For this part, $($a$)$ determine how long will it take for the fluid to travel along the channel having dimensions and then $($b$)$ through a first porous paper layer of the test strip. Typical microfluidic channel dimensions in a glucometer of rectangular shape are: a width of approximately $1mm,$ a thickness on the order of $0\mathrm{.}1mm,$ and lengths of a few millimeters. For the first layer of the test strip, a common material used in lateral flow assays Whatman Qualitative filter paper, Grade $1.$

As discussed in today's prototype lab session, one approach to assess transport time for these segments, is to use the Washburn expressions given below. For sample volumes ranging from $($i$)100L$ to $($ii$)10L$ to $($iii$)1L,$ please determine the time it will take for each of the sample sizes to reach the amperometric transduction sub$-$function.

Time to fill the sample chamber can be modeled by the Washburn equation which can be modified to describe capillary flow between two parallel plates:

$t=3\frac{L^2}{cos({}_w)}s$

where

$t=$ filling time

$=$ viscosity

$L=$ channel length $($along fill axis$)$

$=$ liquid surface tension

$w=$ contact $($wetting$)$ angle $...$and...

s $=$ capillary thickness $($channel height$)$