COMSOL 6.4 - Rotating Channel

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Rotating Channel

A lab-on-a-chip platform can be realized on a rotating disc by designing channels and other features to use the Coriolis or centrifugal forces to manipulate the flow. These forces are controlled by changing the angular velocity of the disc, so the platform is programmed by using a controlled sequence of angular velocities. In a microchannel, the centrifugal force induces a parabolic flow profile pointing in the radial direction. This is analogous to a Poiseuille or pressure-driven flow. The velocity-dependent Coriolis force produces an inhomogeneous transverse force in the tangential direction, which has its highest value in the center of the channel. This results in a change in the pressure distribution from that of a standard Poiseuille flow, which is assessed in this model. Ref. 1 computes the pressure distribution in the channel as part of a benchmarking exercise, and the results computed by COMSOL compare well with those given in this paper.

Model Definition

The geometry consists of a square cross section channel of length 10 mm with side 200 μm (see Figure 1). The channel points in the radial direction and begins at a radius of 20 mm from the center of rotation of the disc.

Figure 1: Model geometry. The radial direction corresponds to the x direction.

Results and Discussion

Figure 2 shows the pressure along the channel axis. The results are in good agreement with those presented by Glatzel and others (Ref. 1). It should be noted that the inlet boundary condition used by Glatzel and others is unphysical, because the Coriolis force acting at the inlet implies that there should be a pressure gradient in the y direction. Just as there is a pressure perpendicular to the flow when gravity acts in the perpendicular direction, so pressure gradients in the y direction are produced by the Coriolis force. This unphysical boundary condition accounts for the “kink” in the curve observed at the inlet and the complex pressure distribution at the inlet. Alternative approaches in this instance include using a point constraint on the pressure with the open boundary condition, explicitly including the pressure gradients in the pressure constraint and locating the inlet at the center of rotation of the disc. Because these methods invalidate comparisons with the results in Ref. 1, this model uses the unphysical boundary condition.

Figure 2: Pressure along the central axis of the channel.

The total flow rate through the channel is about 15 μl/s, in good agreement with the results in Ref. 1.

1. T. Glatzel, C. Litterst, C. Cupelli, T. Lindemann, C. Moosmann, R. Niekrawietz, W. Streule, R. Zengerle, and P. Koltay, “Computational fluid dynamics (CFD) software tools for microfluidic applications - A case study,” Computers & Fluids, vol. 37, pp. 218–235, 2008.

Notes About the COMSOL Implementation

The model is straightforward to set up using a Laminar Flow interface. Two different implementations are compared in the modeling instructions. In a first implementation the Coriolis and centrifugal forces are added explicitly as body forces. The second implementation uses the Rotating Frame feature.

Microfluidics_Module/Fluid_Flow/rotating_channel

Modeling Instructions

From the menu, choose .

In the window, click

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In the window, click

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In the tree, select > > .

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In the tree, select > .

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Global Definitions

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In the window, under click .

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In the window for , locate the section.

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In the table, enter the following settings:


Name	Expression	Value	Description
omega	100[rad/s]	100 rad/s	Angular velocity

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In the window, under click .

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In the window for , locate the section.

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From the list, choose .

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In the toolbar, click

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In the window for , locate the section.

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In the text field, type 10.

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In the text field, type 0.1.

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In the text field, type 0.1.

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Locate the section. In the text field, type 20.

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In the toolbar, click

and choose .

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Select the object only.

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In the window for , locate the section.

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In the text field, type 2.

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In the text field, type 2.

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Locate the section. In the text field, type 0.1.

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In the text field, type 0.1.

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button in the toolbar.

Material 1 (mat1)

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In the window, under right-click and choose .

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In the window for , locate the section.

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In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Density	rho	977	kg/m³	Basic
Dynamic viscosity	mu	8.55e-4	Pa·s	Basic

The large aspect ratio of the channel is not practical for creating the model. To continue more easily, it is useful to define a different view.

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In the window, under right-click and choose .

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In the window, click .

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In the window for , locate the section.

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Select the checkbox.

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In the window, click .

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In the window for , locate the section.

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From the list, choose .

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From the list, choose .

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In the text field, type 6.

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button in the toolbar.

Define a nonlocal integration coupling for the outlet boundary.

Integration 1 (intop1)

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In the toolbar, click

and choose .

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In the window for , locate the section.

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From the list, choose .

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Select Boundaries 17–20 only.

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In the toolbar, click

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In the window for , locate the section.

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In the table, enter the following settings:


Name	Expression	Unit	Description
Q	intop1(u)	m³/s	Total flow rate

Laminar Flow (spf)

Centrifugal force

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In the toolbar, click

and choose .

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In the window for , type Centrifugal force in the text field.

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Locate the section. From the list, choose .

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Locate the section. Specify the F vector as


spf.rhoxomega^2	x
0	y
0	z

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In the toolbar, click

and choose .

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In the window for , type Coriolis force in the text field.

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Locate the section. From the list, choose .

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Locate the section. Specify the F vector as


-2spf.rhoomega*v	x
2spf.rhoomega*u	y
0	z

Open Boundary 1

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In the toolbar, click

and choose .

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Select Boundaries 1, 4, 8, 11, and 17–20 only.

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In the toolbar, click

and choose .

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Select Boundaries 1, 4, 8, and 11 only.

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Right-click and choose .

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Select Edges 1, 2, 4, 5, 7, 9, 10, 12, 13, 15, 17, and 19 only.

In the toolbar, click

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Right-click and choose .

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In the window for , locate the section.

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In the text field, type 150.

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In the toolbar, click

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Unlike pressure-driven flows, the pressure drop along the channel is not linear. Add a 3D edge dataset to enable the creation of a pressure line plot.

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In the toolbar, click

and choose .

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Select Edge 14 only.

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In the toolbar, click

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In the window for , type Pressure drop in the text field.

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Locate the section. From the list, choose .

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Right-click and choose .

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In the window for , click in the upper-right corner of the section. From the menu, choose > > > .

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Click in the upper-right corner of the section. From the menu, choose > > > .

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In the toolbar, click

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Compare the result with Figure 2.

Finally, evaluate the total flow rate.

Global Evaluation 1

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In the toolbar, click

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In the window for , click in the upper-right corner of the section. From the menu, choose > > > .

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Locate the section. In the table, enter the following settings:


Expression	Unit	Description
Q	dm^3/s	Total flow rate

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Go to the window.

1.56e-5 dm^3/s corresponds to 15.6 μl/s.

Add a second laminar flow interface to set up the same simulation, but now using the Rotating Frame feature instead of adding the Coriolis and centrifugal forces explicitly.

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In the toolbar, click

to open the window.

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Go to the window.

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In the tree, select > .

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Click the button in the window toolbar.

Laminar Flow 2 (spf2)

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In the window for , locate the section.

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Select the checkbox.

Rotating Frame 1

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In the window, under > click .

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In the window for , locate the section.

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In the Ωf text field, type omega.

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From the list, choose .

Open Boundary 1

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In the toolbar, click

and choose .

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Select Boundaries 1, 4, 8, 11, and 17–20 only.

Initial Values 1

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In the window, click .

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In the window for , locate the section.

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Clear the checkbox.

In the toolbar, click

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In order to compare the result of the first and second approach, duplicate the pressure plot along the middle edge.

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In the window, under > right-click and choose .

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In the window for , locate the section.

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In the text field, type p2.

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In the toolbar, click

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The two pressure curves overlap. However, in order to get a better idea of the true difference, plot the difference of the pressures on a second axis.

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In the window, click .

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In the window for , locate the section.

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Select the checkbox.

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In the table, select the checkbox for .

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In the window, click .

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In the window for , locate the section.

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In the text field, type p-p2.

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In the toolbar, click

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The relative difference of the pressures is in the order of 0.01%. The difference can be made smaller by realizing that the centrifugal force as defined explicitly as a body force in the first Laminar Flow interface is an approximation: only the x-component is taken into account. Add the y-component and compare the results again to see that in this case the difference of the pressures is much smaller.

Laminar Flow (spf)

Centrifugal force

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In the window, under > click .

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In the window for , locate the section.

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Specify the F vector as


spf.rhoyomega^2	y

In the toolbar, click

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In the window, under click .

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In the toolbar, click

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