Abstract
Rotation bifurcation in a steady axisymmetric thermocapillary flow of an incompressible fluid filling a semi-infinite space bounded by the free surface with a nonuniform distribution of temperature is studied. The fluid flow is calculated on the basis of Navier–Stokes equations under the assumption of small diffusion coefficients. It is shown that the bifurcation triggers rotational motion in a thin Marangoni boundary layer in the case of local cooling of the free boundary near the axis of symmetry and in the presence of an external flow; there is no rotation outside this layer. In the case of local heating of the free boundary, rotation is not observed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
L. G. Napolitano, “Marangoni Boundary Layers,” in Proc. of the 3rd European Symposium on Material Science in Space, Grenoble, April 24–27, 1979 (European Space Agency, Paris, 1979), pp. 313–315.
V. V. Pukhnachev, “Group Analysis of Equations of an Unsteady Marangoni Boundary Layer,” Dokl. Akad. Nauk SSSR 279 (5), 1061–1064 (1984).
V. Ya. Shkadov, “Wave Formation on the Surface of a Heavy Viscous Fluid under the Action of Shear Stress,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 3, 133–137 (1970).
V. A. Batishchev, “Bifurcation of Self-Similar Solutions Describing a Thermocapillary Flow of a Fluid in a Thin Layer,” Prikl. Mekh. Tekh. Fiz. 40 (3), 137–142 (1999) [J. Appl. Mech. Tech. Phys. 40 (3), 479–484 (1999)].
V. A. Batishchev and E. V. Khoroshunova, “Emergence of Rotational Regimes in a Layer of a Thermocapillary Flow of a Nonhomogeneous Fluid,” Prikl. Mat. Mekh. 64 (4), 560–568 (2000).
Bifurcation Theory and Nonlinear Eigenvalue Problems, Ed. by J. B. Keller and S. Antman (W. A. Benjamin, New York, 1969).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.A. Batishchev.
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 59, No. 3, pp. 26–35, May–June, 2018.
Rights and permissions
About this article
Cite this article
Batishchev, V.A. Emergence of Fluid Rotation in the Marangoni Boundary Layer in the Region of Local Cooling of the Free Boundary. J Appl Mech Tech Phy 59, 407–415 (2018). https://doi.org/10.1134/S0021894418030033
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021894418030033