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HYDRODYNAMICS AND ACOUSTICS

2018 ◊ Volume 1 (91) ◊ Issue 2 ◊ p. 191-222

V. V. Meleshko*, A. A. Gourjii**, T. S. Krasnopolskaya***

* Taras Shevchenko National University of Kyiv, Ukraine
**National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute"
*** Institute of Hydromechanics of NAS of Ukraine, Kyiv, Ukraine

Mixing of viscous fluid in rectangular microchannels

Gidrodin. akust. 2018, 1(2):191-222

https://doi.org/10.15407/jha2018.02.191

TEXT LANGUAGE: Russian

ABSTRACT

The paper deals with the analysis of microfluidics mixing processes in straight microchannels with a rectangular cross-section and system of grooves on one of the channel surfaces. A general technique for studying of the flow of a viscous incompressible fluid in microchannels with a rectangular cross-section is constructed and the model representation of the flow in the Stokes approximation is developed. The mentioned technique is reduced to solving of the Stokes equations for the longitudinal fluid velocity component (the Poiseuille flow is postulated) and solving of the biharmonic equation with respect to stream function for the transversal fluid velocity components. The corresponding solutions are constructed basing on of the formulated correct mathematical problem for the flow of a viscous incompressible fluid in a rectangular microchannel. The biharmonic problem solution is expanded in a form of a superposition of the solutions with a symmetric and antisymmetric stream function distributions with respect to both coordinates of the channel cross-section. Each of the last ones is presented as an expansion in eigenfunctions. The accuracy of the fulfillment of the boundary conditions at the microchannel surfaces was analyzed to control the quality of the obtained results. It is shown that the retaining of as much as five terms in the analytical solution of the biharmonic problem provides the fulfillment of the boundary conditions with the error not exceeding 0.1% of motion velocity of the boundaries. The obtained solutions for the longitudinal and transversal components of the fluid flow velocity field in the domain under consideration are used to analyze the fluid mixing process under various initial conditions. The numerical modeling of the passive fluid advection process and comparison of the obtained results with the experimental data lead to the conclusion that the model representation is in a good accordance with a real flow in the microchannel.

KEY WORDS

microfluidics, the Stokes equations, chaotic advection

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