On the boundary conditions in the Stokesian flows
- PDF / 602,448 Bytes
- 14 Pages / 595.276 x 790.866 pts Page_size
- 34 Downloads / 246 Views
O R I G I NA L A RT I C L E
Daria Yu. Khanukaeva
· Leonid A. Ostrer
On the boundary conditions in the Stokesian flows
Received: 5 June 2020 / Accepted: 8 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The problem of the boundary condition setting is considered for creeping flows over cylindrical and spherical obstacles. The interaction of Newtonian and micropolar liquid with the solid surface is discussed in the context of the Stokes paradox and the cell model technique. Mathematical and mechanical aspects of various types of boundary conditions at the hypothetical liquid surface are considered in the framework of the spherical cell model used for the simulation of membrane flows. New properties of the flow pattern in a spherical cell are found, and their independence of the boundary conditions is rigorously proved. The criteria of the boundary conditions equivalence are derived in terms of the membrane porosity and hydrodynamic permeability. Keywords Creeping flow · Boundary conditions · Micropolar fluid flow · Cell model · Porous medium · Hydrodynamic permeability
1 Introduction The problem of liquid interaction with overflowed surfaces represents a topic for the discussion since the beginning of hydrodynamics development. Any flow is confined by some boundaries, and even if it may be treated as an infinite one, the conditions at infinity as well as the conditions at any other surface should be set for the correct statement of the mathematical problem. Each condition reflects mechanical and sometimes physicochemical nature of the liquid–material interaction. This interaction occurs at the micro- and nanoscales, but it can be observed as a flow pattern only at the macroscale or measured in terms of some macrocharacteristic of the flow. Therefore, only assumptions of what is happening with the liquid at the surface can be made and further verified. At the same time, the influence of any obstacle on the flow is restricted by the vicinity of this obstacle. By this reason, the problem of the boundary conditions statement has not crucial importance for large-scaled flows, where the major part of the stream is far from the boundaries. Modern technologies deal with the micro- and nanoscale problems, where the flow is considered in confined domains, surrounded by various boundaries. So, the variation of the boundary conditions has an effect on the whole flow pattern. Doubtless, the type of the boundary condition at the solid surface must be chosen based on its characteristics, such as roughness or chemical activity and lyophilic or lyophobic property. A big review of the investigations Communicated by Peter Duck. D. Yu. Khanukaeva (B) · L. A. Ostrer Gubkin Russian State University of Oil and Gas (National Research University), Leninsky Prospect, 65-1, Moscow, Russia 119991 E-mail: [email protected] L. A. Ostrer E-mail: [email protected]
D. Khanukaeva, L. Ostrer
of the boundary conditions used in the flows of Newtonian liquids is given by Neto et al. [1]. The authors collected ma
Data Loading...
