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

Sample solution

Dante Alighieri played a critical role in the literature world through his poem Divine Comedy that was written in the 14th century. The poem contains Inferno, Purgatorio, and Paradiso. The Inferno is a description of the nine circles of torment that are found on the earth. It depicts the realms of the people that have gone against the spiritual values and who, instead, have chosen bestial appetite, violence, or fraud and malice. The nine circles of hell are limbo, lust, gluttony, greed and wrath. Others are heresy, violence, fraud, and treachery. The purpose of this paper is to examine the Dante’s Inferno in the perspective of its portrayal of God’s image and the justification of hell. 

In this epic poem, God is portrayed as a super being guilty of multiple weaknesses including being egotistic, unjust, and hypocritical. Dante, in this poem, depicts God as being more human than divine by challenging God’s omnipotence. Additionally, the manner in which Dante describes Hell is in full contradiction to the morals of God as written in the Bible. When god arranges Hell to flatter Himself, He commits egotism, a sin that is common among human beings (Cheney, 2016). The weakness is depicted in Limbo and on the Gate of Hell where, for instance, God sends those who do not worship Him to Hell. This implies that failure to worship Him is a sin.

God is also depicted as lacking justice in His actions thus removing the godly image. The injustice is portrayed by the manner in which the sodomites and opportunists are treated. The opportunists are subjected to banner chasing in their lives after death followed by being stung by insects and maggots. They are known to having done neither good nor bad during their lifetimes and, therefore, justice could have demanded that they be granted a neutral punishment having lived a neutral life. The sodomites are also punished unfairly by God when Brunetto Lattini is condemned to hell despite being a good leader (Babor, T. F., McGovern, T., & Robaina, K. (2017). While he commited sodomy, God chooses to ignore all the other good deeds that Brunetto did.

Finally, God is also portrayed as being hypocritical in His actions, a sin that further diminishes His godliness and makes Him more human. A case in point is when God condemns the sin of egotism and goes ahead to commit it repeatedly. Proverbs 29:23 states that “arrogance will bring your downfall, but if you are humble, you will be respected.” When Slattery condemns Dante’s human state as being weak, doubtful, and limited, he is proving God’s hypocrisy because He is also human (Verdicchio, 2015). The actions of God in Hell as portrayed by Dante are inconsistent with the Biblical literature. Both Dante and God are prone to making mistakes, something common among human beings thus making God more human.

To wrap it up, Dante portrays God is more human since He commits the same sins that humans commit: egotism, hypocrisy, and injustice. Hell is justified as being a destination for victims of the mistakes committed by God. The Hell is presented as being a totally different place as compared to what is written about it in the Bible. As a result, reading through the text gives an image of God who is prone to the very mistakes common to humans thus ripping Him off His lofty status of divine and, instead, making Him a mere human. Whether or not Dante did it intentionally is subject to debate but one thing is clear in the poem: the misconstrued notion of God is revealed to future generations.

 

References

Babor, T. F., McGovern, T., & Robaina, K. (2017). Dante’s inferno: Seven deadly sins in scientific publishing and how to avoid them. Addiction Science: A Guide for the Perplexed, 267.

Cheney, L. D. G. (2016). Illustrations for Dante’s Inferno: A Comparative Study of Sandro Botticelli, Giovanni Stradano, and Federico Zuccaro. Cultural and Religious Studies4(8), 487.

Verdicchio, M. (2015). Irony and Desire in Dante’s” Inferno” 27. Italica, 285-297.