Lab-on-a-chip

Lab-on-a-chip is a concept enabled by small microfluidic devices is being developed for point-ofcare (POC) diagnositics. Microfluidic devices offer numerous advantages: size, portability, small
sample volumes, high throughput capability, superior process control, and affordability. One
major challenge with microfluidic devices is sufficiently mixing two reactants together to
facilitate a chemical reaction as a diagnostic signal. The difficulty in mixing fluids stems from the
extremely low Reynolds numbers of fluids in micro-sized channels. Here, you will be mixing 1.)
blood and 2.) fluorescent molecules that bind specifically to human COVID-19 antibodies. The
fluorescence signal can then be measured using a fluorometer to rapidly determine whether or
not someone has antibodies for the COVID-19 virus.
Your job is to design the smallest possible microfluidic device (no larger than 1 mm x 1 mm) that
mixes the two solutions such that the quality of the mixture is ≥ 99% defined by the following
equation:
�!”# =
⎣
⎢
⎢
⎡ 1
‘[�]$
2
[�]$
2

.[�][�]
%
&’$
��
⎦
⎥
⎥
⎤
× 100%
where �!”# is the mixture quality percentage, [�]$ and [�]$ are the inlet concentrations for
each respective species, and [�] and [�] are the concentrations of each species at any point
across the channel width, �. Note: Here, the �-axis is along the channel length and the �-axis is
along the channel width (see Figure 1).
Design Requirements:
• Mixture quality at outlet: ≥ 99%
• Inlet flow rate: 60 µL/min (100 mm/s for the given inlet dimensions)
• Fluid: water
• Diffusion constant for both species: 1 × 10())m2
/s
• Concentration of fluorescent detector species: 1 mM
• Concentration of sample species in blood: 1 mM
• Minimum feature size: 2 µm
• Minimum wall thickness: 5 µm
• Maximum velocity at any point: 500 mm/s
• Maximum pressure drop: 7 kPa
• Your two inlets and outlet must have the dimensions shown in the figure below. Your
channel design should fit within the 1 x 1 mm square footprint:
• You cannot modify the inlet and outlet portions in Figure 1 in any way
• Your design must fit within a 1 mm x 1 mm square
• Mixing efficiency should be obtained 50 µm before the outlet (similar to HW 9)
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Project 2 – Microfluidics Chemical Engineering Computations Fall 2020
ECH 3854 Dr. Thourson
2
Figure 1: Schematic drawing of the 2D dimensions for your microfluidic design where x is along
the channel and y is transverse to the channel. The inlets and outlets must be built as shown in
this figure. The channel design that connects the inlets to the outlet is entirely up to you but
must fit within the 1 x 1 mm square footprint shown. You may move the inlets and outlet
anywhere around the 1 x 1 mm square, but they must not otherwise be modified.
Assumptions:

No slip condition at wall
Isothermal conditions
Neglect inertial term of Navier Stokes equation (use creeping flow physics)
Isotropic diffusion
Flow profile is developed at inlets (use laminar inflow boundary condition for inlet with
a 100 µm entrance length)
Tasks:
Plot mixture quality (in %) as a function of channel length using at least 7 points (if you
do not have a conventionally shaped channel, think of another way to make a similar
plot).
Create a custom fluid material with the properties of blood at 37˚C. Assume blood
behaves as a Newtonion fluid (although it does not). Re-run your model using the
density and viscosity of blood for the whole model and add the results to your plot in
Task #1. In your proposal, discuss whether your device meets design requirements if
using blood.
Perform a time-dependent study to determine how long it takes for fluid to flow
through your device from the inlet to the outlet using inlet velocities of 10 mm/s. Start
by making an estimate using the average fluid velocity and the length of your channel.
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Project 2 – Microfluidics Chemical Engineering Computations Fall 2020
ECH 3854 Dr. Thourson
3
Use a parametric sweep to plot mixture quality (%) as a function of any one geometric
dimension (e.g. channel width, channel length, # of pillars, # of spikes, # of turns, or any
other key feature of your design that you choose).
Obtain and report the following from your model:
a. Average fluid velocity
b. Maximum fluid velocity
c. Total pressure drop from inlet to outlet
Hints/tips:
Use the following equation to calculate mixture quality based on a cross-sectional line:
For your input velocity, make the boundary condition “Laminar inflow”
a. Average velocity: 100 mm/s
b. Entrance length: 100 µm
Although not required, it can help to add 2-5 µm radius fillets to all of your sharp
corners. This can help with meshing and cut down on computation time.
Mesh + convergence tips
a. Use a physics-controlled mesh at the beginning to ensure convergence of the
solution.
b. Refine the mesh using a bounding box around the locations which you want to
obtain data.
c. Refine your mesh around very small feature sizes to help convergence.
d. Too small of a mesh can sometimes prevent convergence.
Use arrays and/or custom geometry parts to make duplicates of geometric features that
might be repeated in your design.
Do not wait to run your model the day before the project is due! VLab will run very
slowly for everyone because you will all be using it at the same time. I cannot extend the
deadline beyond the last week of classes!
Proposal Writing Guidelines
• Two pages maximum (excluding figures)
• Briefly summarize the task.
• Describe your device including the details of the design.
• Explain why your design works.
• Report the key results on the performance of your design (see #4 in tasks).
• Also report your best mixture quality and overall 2D footprint.
• Summarize/conclude with the reasons why your design is best suited to meet the
specified design requirements.
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Project 2 – Microfluidics Chemical Engineering Computations Fall 2020
ECH 3854 Dr. Thourson
4
Rubric:
COMSOL fundamentals Points
Model runs without errors 5
Model appears to be built from scratch (nothing imported from external
sources) 5
Geometry is made efficiently (e.g. using an array instead of creating individual
objects) 5
Material is correctly assigned to the model 2
Inlet and outlet boundary conditions are correctly applied (using laminar inflow
at inlet) 4
Inflow and outflow boundary conditions are correctly applied 3
Physics are coupled through the velocity gradient 4
A second species is added to the transport physics 2
The model is reasonably meshed 5
COMSOL results contain relevant plots and images with axis labels 5
At least (1) example of a unique geometric design feature not learned in class
(i.e. pillars placed inside a straight channel does not count) 3
At least (1) example of using a Boolean in geometry (e.g. Difference, Union,
etc.) 3
At least (1) example of using a Transform in geometry (e.g. Array, Mirror, etc.) 3
At least (1) example of a Parameter to define the geometry 3
At least (1) example of a custom fluid material with properties different than
water
3
At least (1) example of a using a boundary box to refine the mesh 3
At least (1) example of modifying the model to improve the mesh quality (e.g.
adding fillets, union w/ no boundaries) 3
At least (1) example of 1D plot in COMSOL results 3
At least (1) example of exporting raw data points from COMSOL 3
At least (1) example of exporting a 2D image from COMSOL (no screenshots) 3
At least (1) demonstration of using a multiphysics simulation 8
At least (1) demonstration of a time-dependent study 8
At least (1) demonstration of a parametric study 8
MATLAB fundamentals
Correctly imports and stores CSV files containing COMSOL results 3
Code is versatile to accommodate a range of data sizes (number of data points
in results) 3
Code is structured efficiently using concepts learned in class 3
Code is organized and clear with comments on each line of code 3
Plots are clear and labeled (appropriate font size, axes labels, titles, legends,
etc.) 3
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Project 2 – Microfluidics Chemical Engineering Computations Fall 2020
ECH 3854 Dr. Thourson
5
Task completion
Plot mixture quality (in %) as a function of channel length using at least 7
points. 5
Obtain and plot simulation results using blood fluid properties instead of water. 5
Perform time-dependent study to determine the time for fluid to flow through
device. 5
Use a parametric sweep to determine performance dependence on a
geometric dimension. 5
Calcualte fluid performance results of your microfluidic device in COMSOL. 5
Device design
Microfluidic device design meets the design requirements 10
Device design is unique 6
Report
Introduction/task summary 10
Device description 10
Explanation of why your device is able to successfully mix the two sample
solutions within the design constraints 10
Discussion of results is meaningful and relevant but concise 15
Neatly formatted and organized 15
References (cite any design inspirations, where you got blood fluid properties,
etc.) 10
Bonus: How does the Péclet number affect mixing efficiency? 5

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