Polymers in Medicine
Stoke’s law to delivery of large porous particles to the lungs.
In the middle of the 19th Century, Stokes looked at the drag on spheres for which the Reynold’s number was low.
Fd=6pµRvs
µ is the dynamic viscosity, R is the radius of the sphere, vs is the settling velocity
And
Fg=(?p-?f)g(4/3)pR3
Where ?p is the density of the particle and ?f is the density of the fluid.
1)How does the settling velocity depend on the radius of the particle?
2)Why is the settling velocity a suitable measurement for delivery to the deep lungs? Draw a picture of the delivery and explain.
3)What is the necessary settling velocity for delivery to the deep lungs?
4)What radius of particles corresponds to this?
Particles that are small tend to be taken up extremely efficiently by alveolar macrophages. Therefore, groups tried to determine whether making large, porous 5)particles would be equivalent to the small, dense particles.
Start with the definition of the mean aerodynamic diameter:
MMADt=(?/?1)1/2d
Now, work through the derivation in the Vandever et al. paper, step by step explaining all the assumptions for a particle with radius, R, and n pores with radii rp. What is the dependence of the settling velocity on R, n, and rp? (Hint: You will use the equations from the beginning.)
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