Split and Recombine Mixer Benchmark

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Split and Recombine Mixer Benchmark

Benchmarking is an important part of CFD research and code validation. This model uses COMSOL to compute multilamination by a split and recombine mixer. The flow pattern is visualized using a tracer and diffusion is suppressed by setting the diffusion coefficient to an extremely low value of 2·10–20 m2/s. Thus only numerical diffusion is significant in the model.

This model performs two separate stationary analyses, solving first for the flow and then for the convection/diffusion.

Model Definition

The geometry is constructed with two inlets and a single outlet to allow a flow of high concentration to mix with a flow of low concentration. The two flows primarily mix via multilamination as the flows get split and subsequently recombined as they proceed along the geometry.

Figure 1: Model geometry. The flow lamination pattern is studied at the cross sections indicated.

The model studies the flow lamination pattern at various places along the mixer channel, labeled A–A, B–B, C–C, and D–D in Figure 1.

Results and Discussion

Figure 2 shows the lamination patterns at the four locations. The blur on the interfaces is due to numerical diffusion within the simulation. High numerical diffusion would result in a more pronounced blurring of the interface. It is clear that the calculated interfaces are sharp indicating little numerical diffusion in the results. These flow patterns are in good agreement with those presented by Glatzel and others (Ref. 1).

Figure 2: Flow lamination patterns at locations A–A, B–B, C–C, and D–D.

The total pressure drop at a given flow rate (fluidic resistance) across the mixer is calculated to be 1.63 Pa. This result is slightly lower that obtained by the other codes in Ref. 1. However a lower value is expected as the finite-element method adds less artificial diffusion to the problem than the finite-volume method. Adding artificial diffusion to a flow problem increases the effective viscosity of the fluid and is therefore expected to artificially increase the pressure drop across the system.

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 together with a Transport of Diluted Species interface. The Transport in Diluted Species interface uses the solution from the Laminar Flow interface. This solution coupling is demonstrated in this model.

Microfluidics_Module/Micromixers/split_recombine_mixer

Modeling Instructions

From the menu, choose .

In the window, click

.

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In the window, click

.

2

In the tree, select .

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4

5

In the tree, select .

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For convenience, the device geometry is inserted from an existing file. You can read the instructions for creating the geometry in the Appendix — Geometry Instructions.

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In the toolbar, click and choose .

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Browse to the model’s Application Libraries folder and double-click the file split_recombine_mixer_geom_sequence.mph.

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In the toolbar, click

.

The geometry should look like that in Figure 1.

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In the window, under right-click and choose .

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In the window for , type Fluid in the text field.

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Locate the section. 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

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
v0	1[mm/s]	0.001 m/s	Inflow velocity
d	500[um]	5E-4 m	Channel side length

Laminar Flow (spf)

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In the window, under click .

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In the window for , click to expand the section.

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From the list, choose .

Two inlets are defined to allow the introduction of the two fluid streams. One stream will carry the tracer.

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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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Locate the section. In the U0 text field, type v0.

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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 .

Transport of Diluted Species (tds)

Streamline and crosswind diffusion are activated by default. There are two options available for the type of crosswind diffusion used to provide numerical stabilization. The default option, is more effective at suppressing undershoots and overshoots in the concentration, whereas the second option, produces less artificial diffusion in the crosswind direction. Make the stabilization settings available following the steps below.

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button in the toolbar.

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In the dialog box, in the tree, select the check box for the node .

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4

In the window, under click .

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In the window for , click to expand the section.

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From the list, choose .

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Click to expand the section. From the list, choose .

Choosing cubic discretization for the concentration reduces the numerical diffusion. To suppress physical diffusion, set the diffusion coefficient to an extremely low value. Any diffusion seen in the results will now be due only to numerical diffusion.

Transport Properties 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 Dc text field, type 2e-20[m^2/s].

Set the initial concentration to 0.5 mol/m^3 to help with numerical convergence when solving.

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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In the c text field, type 0.5.

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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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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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Locate the section. In the c0,c text field, type 1.

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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 .

In the toolbar, click

.

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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 .

4

.

The Transport of Diluted Species interface uses the solution from the Laminar Flow interface. Therefore, only solve for the velocity variables in the first stationary study step and add a second one to compute the concentration of the tracer.

Step 1: Stationary

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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, clear the check box for .

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In the toolbar, click

and choose .

2

In the window for , locate the section.

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In the table, clear the check box for .

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In the toolbar, click

.

To visualize the lamination at various locations along the mixer, add four datasets, labeled A-A, B-B, C-C, and D-D.

1

In the window, expand the node.

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Right-click and choose .

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In the window for , locate the section.

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From the list, choose .

5

In the text field, type z.

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Locate the section. From the list, choose .

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In the text field, type A-A.

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Right-click and choose .

2

In the window for , type B-B in the text field.

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Locate the section. In the text field, type -y.

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Locate the section. From the list, choose .

1

Right-click and choose .

2

In the window for , type C-C 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 , type D-D in the text field.

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Locate the section. From the list, choose .

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

Flow Lamination Pattern

To visualize all lamination results, add four plots to the same plot group and then displace them to allow their viewing side by side.

1

In the toolbar, click

.

2

In the window for , type Flow Lamination Pattern in the text field.

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Click to expand the section. From the list, choose .

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Locate the section. From the list, choose .

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Locate the section. Clear the check box.

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Right-click and choose .

2

In the window for , locate the section.

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In the text field, type c.

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Locate the section. In the text field, type 10.

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Locate the section. From the list, choose .

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.

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In the dialog box, select in the tree.

8

1

Right-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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Click to expand the section. From the list, choose .

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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 d/2.

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In the text field, type -d.

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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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From the list, choose .

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In the window, expand the node, then click .

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In the window for , locate the section.

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In the text field, type -5*d.

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In the text field, type 0.

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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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From the list, choose .

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In the window, expand the node, then click .

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In the window for , locate the section.

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In the text field, type 4.5*d.

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In the toolbar, click

.

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button in the toolbar.

Flow Lamination Pattern

In the window, under click .

Table Annotation 1

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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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In the table, enter the following settings:


x-coordinate	y-coordinate	Annotation
0.75	-0.075	A-A
1.5	-0.075	B-B
2.25	-0.075	C-C
3	-0.075	D-D

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Locate the section. Clear the check box.

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From the list, choose .

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In the toolbar, click

.

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button in the toolbar.

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button in the toolbar.

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button in the toolbar.

Surface Average 1

Calculate the pressure drop across the mixer by adding a feature to both inlets.

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


Expression	Unit	Description
p	Pa	Pressure

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Appendix — Geometry Instructions

From the menu, choose .

In the window, click

.

In the toolbar, click

and choose .

1

In the window for , locate the section.

2

From the list, choose .

1

In the toolbar, click

.

2

In the window for , locate the section.

3

In the text field, type 0.5.

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In the text field, type 2.

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In the text field, type 0.5.

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Right-click and choose .

2

In the window for , locate the section.

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In the text field, type 1.

1

Right-click and choose .

2

In the window for , locate the section.

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In the text field, type 0.5.

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In the text field, type -1.5.

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Click to expand the section. In the table, enter the following settings:


Layer name	Thickness (mm)
Layer 1	1

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Find the subsection. Clear the check box.

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Select the check box.

1

Right-click and choose .

2

In the window for , locate the section.

3

In the text field, type 2.

4

In the text field, type 0.5.

5

Locate the section. In the text field, type 0.5.

6

Locate the section. Find the subsection. Clear the check box.

7

Select the check box.

1

Right-click and choose .

2

In the window for , locate the section.

3

In the text field, type 0.5.

4

In the text field, type 1.5.

5

Locate the section. In the text field, type 2.

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In the text field, type -3.

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Locate the section. Find the subsection. Clear the check box.

1

Right-click and choose .

2

In the window for , locate the section.

3

In the text field, type 1.5.

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In the text field, type -4.

1

Right-click and choose .

2

In the window for , locate the section.

3

In the text field, type 2.5.

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Locate the section. In the text field, type -5.

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In the text field, type 2.5.

1

Right-click and choose .

2

In the window for , locate the section.

3

In the text field, type 2.

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In the text field, type 0.5.

5

Locate the section. In the text field, type 0.

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In the text field, type -4.

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In the text field, type 0.

1

Right-click and choose .

2

In the window for , locate the section.

3

In the text field, type 1.

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In the text field, type -5.

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Locate the section. Find the subsection. Select the check box.

Block 10 (blk10)

1

Right-click and choose .

2

In the window for , locate the section.

3

In the text field, type 1.5.

4

Locate the section. In the text field, type 0.

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In the text field, type -5.5.

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Locate the section. Find the subsection. Clear the check box.

Block 11 (blk11)

1

Right-click and choose .

2

In the window for , locate the section.

3

In the text field, type 0.5.

4

In the text field, type 1.

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Locate the section. In the text field, type -5.

Block 12 (blk12)

1

Right-click and choose .

2

In the window for , locate the section.

3

In the text field, type 0.5.

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In the text field, type -6.5.

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


Layer name	Thickness (mm)
Layer 1	0.5

6

Find the subsection. Select the check box.

Partition Domains 1 (pard1)

1

In the toolbar, click

and choose .

2

button in the toolbar.

3

In the window for , locate the section.

4

From the list, choose .

5

button in the toolbar.

Form Union (fin)

1

In the window, click .

2

In the window for , click

.

1

In the toolbar, click

and choose .

2

In the window for , locate the section.

3

From the list, choose .

4

In the text field, type Geometry.

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Select the object only.

1

In the toolbar, click

and choose .

2

In the window for , type Inflow in the text field.

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Locate the section. From the list, choose .

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In the text field, type Inflow 1.

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On the object , select Boundary 101 only.

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In the toolbar, click

and choose .

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In the window for , type Inflow 2 in the text field.

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Locate the section. From the list, choose .

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On the object , select Boundary 26 only.

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In the toolbar, click

and choose .

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In the window for , type Outlet in the text field.

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Locate the section. From the list, choose .

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On the object , select Boundary 28 only.

1

In the toolbar, click

and choose .

2

In the window for , type Inlet in the text field.

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Locate the section. From the list, choose .

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Locate the section. Click

.

5

In the dialog box, in the list, choose and .

6

1

In the toolbar, click

and choose .

2

In the window for , type A-A in the text field.

3

Locate the section. From the list, choose .

4

On the object , select Boundary 60 only.

1

In the toolbar, click

and choose .

2

In the window for , type B-B in the text field.

3

Locate the section. From the list, choose .

4

On the object , select Boundary 125 only.

1

In the toolbar, click

and choose .

2

In the window for , type C-C in the text field.

3

Locate the section. From the list, choose .

4

On the object , select Boundary 132 only.

1

In the toolbar, click

and choose .

2

In the window for , type D-D in the text field.

3

Locate the section. From the list, choose .

4

On the object , select Boundary 32 only.

Walls - exterior

1

In the toolbar, click

and choose .

2

In the window for , type Walls - exterior in the text field.

3

Locate the section. Click

.

4

In the dialog box, select in the list.

5

Walls - interior

1

In the toolbar, click

and choose .

2

In the window for , type Walls - interior in the text field.

3

Locate the section. Click

.

4

In the dialog box, select in the list.

5

6

In the window for , locate the section.

7

Clear the check box.

8

Select the check box.

1

In the toolbar, click

and choose .

2

In the window for , type Mesh Control in the text field.

3

Locate the section. From the list, choose .

4

Locate the section. Click

.

5

In the dialog box, select in the list.

6

7

In the window for , locate the section.

8

9

In the dialog box, in the list, choose , , , and .

10

Mesh Control Faces 1 (mcf1)

1

In the toolbar, click

and choose .

2

In the window for , locate the section.

3

From the list, choose .

1

In the toolbar, click

and choose .

2

In the window for , type Exterior Walls in the text field.

3

Locate the section. From the list, choose .

4

Locate the section. Click

.

5

In the dialog box, select in the list.

6

7

In the window for , locate the section.

8

9

In the dialog box, in the list, choose and .

10