You are tasked to design a lateral flow assay to detect the presence of the protein…

You are tasked to design a lateral flow assay to detect the
presence of the protein unobtainien in urine as a sign of motaba
infection. You’re given the following information:

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  • The unobtainien first binds to an antibody in solution that is
    linked to a gold nanoparticle – this part of the device has already
    been designed, and is so effective that you can assume that every
    molecule of unobtainien that reaches the detection strip is already
    bound to one gold nanoparticle-linked antibody
  • The concentration of unobtainien in the urine is approximately
    constant (i.e., a detection strip fully loaded with unobtainien
    only binds a small fraction of the total unobtainien in the
    urine)
  • The kr for the antibody on the detection strip is low enough
    that the reverse reaction can be neglected
  • The urine will be at room temperature and has a viscosity of
    8.891E-4 kg/(m*s) and a surface tension roughly equivalent to water
    at 25C
  • The kf for the antibody on the detection strip is 5.3
    1/[(mol/m3)s]
  • The total surface concentration of antibody on the detection
    strip is 3.0E-12 mol/m2
  • The concentration of unobtainien in the urine is 8.1E-5
    mol/m3
  • Signal should preferably be visible in 6 minutes.

a) If the distance between the loading area and the detection
strip is 46 mm, how long (in seconds, with two significant digits)
will it take for sample to reach the detection strip if the strip’s
membrane has an effective pore diameter of 79 microns?

b) Once the same has reached the detection strip, how long (in
seconds, with three significant digits) will it take before a
visible signal appears? A minimum surface concentration of 6.0 E-13
mol/m2 of gold nanoparticle-linked antibody is required
for a visible signal.