholar

Download


Published
2026-04-22

Cited by

Wołowicz, J., & Wojnar, R. (2026). Diffusion, viscosity, convection and the boundary layer. Technical Sciences, 29(29), 25–48. https://doi.org/10.31648/ts.12394

Jolanta Wołowicz 

Ryszard Wojnar 




License

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.