Acoustic Microfluidic Pump

Microfuidic devices are becoming increasingly popular in the field of biomedical research and diagnostics, especially for preparing and analyzing fluid samples. To create functional microfluidic systems, pumps, valves, mixers, and so on, are needed also in macrofluidic systems. This model investigates an acoustically driven microfluidic pump which can drive a flow in a closed microfluidic system. The model geometry is inspired by, but not identical to, the one investigated experimentally and numerically by Huang et al. in Ref. 1.

The acoustic microfluidic pump is driven by the nonlinear acoustic phenomenon known as acoustic streaming. Acoustic streaming is a steady fluid flow created by an acoustic field due to nonlinear terms in the Navier–Stokes equations. In a mathematical sense, where the acoustic field is the linearized first-order field of the Navier–Stokes equations, the acoustic streaming field is the time-averaged second-order field in the perturbation scheme.

In the acoustic microfluidic pump, the streaming is driven by nonlinear contributions arising close to sharp edge structures in the microfluidic channel.

Model Definition

The model is of a 2D acoustic microfluidic pump consisting of a water-filled microfluidic channel of width Wc = 0.6 mm and the channel is closed. One section of the channel includes an array of sharp edge structures on the boundary, as seen in Figure 1. It is assumed that the surrounding solid is acoustically hard and therefore only the fluid domain is modeled.

The acoustic streaming is induced by an acoustic body force that is induced due to nonlinearities in Navier-Stokes equation; see Ref. 2. The acoustic body force, faco, is given as

(1)

The angle brackets represent the time-average of the oscillating acoustic fields. To model the thin viscous and thermal boundary layers and the acoustic body force correctly, it is necessary to use a fine mesh around the sharp edge structures. The sharp edge structures has a thickness of 0.2 µm at the tip. In the region around the sharp edge structure, a full thermoviscous acoustic model is used, and in the large domain a pressure acoustic model is used to limit the computational requirements. It is necessary to use the interface around the sharp edge structures because the geometry features are of a length scale comparable to the viscous and thermal boundary layers in the fluid.

Figure 1: Geometry of the microfluidic pump.

The acoustic domain force is computed and applied to the interface by the multiphysics feature that couples the interface with the interface. The complementary , available for both and , is not used since its contributions are negligible in this setup (it can be included but will be dominated by the other feature). The boundary coupling from thermoviscous acoustics is only important if the boundary vibrates. Thus, if the vibrations of the thin flaps were modeled, the should be included for modeling the resulting steady fluid flow.

Results and Discussion

The acoustic field is modeled as a in the big domain with a thermoviscous fluid model (viscous bulk losses), and with a in the 13 small domains surrounding the sharp edge structures.

Figure 2: Acoustic pressure field in the microfluidic channel.

The acoustic field is actuated on the four vertical boundaries in the large pressure acoustic domain; see Figure 1. To get the correct pressure levels of the standing acoustic field, the dissipation in the thermal and viscous boundary layers in the pressure acoustics domain is included by using the boundary condition on the boundaries.

In Figure 2, the pressure field for an actuation at 2 MHz and actuation displacement of 1 nm is shown. The steady acoustic-streaming flow is solved in a stationary study step using the solved acoustic fields. The streaming is induced by an acoustic body force faco (see Equation 1) near the sharp edge structures (added by the ). The acoustic body force around one of the sharp edge structures is shown in Figure 3. Note that the acoustic body force is located at the tip of the thin edge structure.

Figure 3: Acoustic body force generated at the tip of the sharp edge structure.

The acoustic body force at each thin edge structure creates a complicated fluid flow at the bottom half of the microfluidic channel. But because all the thin edge structures have the same direction, a nonzero flow field is created in the entire channel. The resulting fluid flow is shown on a logarithmic scale in Figure 4. The acoustic microfluidic pump creates a counterclockwise fluid flow. The logarithmic scale is chosen to capture both the complicated and fast flow around the thin edge structures and the fluid flow in the rest of the microfluidic channel.

The example demonstrates how an acoustic field can induce a steady fluid flow in closed microfluidic systems, also demonstrated experimentally by the research group of Tony J. Huang in Ref. 1.

Figure 4: Steady streaming flow in the microfludic channel driven by the acoustic source terms.

Notes About the COMSOL Implementation

The force and stresses implemented on the fluid domain depend on the derivatives of the acoustic fields. It is therefore recommended to increase the element order of the dependent variables of the Thermoviscous Acoustics, Frequency Domain interface to quadratic serendipity for the acoustic pressure and cubic serendipity for the acoustic velocity and temperature.

References

1. P.-H. Huang and others, “A reliable and programmable acoustofluidic pump powered by oscillating sharp edge structures,” Lab Chip, vol. 14, pp. 4319–4323, 2014.

2. P.B. Muller and H. Bruus, “Numerical study of thermoviscous effects in ultrasound-induced acoustic streaming in microchannels,” Phys. Rev. E, vol. 90, p. 043016, 2014.

Acoustics_Module/Nonlinear_Acoustics/acoustic_microfluidic_pump

Modeling Instructions

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Geometry 1

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

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Having imported the geometry, it can easily be modified as it is parameterized. Simply change the value of a dimension in the parameters list; this will update the geometry automatically.

Global Definitions

Parameters - Geometry

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Parameters - Model

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In the window for , type Parameters - Model in the text field.

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Browse to the model’s Application Libraries folder and double-click the file acoustic_microfluidic_pump_parameters.txt.

Add Material

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to open the window.

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to close the window.

Pressure Acoustics, Frequency Domain (acpr)

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Select Domain 1 only.

Pressure Acoustics 1

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Thermoviscous Boundary Layer Impedance 1

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Thermoviscous Boundary Layer Impedance - Actuation

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In the window for , type Thermoviscous Boundary Layer Impedance - Actuation in the text field.

Select Boundaries 1, 4, 111, and 112 only.

Locate the section. From the list, choose .

Specify the v0 vector as


act_v0	x
0	y

The boundary condition is used to actuate the system by using the velocity boundary condition.

Thermoviscous Acoustics, Frequency Domain (ta)

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Select Domains 2–14 only.

Thermoviscous acoustics is used in all the domains with sharp edges to capture the effect in the viscous boundary layers.

In the window, click .

In the window for , click to expand the section.

From the list, choose .

To accurately model the acoustic body force in the , it is necessary to increase the element order of the acoustic fields.

Multiphysics

Acoustic-Thermoviscous Acoustic Boundary 1 (atb1)

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and choose .

In the window for , locate the section.

From the list, choose .

Acoustic Streaming Domain Coupling 1 (asdc1)

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Laminar Flow (spf)

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Pressure Point Constraint 1

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Mesh 1

Free Triangular 1

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Size 1

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Size

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Distribution 1

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Select Boundaries 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, and 168 only.

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In the text field, type 6.

The distribution node is added at the tip of the sharp edges to ensure that the edge on the tip is well resolved.

Boundary Layers 1

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Boundary Layer Properties

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Select Boundaries 1–6, 8, 10–12, 14, 17–20, 22, 25–28, 30, 33–36, 38, 41–44, 46, 49–52, 54, 57–60, 62, 65–68, 70, 73–76, 78, 81–84, 86, 89–92, 94, 97–100, 102, 105–108, and 110–172 only.

Locate the section. In the text field, type 6.

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In the text field, type 0.2E-6.

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Study 1

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Stationary

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The study consists of two steps: first a Frequency Domain study step to model the acoustic fields and, second, a Stationary study step to model the fluid flow.

Step 1: Frequency Domain

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In the text field, type f0.

Step 2: Stationary

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In the table, enter the following settings:


Multiphysics couplings	Solve for	Equation form
Acoustic-Thermoviscous Acoustic Boundary 1 (atb1)		Automatic (Frequency domain)

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Results

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Add Predefined Plot

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Results

Acoustic Pressure (atb1)

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Acoustic Body Force

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In the window for , type Acoustic Body Force in the text field.

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Select Domain 2 only.

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Surface 1

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In the window for , locate the section.

In the text field, type sqrt(spf.F_acox^2+spf.F_acoy^2).

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The acoustic body force that induces the fluid flow is located at the tip of the thin flaps.

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Results

Velocity (spf)

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Surface

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Streamline 1

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In the text field, type v2.

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In the text field, type 0.02.

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Velocity (spf) - Logarithmic

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Surface

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The fluid flow is represented on a logarithmic scale since the velocity amplitude varies by orders of magnitude.

Geometry Sequence Instructions

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In the window, click

In the window, under click .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file acoustic_microfluidic_pump_geom_sequence_parameters.txt.

Geometry 1

Rectangle 1 (r1)

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In the text field, type L.

In the text field, type W.

Rectangle 2 (r2)

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In the text field, type L-channel_w*2.

In the text field, type W-channel_w*2.

Rectangle 1 (r1)

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Rectangle 2 (r2)

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Fillet 1 (fil1)

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button in the toolbar.

On the object , select Points 1–4 only.

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In the text field, type corner.

Polygon 1 (pol1)

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In the table, enter the following settings:


x (m)	y (m)
-10*flap_w	-W/2
cos(flap_angle)*flap_L	-W/2+sin(flap_angle)*flap_L
+10*flap_w	-W/2

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Circle 1 (c1)

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In the text field, type flap_L/4.

In the text field, type 180.

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Rectangle 3 (r3)

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In the window for , locate the section.

In the text field, type 2*flap_L.

In the text field, type 0.7*flap_L.

Locate the section. In the text field, type -0.75*flap_L.

In the text field, type -W/2.

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Copy 1 (copy1)

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Select the objects , , and only.

In the window for , locate the section.

In the text field, type range(-3*flap_dist,(3*flap_dist-(-3*flap_dist))/6,3*flap_dist).

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Polygon 2 (pol2)

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In the window for , locate the section.

In the table, enter the following settings:


x (m)	y (m)
-10flap_w-0.5flap_dist	-W/2+channel_w
cos(flap_angle)flap_L-0.5flap_dist	-W/2+channel_w-sin(flap_angle)*flap_L
+10flap_w-0.5flap_dist	-W/2+channel_w