Table I.
A table of the parameter values required to determine the retentate and permeate flowrates from Equation 15.
| Parameter | Description | Value | Units |
|---|---|---|---|
| Geometrical properties of the setup | |||
| d | Radius of the lumen | 200 | µm |
| s | Depth of the membrane wall | 200 | µm |
| l | Depth of the ECS | 600 | µm |
| L | Length of the fiber | 10 | cm |
| Experimentally imposed quantities | |||
| Ql,in | Lumen inlet flowrate | * | mL/min |
| P0 | ECS outlet pressure (atmospheric) | 14.69 | psia |
| P1 | Lumen outlet pressure | * | psia |
| Unknown membrane characteristics | |||
| k | Membrane permeability | Unknown | m2 |
| α | Membrane slip parameter | Unknown | dimensionless |
| Modeling parameters | |||
| ε | Aspect ratio of a fiber | 2 × 10−3 | dimensionless |
| a | Dimensionless depth of the membrane wall | 1 | dimensionless |
| b | Dimensionless depth of the ECS | 3 | dimensionless |
| κ | Dimensionless membrane permeability [see (14)] | Unknown | dimensionless |
|
Importance of slip versus permeability on the membrane surface [see (14)] | Unknown | dimensionless |
|
Dimensionless fluid flowrate into the lumen [see (14)] | 1 | dimensionless |
|
Dimensionless lumen exit pressure [see (14)] | * | dimensionless |
| λ | Dimensionless parameter defined by (16) | * | dimensionless |
These are made up of parameters that are fixed by the setup (i.e., geometrical parameters), parameters that are experimentally imposed, the unknown membrane characteristics, and dimensionless parameters identified by the modeling. * represents quantities which are fixed experimentally, but which we vary from experiment to experiment to complete the model parameterization and validation.