Chemical Engineering Computations

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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:
6. 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).
7. 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.
8. 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
9. 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).
10. 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:
11. Use the following equation to calculate mixture quality based on a cross-sectional line:
12. For your input velocity, make the boundary condition “Laminar inflow”
    a. Average velocity: 100 mm/s
    b. Entrance length: 100 µm
13. 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.
14. 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.
15. Use arrays and/or custom geometry parts to make duplicates of geometric features that
    might be repeated in your design.

Sample Solution

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