Team:BostonU HW/Model

Fluid Functionality

Summary

During the process of developing the MARS repository there were many questions that we found ourselves asking consistently:

1. Why is this chip not working?
2. Is this what this chip should be doing right now?
3. What part of this chip is failing?

The common theme underlying these questions was our inability to explain why our microfluidics chips were not functioning correctly. When we had performed a literature review there were no papers published regarding a standardized method of evaluating microfluidic chips. With that problem in mind the team went on to create an evaluation system known as Fluid Functionality.

Fluid Functionality is based around analyzing the functionality of each primitive in a microfluidic chip (refer to Microfluidics 101 on our Wiki for more information regarding primitives.) These primitives can be thought of as the individual electrical components that are a part of a larger circuit. If one and/or more primitive malfunctions the entire system will not work. However, how do we go about analyzing each primitive? Primitive analysis can be broken up into two parts:

1. Qualitative: Observations that provide any indication of failure.
2. Quantitative: Calculations that show whether your primitive failed or not.

By inter-relating the qualitative failures we have observed with a corresponding quantitative analysis method we can explain why a microfluidic chip is not working. If, for example, a primitive has a qualitative failure and fails its quantitative test, then there is something wrong with the primitive's dimensions. But if a primitive has a qualitative failure and passes its quantitative test, then there is some other source of error such as poor assembly. At this time these relationships are not fully defined. More work in the future can yield a better relationship between which qualitative failure pairs with quantitative test. Fluid Functionality can primarily be utilized as a modeling framework.

iGEM has done an excellent job of defining modeling projects related to wet lab experiments, however since MARS is a hardware project this was our team’s approach of modeling our work. The sections below describe the qualitative and quantitative analyses we have developed.

Qualitative Failure Modes

Leak (Initial)

This qualitative failure is characterized by liquid leaking out of a channel and/or primitive into the space between the PDMS and flow layer. An initial leak occurs almost immediately after a liquid passes the area of the leak. Regardless of scale, these leaks are considered a failure mode.

Leak (Over Time)

This qualitative failure is characterized by liquid leaking out of a channel and/or primitive into the space between the PDMS and flow layer. A leak that occurs over time is not characterized by an initial leak growing over time but as a leak that appears a significant amount of time after liquid has passed the location of a leak. These leaks can be seen in situations where a seal degrades during incubation period, leading to a new leak forming minutes after liquid initially passed through a section. Regardless of scale, these leaks are considered a failure mode.

An initial leak. The red liquid has leaked out of the channel into the area between the PDMS and the flow layer.

Air Bubble

This qualitative failure is characterized by an air bubble being present within a channel or primitive. Air bubbles can affect proper liquid flow and can reduce the accuracy of design features such as time-dependent mixers and metering. Regardless of scale, air bubbles are considered a failure mode.

Multiple air bubbles are present in this chip. The red and blue liquids should extend down and up respectively to the circle valve between them, however air bubbles are present that are preventing these liquids from completely filling their respective channels.

Liquid does not cross an OPEN Valve

This qualitative failure is characterized by liquid not crossing over a valve that has been opened by actuating the corresponding syringe on the control layer. This failure can exist in many forms, such as liquid pausing after filling the first portion of the valve and never crossing into the second section or leakage around the first portion of a valve. This failure is often accompanied by leakage due to pressure buildup.

Liquid is not properly crossing over a valve in this chip. After filling the first portion of the valve the red liquid should be crossing into the other section and filling the following channels. However, it is not crossing, which can cause leaks and improper liquid flow.

Liquid crosses a CLOSED Valve

This qualitative failure is characterized by a liquid crossing over a valve that is closed, meaning that it’s corresponding control syringe has not been actuated. This failure can exist in many forms, such as liquid leaking over a valve that has never been opened before or leaking over a valve that was previously opened by is not closed. This failure can lead to contamination of liquids as well as inaccuracies with features such as metering.

Liquid is crossing over a close valve in this chip. The blue liquid has crossed over the valve above it, a valve that is
closed, and is contaminating the red liquid, as seen by the dark-purple liquid in the red metering section.

Mixer does not mix liquids sufficiently

This qualitative failure is characterized by the final output of a mixer not being sufficiently mixed. This failure can be dependent on the chip being tested, as certain procedures will have varying levels of tolerance regarding mixture homogeneity. In general, liquids exiting a mixer should be relatively homogeneous; a quantitative calculation of mixing can be performed to calculate how homogeneous the final mixture is.

Liquid is not fully mixing in the mixer. Ideally, the liquid would enter the mixer on the left, mix as it passes through the primitive, and exit as a homogeneous liquid on the right side of the mixer. However, in this mixer the liquids exiting are not homogeneous, as seen by the distinct sections of color.

Metering dispenses inaccurate volume of liquid

This qualitative failure is characterized by an incorrect volume of liquid being dispensed by a metering primitive. This failure is almost always observed in conjunction with other failures such as leaks and liquid crossing over closed valves. Therefore, if any of the above failures occur prior to or during metering, it is extremely likely metering will dispense an incorrect volume of liquid(s). To calculate the volume of liquid being measured and/or dispensed from a metering primitive, please refer to the metering quantitative analysis portion of Fluid Functionality.

Liquid crossing over closed valves is causing a metering failure. The presence of oil in the output (horizontal) channels of a metering primitive suggests that valves have not properly caused, as liquid should not be displaced in output channels (horizontal) as their accompanying valves should be closed. This would cause inaccurate volumes of liquid to be dispensed by the metering primitive.

Quantitative Analysis & Evaluation

Maximum Pressure Calculation

When a chip's internal pressure exceeds the maximum pressure that the sealing can withstand many complications such as leaks will ensue. In order to evaluate whether the chip will be able to function without these issues a PSI calculation is needed to be performed. This quantitative test is utilized to measure the internal pressure of a specific primitive inside your microfluidic chip. The MARS chips have all been manufactured using Makerfluidics, and have been evaluated to withstand an internal pressure of up to 5 PSI^[1]. To calculate the pressure in a given primitive the following three equations need to be used.

1. \[10h < w \Rightarrow R_{fluid} \approx 12\mu L/wh^{3}\]


2. \[2h > w \Rightarrow R_{fluid} \approx 32\mu L/wh^{3}\]


3. \[\Delta P=R_{fluid}Q\]

Equations a-c are used to describe the relationship of pressure within a channel of a given length (L), width (w), and height (h). Equations a and b are utilized to determine which formula would provide a better approximation for fluid resistance based on the height and width of the channel. After determining an approximate value of fluid resistance, PSI can be calculated using equation c. Equation c is analogous to Ohm’s law but is used for fluid dynamics. The PSI value is directly proportional to both the fluid resistance and the flow rate (Q). These calculations were written as a C++ file which can be compiled and executed.
Download File Here!get_app

Mixing Efficiency

The mixing of two fluids is something that can often be qualitatively observed, however in order to properly perform an experiment certain amounts of mixing must be achieved. In order to evaluate the degree of which fluids are being mixed in a mixer primitive a mixer efficiency test is needed to be performed. This quantitative test is broken down into a two-part process:

1. Image Processing
After running fluid through your mixer, pictures need to be taken at the regions prior to entering the primitive and after it exits the primitive. In order to obtain RGB data from these images, image processing software such as ImageJ need to be implemented. Using ImageJ a 1-pixel wide box is created that spans the length of the channel. The two important pieces of data that need to be obtained using this box are the average RGB value over that area, and all RGB values over the length of the 1-pixel wide box. After collecting this data, you can move on to calculate the mixing efficiency.


Using the RGB Profile Plot plugin on ImageJ we can acquire the RGB values for each pixel in our box. In a well-mixed output the plot will reflect similar RGB values and the opposing ends of the output channel.



Using the RGB Measure plugin on ImageJ we can acquire the average RGB values over the total area of the box.

2. Efficiency Calculation
The efficiency of the mixing itself can be measured using the following equation^[2]:

\[\gamma = 1-2\left [ \frac{\int RGB-RGB_{avg}dL}{\int dL} \right ]\]

Once this value is obtained the channel primitive can be measured to see if it is suitable to perform the needed function.

Valve Actuation

Even though it can be easily observed that a fluid is not traveling over a valve, it is not easy to determine whether the PDMS is being properly actuated by the primitive. In order to evaluate each valve’s functionality a valve actuation test can be performed.

This quantitative test involves modeling the deflection of the PDMS as a beam using Euler–Bernoulli beam theory, and modeling the valves as a simply supported beam at both ends with a uniformly distributed load. This is an acceptable approximation since the valve geometry is axisymmetric. The maximum deflection of the beam would be equivalent to the PDMS deflecting into the circle valve. In this equation E is equal to the value of the modulus of elasticity for PDMS, and I is equal to the moment of inertia.

\[\Delta Z = \left ( \frac{5}{358} \frac{Fl^{3}}{EI}\right )\]

We would substitute the value of length in the max deflection equation with the diameter value of the valve. We can than calculate the force needed in order to fully actuate the PDMS into the circle valve.

\[F = \left (\frac{358\Delta Z E I }{5D^{2}}\right )\]

The next step is to convert that value of force into a value of pressure. Can use the formula:

\[P = F \times A\]

Lastly, since we know the volume within the chip and tubing the syringe is connected to we can use Boyle's law to calculate for the amount of volume we would need to pull the syringe back to actuate the valve.

\[P_{1}V_{1} = P_{2}V_{2}\]

Metering Accuracy

The metering primitive was developed to dispense relatively accurate volumes of liquid. However, for biological experiments a certain level of accuracy is required when it comes to volumes used. In order to ensure this primitive is dispensing relatively accurate volumes of liquid, a metering accuracy test must be performed. This quantitative test is broken down into a two part process:

1. Image Processing
After running the metering portion of your chip, pictures need to be taken before and after the oil has dispensed all the liquid from the metering section. An image processing software, such as ImageJ is then used to analyze how much liquid was metered and how much was actually pushed.

To analyze the amount of metered liquid, first set the scale for ImageJ in units of microns. Then, using the Rectangle selection tool, draw a rectangle encapsulating the first metered liquid section. This can be seen below:





Using the rectangle select tool in ImageJ to trace the amount of black liquid metered. The area of this rectangle will then be measured using the "Measure" tool. Using the area of this rectangle and the depth of the corresponding section, volume of metered liquid can be calculated.


Then, using the measurement tool calculate the area in microns of the metered section. To find the volume of this metered section, use the following formula:

\[Volume Metered (\mu L)=Area(\mu m^{2}) \times Depth(\mu m) \times (\frac{1.00 \mu L}{ 10^{9} \mu m^{3}})\]

Repeat this process for each individual metering sections, summing them together as follows to find the total metered volume:

\[Total Volume Metered (\mu L)=\sum_{i}^{n}Area_{i}(\mu m^{2}) \times Depth_{i} (\mu m) \times (\frac{1.00 \mu L}{10^{9} \mu m^{3} } )\]

To analyze the amount volume of liquid dispensed, perform the same analysis as before on the image taken after all of the liquid has been displaced by the mineral oil.

\[Volume Dispensed (\mu L)=Area(\mu m^{2}) \times Depth(\mu m) \times (\frac{1.00 \mu L}{ 10^{9} \mu m^{3}})\]



2. Accuracy Calculation
The metering accuracy can be calculated using the following formula:

\[Percent Accuracy = \frac{Volume Metered(\mu L)}{Volume Dispensed(\mu L)} \times 100\]

The metering error can be calculated using the following formula:

\[Error (\mu L)= Volume Metered(\mu L) - Volume Dispensed(\mu L)\]

If there is a significant error in metering, this suggests that there was either a milling inaccuracy or a leak at a channel and/or valve during the pushing process.

Citations

1. Mcdonald JC, Whitesides GM. Poly(dimethylsiloxane) as a material for fabricating microfluidic devices. Acc Chem Res. 2002;35(7):491-9.
2. Rasouli, M. R., A. Abouei Mehrizi, and A. Lashkaripour. "Numerical Study on Low Reynolds Mixing ofT-Shaped Micro-Mixers with Obstacles." Transport Phenomena in Nano and Micro Scales 3.2 (2015): 68-76.

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