Friction pressure drops for streams 
through channels of small diameter

Bogomolov A. R.

Institute of Thermophysics SB RAS, Novosibirsk, Russia

Petrik P. T., Azichanov S. S.,  Tubol'tseva O. A.

Kuzbass State Technical University, Kemerovo, Russia

The field of investigation of flow of fluid in microchannels is substantiated by its use in different applications: chemical separating processes, computer chips, generation of microenergy and other micro-technologies.

One of the most simple methods of research of veracity of the theory of flow at a level of macroscale concerning transfer of impulse is a conducting of study of a pressure drop on known length of a channel. For an incompressible flow through horizontal channels (tubes) of a constant cross-section the pressure drop can be expressed on the law of a Darcy. This expression can be resolved concerning a friction coefficient

,                                                       (1)

where l - friction coefficient;  - sum of losses because of conditions of an input, exit and original hydrodynamic sector; Q – rate of flow; m - dynamic viscosity. The product of a measured friction coefficient and Reynolds number lRe then is compared to theoretical magnitude for laminar flows (64 for round channels). 

The disparities between microchannel flow and microscale theory of a flow of the Stokes were debated in the review [1]. It is widely accepted, that the deflection observed in gas flows, can be explained by slip on a wall. However, the slip along the wall is not justified in explanation of present deflections observed in incompressible streams. For a laminar, incompressible flow through microtubes a series of previous works communicated both about magnification, and about a decrease of a pressure drop from the calculated value grounded on the theory of a flow of the Stokes. In work [2] the results of a comprehensive experimental research of a friction coefficient for a laminar incompressible flow in a wide range of variation of cannel diameters and Reynolds numbers on three fluids grounded on clear properties of good wettability are introduced. Visible deflection from the theory of Stokes flow the writers have not detected.

The given work is directed on an experimental research of dependence of rate of a laminar incompressible fluid flow through tubes of small diameters from an contact angle of wetting. The datas are compared to the theory of a flow of the Stokes. In study the distilled water, quartzy tubes a diameter 0.55, 0.68, and 1.24 mm of different length was used. The surfaces of tubes were in one case well wetting, and in the other - restrictedly wetting and had an finite angle of wetting 18о and 87о, accordingly. The geometry of channels from the point of view of relative dimensionless quantities represented values L/D in limits from 460 up to 885. Modification (hydro-phobication) of an internal surface of handsets was maked under the usual method depicted in [3]. Thus, the problem was suggested to investigate the performances of a friction coefficient for the indicated diameters of tubes under condition of adhesion of medium on a wall and at its partial slip.

The experimental approach includes up measuring a pressure drop in cross-sections of a tube of known diameter and length. After measurement of rate and speed of fluid in a channel, and also properties of fluid, the friction coefficient was counted on an equation (1) and is compared to the theory of the Stokes. The set up for study represented a working section (tube about a small diameter of an aperture), arranged horizontally between a high pressure camera, filled fluid, and measuring cylinder. The working section on an exit was drowned in fluid for removal of oscillations on an exit at a breakoff of a spray resulting in turbulence of flow. Temperature of fluid was measured on an input and output of a working section. For minimization of influencing of an air diffusion on rheology properties of distilled water it was boiled during 10 minutes before feeding in a high pressure camera. The error estimation of experiment component 11 % is conducted which basically depends on an error in measuring diameter of a tube.

The experimental data on a friction coefficient l were obtained depending on rate of flow (Reynolds number) and is plotted graph (see fig. 1). The datas on l do not demonstrate considerable deflection from macro-scale the theory of Stokes flow as for a condition of adhesion of fluid to a wall, and for a condition of partial slip, at datas regime parameters.

It is possible to tell, that for an finite angle of wetting 87о, investigated in this study, not exists the phenomens of non-Stokes flow and the influencing of an contact angle beings within the limits inaccuracies of experiment.

References

  1. C. Ho, Y. Tai. Micro-electro-mechanical systems (MENS) and fluid flows, Annu. Rev. Fluid Mech. 30 (1998) 579-612.

  2. J. Judy, D. Maynes, B.W. Webb. Characterization of frictional pressure drop for liquid flows through microchannels, Int. J. of Heat and Mass Transfer 45 (2002) 3477-3489.

  3. Bogomolov A.R., Petrik P.T., Azikhanov S.S., Temnikova E. Yu. Concerning modification of glass serfaces // Thermophysics and Aeromechanics, 2002, Vol. 9, No. 3, P. 477-480