Fick's Laws
Define flux
amount of material crossing a unit area normal to the direction of transport in a given unit of time
What is the frictional drag coefficient for a sphere?
6 pi mu R
If the Peclet number is zero, transport is limited by convection.
False
When estimating how far a particle is likely to diffuse over time using the root-mean-square displacement (RMSD), we model its path as a series of small steps. What is this type of motion called?
random walk or Brownian motion
For short contact time analysis, which are true:
1. parabolic velocity assumed
2. curvature can be neglected
3. concentration appears semi-infinite
2 & 3
What is the criteria for the dilute solution assumption?
solvent concentration is much greater than Ci
We're considering a protein that has been measured to be 3.5 nm x 2 nm x 2 nm. What equation would you use to estimate the mean frictional drag coefficient using Stokes-Einstein with the shape of a prolate ellipsoid?
See eqn sheet.
The concentration profile is ____ through the membrane if the Pe number is very, very small.
linear
Flow mediated dilation causes conduit arteries to decrease or increase resistance during high flow?
decrease
A fluorescent dye with diffusion coefficient D=8×10^(−6) cm2/s is injected at the inlet of a small capillary vessel of diameter 80 µm and length 1 mm. Blood flows through the vessel at a rate of 1.0 µL/min.
Assuming convection dominates over diffusion, and that the velocity profile can be approximated as uniform, what equation would you use to estimate how long it takes for the dye to reach the downstream end of the vessel, and what is the approximate travel time?
(You may assume cylindrical geometry and use the average velocity.)
time = Length/velocity
velocity is calculated with Q/A or Q/ (pi r^2)
A is about 5.0x10^-5
v is about .33 cm/s
so time convection is .1/.33 so 0.30 seconds
To derive Fick’s First Law, what conservation equation do we start with? (ie what is conserved)?
mass
What does mu represent in this equation?
solvent viscosity
What does v_f represent?
filtration velocity
A small signaling molecule diffuses inside a cell with an effective diffusion coefficient D = 5.0 x 10 ^ (-11) m^2/s.
If the molecule is confined to move along a microtubule—i.e., diffusion occurs only along one spatial dimension—what is the appropriate mean-square displacement (MSD) equation to calculate its expected displacement over time?
2Dt
We want to calculate the distance a molecule travels in one minute. Assume no convection, 37 degrees, water as the solvent with a viscosity of .62 cP. The molecular has a molar volume of 19,300 cm3/mol. What is Dij?
1.86x10-6 cm2/s
What does the steady state assumption in a diffusion problem tell you?
dCi/dt = 0
We're considering a protein that has been measured to be 3.5 nm x 2 nm x 2 nm. What is the estimate for the diffusion coefficient? Assume no convection, 37 degrees, water as the solvent with a viscosity of .62 cP
2.09 x 10-6 cm2/s
In the context of applying a semi-infinite diffusion model to biological systems, what key assumption about time must hold for the model to remain valid relative to diffusion across the full domain?
The time must be short enough that diffusion has not yet reached the far boundaries of the domain—i.e., short relative to full-domain diffusion.
Consider a steady-state, 1D diffusion and convection across a membrane of thickness L. No chemical reactions are occurring. At z=0, Ci = partition coefficient Co and at z=L, Ci = partition coefficient CL. What is the governing equation?
vf partial Ci/ partial z = Deff partical 2 Ci/ partial z2
A synthetic membrane is placed between two reservoirs of equal volume. Initially, C1 = .0018M and C2 is zero. If the volumes are 110mL and at steady state C1=C2=Csolution, what is the final solution concentration Csolution?
9 x 10-4
What do we use Fick’s 2nd Law to calculate?
dc/dx
We're considering a protein that has been measured to be 3.5 nm x 2 nm x 2 nm. It's diffusion coefficient in 20 degree C water was measured at 1.07 x 10-6 cm2s-1. What is your percent error?
61.76%
If a solute is roughly the same size as the solvent—making the Stokes–Einstein equation invalid—which alternative correlation should be used to estimate its diffusivity? And name two variables it depends on.
Wilkie–Chang correlation:molecular weight of solvent, solution viscosity, absolute temperature, association parameter of solvent,or molar volume of solute
Consider a steady-state, 1D diffusion and convection across a membrane of thickness L. No chemical reactions are occurring. At z=0, Ci = partition coefficient Co and at z=L, Ci = partition coefficient CL. What is the concentration profile?
phi C_o - phi(C_o - C_L) [(1-exp(Pe(z/L))/(1-exp(Pe))]
A synthetic membrane is placed between two reservoirs of equal volume. Initially, C1 = .0018M and C2 is zero. If the volumes are 110mL and at steady state C1=C2=Csolution, what is the partition coefficient between the membrane and tissue if Cmembrane is 2.4 x 10-5M?
0.027