Gas flow through micro-capillaries - which flow law is most suitable to predict the flow rate through...

Area of Science:

• Pharmaceutical Science
• Fluid Dynamics
• Analytical Chemistry

Background:

• Capillaries are crucial positive controls for Container Closure Integrity (CCI) testing in pharmaceutical quality control.
• Standard gas flow models struggle with the transitional flow regime in capillaries, impacting the reliability of detecting sub-micron defects.

Purpose of the Study:

• To evaluate the predictive performance of classical, slip-flow, and modified Knudsen models for helium flow through capillaries relevant to CCI testing.
• To determine the most suitable model for simulating leak rates under varying pressure conditions.

Main Methods:

• Investigated helium flow through capillaries (sub-micron to 25 μm) across a range of leak rates (10⁻⁹ to 10⁻³ mbar l/s).
• Evaluated classical, slip-flow, and modified Knudsen models under differential pressures (250–4000 mbar).
• Compared model performance at constant 1000 mbar pressure difference versus variable pressure dependencies.

Main Results:

• The slip-flow model demonstrated superior predictive accuracy (within 30% tolerance) under a constant 1 bar pressure difference.
• Simpler models failed to capture the pressure-dependent flow transition in capillaries of varying diameters.
• The modified Knudsen model accurately described the shift in flow behavior across the entire diameter range under variable pressure.

Conclusions:

• Model selection for CCI testing is context-dependent, requiring consideration of pressure conditions.
• The slip-flow model is recommended for constant pressure scenarios, while the modified Knudsen model is better for variable pressure characterization.
• These findings provide a framework for optimizing CCI testing by selecting appropriate flow models for specific leak limits and conditions.