Integral Boundary Layer Relations in the Theory of Wave Flows for Capillary Liquid Films / V. Ya. Shkadov and A. N. Beloglazkin. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2017. № 6. P. 38-50
[Moscow Univ. Mech. Bulletin. Vol. 72, N 2, 2017. P. 133-144].
A generalized method of deriving the model equations is considered for wave flow regimes
in falling liquid films. The viscous liquid equations are used on the basis of integral boundary
layer relations with weight functions. A family of systems of evolution differential
equations is proposed. The integer parameter n of these systems specifies the number
of a weight function. The case n=0 corresponds to the classical
IBL (Integral Boundary Layer) model.
The case n\geq 1 corresponds to its modifications called the
WIBL (Weighted Integral Boundary Layer) models.
The numerical results obtained in the linear and nonlinear approximations for n=0,1,2 are
discussed. The numerical solutions to the original hydrodynamic differential equations are
compared with experimental data. This comparison leads us to the following conclusions:
as a rule, the most accurate solutions are obtained for n=0 in the case of film flows on
vertical and inclined solid surfaces and the accuracy of solutions decreases with
increasing n. Hence, the classical IBL model has an advantage over the WIBL models.
