From: Analytic solutions of a simple advection-diffusion model of an oxygen transfer device
Dimensional Parameters | Symbol | Value | Dimensions |
---|---|---|---|
Geometry | Â | Â | Â |
Lengthscale of device | L | 2 × 10−3 | m |
Oxygen/Haemoglobin | Â | Â | Â |
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 | Â |
Boundaries | Â | Â | Â |
Average longitudinal velocity | w̄ | 4 × 10−5 | m s−1 |
Average transverse velocity | ū | 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 | Â | Â |
Ratio of diffusion/advection | δ | 1.875 × 10−2 |
Boundaries | Â | Â |
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 |