sample to the enzyme reaction chamber. This entails the transport of blood first into a microfluidic channel and then through the first layer of the test strip which is typically comprised a porous medium, such as filter paper. 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$)$

Liquid flow in porous materials like paper can be described by the Lucas$-$Washburn equation:

$L(t)=[\frac{rcosxt}{2}{]}^{\frac{1}{2}}$

where I is the distance of the fluid front, $y$ the solution surface tension, $r$ the effective pore radius of the paper, $$ the solution contact$-$angle with the paper, $$ the viscosity, and $t$ the elapsed time. Lastly, please calculate the diffusion$-$limited current from the equation below arising from a redox reaction of a $1L$ blood sample in a sample chamber having a $0\mathrm{.}1mm$ channel thickness $($d$)$

$i_d=\frac{nFD[S]}{d}$

d