In lecture we saw that in microfluidic systems the minute sample droplet can vaporize very quickly. In this exercise you will calculate the evaporation time for a droplet of finite size trapped in a capillary that has two open ends. The capillary has rectangular -10x10μ㎡ cross section and it is L=1 cm in length. Use Dwvー0.26 x 10" m7s , PWV-3000 Pa, and rho= 1000 kg/m (1) If we assume that the capillary walls are perfectly impermeable, how long does it take for a 1 pL droplet to vaporize when placed at the center of the capillary?
(2) Now assume that the walls of the capillary have a finite permeability. Calculate the time dependent form of sample volume vs. time. Assume that most of the sample diffusing through the wall diffuses on the regions where the droplet wets the walls; hence as the droplet size decreases, the permeation through the wall is reduced yielding a nonlinear process. The diffusivity of water vapor through the wall is Dw and its wall thickness is tw