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.

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

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

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.

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.