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) Created in Master PDF Editor 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: 1. No slip condition at wall 2. Isothermal conditions 3. Neglect inertial term of Navier Stokes equation (use creeping flow physics) 4. Isotropic diffusion 5. Flow profile is developed at inlets (use laminar inflow boundary condition for inlet with a 100 µm entrance length) Tasks: 1. 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). 2. 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. 3. 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. Created in Master PDF Editor Project 2 – Microfluidics Chemical Engineering Computations Fall 2020 ECH 3854 Dr. Thourson 3 4. 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). 5. 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: 1. Use the following equation to calculate mixture quality based on a cross-sectional line: 2. For your input velocity, make the boundary condition “Laminar inflow” a. Average velocity: 100 mm/s b. Entrance length: 100 µm 3. 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. 4. 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. 5. Use arrays and/or custom geometry parts to make duplicates of geometric features that might be repeated in your design. 6. 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. Created in Master PDF Editor 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 Created in Master PDF Editor 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