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Table 1 Values of dimensional and non-dimensional parameters

From: Analytic solutions of a simple advection-diffusion model of an oxygen transfer device

Dimensional Parameters

Symbol

Value

Dimensions

Geometry

   

Lengthscale of device

L

2 × 10−3

m

Oxygen/Haemoglobin

   

Diffusion coefficient

\(D_{d}\)

1.5 × 10−9

m2s−1

Solubility of \(\mathrm{O}_{2}\) in blood

\(\alpha_{\mathrm{O}_{2}}\)

9.98 × 10−6

mol m−3Pa−1

Oxygen binding capacity

\(\beta_{\mathrm{O}_{2}}\)

5.98 × 10−2

mol kg−1

Haemoglobin concentration

\(c_{Hb}\)

120

kg m−3

Maximum bound concentration

\(c_{\max}\)

7.176

mol m−3

Max. part. press. of bound conc.

\(P_{\max}\)

7.19 × 105

Pa

Part. press. of half saturation

\(P_{0.5}\)

3.2 × 103

Pa

Index constant

n

2.8

 

Boundaries

   

Average longitudinal velocity

w̄

4 × 10−5

m s−1

Average transverse velocity

Å«

1 × 10−6

m s−1

Inlet \(\mathrm{O}_{2}\) partial pressure

\(P_{i}\)

5 × 103

Pa

Membrane \(\mathrm{O}_{2}\) partial pressure

\(P_{g}\)

20 × 103

Pa

Non-dimensional parameters

Symbol

Value

Oxygen/Haemoglobin

  

Ratio of diffusion/advection

δ

1.875 × 10−2

Boundaries

  

Ratio of velocities

ν

0.025

Scaled inlet \(\mathrm{O}_{2}\) partial pressure

\(c_{0}\)

0.70 × 10−2

Scaled membrane \(\mathrm{O}_{2}\) part. press.

\(c^{*}\)

2.78 × 10−2

Scaled part. press. of half sat.

\(c_{0.5}\)

0.45 × 10−2

Wall Sherwood number

Sh

50

Inlet correction parameter

ϵ

1 × 10−3