Previous experimental and computational studies have indicated that interfaces formed in steady, converging microchannel flows with similar liquids tend to be planar in nature under a variety of conditions relevant to micro-scale flows, including MEMS/microfluidic devices and even microcirculatory blood flows. Assuming a planar interface, we have developed an analytical framework to predict the fully developed interfacial location downstream of a convergence of identical microchannels. Results have been obtained for microchannels having rectangular, elliptical/circular and triangular cross-sections as a function of the inlet flow ratio. Two-dimensional results have also been obtained for fluids having unequal viscosities. Good agreement is found between this model and 3-D numerical simulations and experimental measurements provided that the flow inertia remains sufficiently small (Re≲10, typically). Where valid, application of this analytical, planar interface method represents a significant decrease in computational effort when compared to using CFD to determine interfacial positions.

Issue Section:
Technical Papers
Keywords:
interface phenomena, channel flow, viscosity, flow simulation
Topics:
Computer simulation, Flow (Dynamics), Fluids, Microchannels, Viscosity, Separation (Technology), Microchannel flow, Reynolds number
1.
Ho
,
C.
, and
Tai
,
Y.
,
1998
, “
Micro-Electro-Mechanical-Systems (MEMS) and Fluid Flows
,”
Annu. Rev. Fluid Mech.
,
30
, pp.
579
–
612
.
2.
Fung, Y.-C., 1997, Biomechanics: Circulation, Springer-Verlag, New York, USA.
3.
Carr
,
R. T.
, and
Kotha
,
S. L.
,
1995
, “
Separation Surfaces for Laminar Flow in Branching Tubes—Effect of Reynolds Number and Geometry
,”
ASME J. Biomech. Eng.
,
117
, pp.
442
–
447
.
4.
Hitt
,
D. L.
, and
Lowe
,
M. L.
,
1999
, “
Confocal Imaging of Flows in Artificial Venular Bifurcations
,”
ASME J. Biomech. Eng.
,
121
, pp.
170
–
177
.
5.
Peach, J. P., Hitt, D. L., and Dunlap, C. T., 2000, “Three-Dimensional Imaging of Microfluidic Mixing Surfaces Using Dual-Channel Confocal Microscopy,” Microelectromechanical Systems (MEMS)—Proceedings of the 2000 ASME International Mechanical Engineering Congress & Exposition, MEMS Vol. 2, pp. 497–504.
6.
Hitt, D. L., 2002, “Confocal Imaging of Fluidic Interfaces in Microchannel Geometries,” in Science, Technology & Education in Microscopy: An Overview, edited by A. Mendez-Vilas, ed., Vol. 1, 622–9.
7.
Enden
,
G.
, and
Popel
,
A. S.
,
1992
, “
A Numerical Study of the Shape of the Surface Separating Flow Into Branches in Microvascular Bifurcations
,”
ASME J. Biomech. Eng.
,
114
, pp.
298
–
404
.
8.
Ong
,
J.
,
Enden
,
G.
, and
Popel
,
A. S.
,
1994
, “
Converging Three-Dimensional Stokes Flow of Two Fluids in a T-Type Bifurcation
,”
J. Fluid Mech.
,
270
, pp.
51
–
71
.
9.
Landau, L. D., and Lifshitz, E. M., 1987, Course of Theoretical Physics: Volume 6. Fluid Mechanics, Pergamon Press, New York, USA.
10.
Rosenhead, L., 1963, Laminar Boundary Layers, Oxford University Press, New York, USA.
11.
Petersen
,
K. E.
,
1982
, “
Silicon as a Mechanical Material
,”
Proc. IEEE
,
2
, pp.
420
–
457
.
12.
Hirt
,
C. W.
, and
Nichols
,
B. D.
,
1981
, “
Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries
,”
J. Comput. Phys.
,
39
, pp.
201
–
225
.
13.
Hitt, D. L., and McGarry, M., 2004, “Numerical Simulations of Laminar Mixing Surfaces in Pulsatile Microchannel Flows,” in Mathematics and Computers in Simulation, Elsevier Mathematics, Elsevier, Amsterdam.
14.
Harris, T. R., 2003, Master’s thesis, University of Vermont.
15.
Harris, T. R., and Hitt, D. L., 2003, “Low Reynolds Number Transition to Core-Annular Flow in Converging Microchannels,” Bulletin APS—Division of Fluid Dynamics.
16.
Thorsen
,
T.
,
Roberts
,
R.
,
Arnold
,
F.
, and
Quake
,
S.
,
2001
, “
Dynamic Pattern Formation in a Vesicle-Generating Microfluid Device
,”
Phys. Rev. Lett.
,
86
, No.
18
, pp.
4163
–
4166
.
17.
Nisisako, T., Fukudome, K., Torii, T., and Higchi, T., 2001, “Nanoliter-Sized Droplet Formation in a Microchannel Network,” Proc. of ISMM2001, pp. 102–103.
18.
Dreyfus
,
R.
,
Tabeling
,
P.
, and
Willaime
,
H.
,
2003
, “
Ordered and Disordered Patterns in Two-Phase Flows in Microchannels
,”
Phys. Rev. Lett.
,
90
, No.
14
, pp.
144505
-
1
.
19.
Harris, T. R., Hitt, D. L., and Macken, N. A., 2003, “Periodic Slug Formation in Converging Immiscible Microchannel Flows,” Bulletin APS—Division of Fluid Dynamics.
20.
Shah, R. K., 1978, Laminar Flow Forced Convection in Ducts, Academic Press, New York, USA.
Copyright © 2004
 by ASME
You do not currently have access to this content.