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Research Papers: Fundamental Issues and Canonical Flows

# Low Reynolds Number Flow in Spiral Microchannels

[+] Author and Article Information
Denis Lepchev

Faculty of Aerospace Engineering, Technion, Haifa 32000, Israel

Daniel Weihs1

Faculty of Aerospace Engineering, Technion, Haifa 32000, Israeldweihs@tx.technion.ac.il

1

Corresponding author.

J. Fluids Eng 132(7), 071202 (Jul 22, 2010) (13 pages) doi:10.1115/1.4001860 History: Received December 12, 2009; Revised May 19, 2010; Published July 22, 2010; Online July 22, 2010

## Abstract

We study the creeping flow of an incompressible fluid in spiral microchannels such as that used in DNA identifying “lab-on-a-chip” installations. The equations of motion for incompressible, time-independent flow are developed in a three-dimensional orthogonal curvilinear spiral coordinate system where two of the dimensions are orthogonal spirals. The small size of the channels results in a low Reynolds number flow in the system, which reduces the Navier–Stokes set of equations to the Stokes equations for creeping flow. We obtain analytical solutions of the Stokes equations that calculate velocity profiles and pressure drop in several practical configurations of channels. Both pressure and velocity have exponential dependence on the expansion/contraction parameter and on the streamwise position along the channel. In both expanding and converging channels, the pressure drop is increased when the expansion/contraction parameter $k$ and/or the curvature is increased.

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## Figures

Figure 1

Orthogonality of α and β coordinates

Figure 2

Spiral microchannel with k=0.04 (left) and k=0.08 (right)

Figure 3

Entrance/exit area ratio of a microchannel with length α=50 as a function of the parameter k

Figure 4

Relation between dimensionless width B and minimum k for a physically achievable channel

Figure 5

Pressure distribution along the middle of the channel

Figure 6

Pressure distribution–dimensional values

Figure 7

Pressure distribution for flow in an expanding channel

Figure 8

Figure 9

Comparison of pressure drops in straight and spiral converging channels

Figure 10

Velocity distribution in α direction in the middle of the channel

Figure 11

Velocity distribution in α direction in the middle of expanding channels

Figure 12

Velocity profile across the channel at α=70

Figure 13

Deviation of the position of the peak streamwise velocity from the center at α=70

Figure 14

The example microchannel

Figure 15

Area coverage as function of k

Figure 16

Area coverage as function of length

Figure 17

The example microchannel (left, converging; right, expanding)

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