Table 2.

Timescale groupings of the various physical processes present in the CXP1 bioreactor.

	Physical process	Timescale
$\mathcal{O}$(hour)	z diffusion glucose in hydrogel	$\frac{{ϵ}^2{L}^2}{D_{CH}}=1.5\times 10^4\text{s}=4.2\text{h}$
	z diffusion glucose in media	$\frac{{ϵ}^2{L}^2}{D_{CM}}=1.5\times 10^4$ s=4.2 h
	z diffusion lactate in hydrogel	$\frac{{ϵ}^2{L}^2}{D_{WH}}=7,500$ s = 2.1 h
	z diffusion lactate in media	$\frac{{ϵ}^2{L}^2}{D_{WM}}=6,400$ s = 1.8 h
$\mathcal{O}$(day)	Flow	$\frac{L}{\left[u\right]}=9\times 10^4$ s = 25 h
	Glucose consumption	$\frac{1}{{\nu }_C{N}_0}=2.7\times 10^5-4\times 10^5$ s = 74−110 h
	Lactate production	$\frac{1}{2{\nu }_C{N}_0}=1.3\times 10^5-2.0\times 10^5$ s = 37−55 h
	Cell proliferation	$\frac{1}{p}=2.6\times 10^5$ s = 72 h
$\mathcal{O}$(month)	x diffusion glucose in hydrogel	$\frac{L^2}{D_{CH}}=1.4\times 10^7\text{s}=3,800\text{h}$
	x diffusion glucose in media	$\frac{L^2}{D_{CM}}=1.4\times 10^7$ s = 3,800 h
	x diffusion lactate in hydrogel	$\frac{L^2}{D_{WH}}=6.8\times 10^6$ s = 1,900 h
	x diffusion lactate in media	$\frac{L^2}{D_{WM}}=5.8\times 10^6$ s = 1,600 h

We use “x” and “z” to denote “vertical” and “horizontal”, respectively. The timescale for each process is the value such that the each dimensionless parameter grouping, defined in Equation (2.21) as the ratio of the timescale of interest to the timescale of the physical process, is equal to one.