"Bioreactors" short$-$answers $(18$ points$)$:

Briefly answer the following questions $(3$ points each$)$ about bioreactors:

What is the functional purpose of a bioreactor? $($please relate your answer to mechanotransduction$)$

If an intracellular signaling pathway $($ISP$)$ is activated first upon mechanical loading of a cell, with which

mechanoreceptor is that ISP most likely associated?

What is the disadvantage of uniaxial strain bioreactors, and how is this addressed with biaxial strain

bioreactors?

What does it mean for a bioreactor to apply an "inhomogenous" loading field?

If the loading equation for a bioreactor does not include an irreducible$/$irremovable variable describing

position within the bioreactor, is loading homogenous or inhomogenous?

Which of the following bioreactors 'systematically' apply shear stress upon cells? $($please specify each

pertinent bioreactor by the preceding letter, i$.$e$.,\text{'}a\text{'},\text{'}b\text{'},\text{'}c\text{'},$ etc., only$)$

a$.$ Platen compression

b$.$ Parallel disk viscometer

c$.$ Biaxial stretch membrane

d$.$ Radial flow chamber

e$.$ Cone$-$and$-$Plate viscometer

"Bioreactors" problem $(32$ points$)$:

For the viscometer set$-$ups shown above $($left $=$ parallel disk, right $=$ cone$-$and$-$plate$)$:

The fluid viscosity $=4{10}^{-3}Pa-$sec

The rotating plate spins at $200ra\frac{d}{sec}$

The circumferential velocity of the fluid within the cell culture is given as $v_{}=\frac{rz}{h}$

The shear stress due to fluid flow is given as $=\frac{d{v}_{}}{dz}$

The cone angle is $0\mathrm{.}2$rad

The maximum distance between plates is $1{10}^{-4}m$

$($a$)$ Derive a simpler expression for the circumferential velocity assuming the cone$-$and$-$plate viscometer by relating $r$

and $h$ and assuming $$ is sufficiently small such that $tan=sin=.(4$ points$)$

$($b$)$ Which viscometer set$-$up applies an 'homogeneous' shear$-$stress field upon the cell culture? $(4$ points$)$

$($c$)$ What is the shear$-$stress magnitude being applied by the cone$-$and$-$plate viscometer? $(12$ points$)$

$($d$)$ What is the ratio of shear stress of the parallel$-$disk viscometer to that of the cone$-$and$-$plate viscometer at the radial

position of $2{10}^{-3}m$ away from the spin axis? $(12$ points$)$