Why Accurate Flow Control is Critical for Cascade Impactor Measurements

Learn how flow rate affects both cascade impactor and product performance and how to ensure precise flow control.

D_50,2/D_50,1=(Q₁/Q₂)^1/2

[Where D is stage cut-off diameter and Q is volumetric air flow rate.]

This simplified equation shows how Stokes Law describes the relationship between stage cut-off diameter and air flow rate for a cascade impactor. It quantifies how the size fractionation performance of cascade impactors shifts with flow rate, rather than being fixed. A deviation of 5% in flow rate, for example, equates to a 2.5% shift in stage cut off diameter.

Flow rate also influences the performance of certain orally inhaled products (OIP), notably dry powder inhalers (DPIs).

Both of these issues provide considerable motivation for effective, accurate, flow rate control in cascade impactor measurements. This blog covers the key issues and how to achieve the precision required for reliable aerodynamic particle size distribution (APSD) measurement.

How flow rate impacts cascade impactor performance

The table below shows the relationship between flow and stage collection performance for the Next Generation Impactor (NGI).

Stokes Law provides a mathematical description of this performance but it’s helpful to understand the aerodynamic behaviour responsible for it. Let’s take a closer look at that.

The mechanical dimensions of a cascade impactor, critically nozzle area and number, are fixed. This means that volumetric air flow rate defines air velocity, and by extension particle velocity through the impactor. Total nozzle area decreases with stage number, causing a corresponding stepwise increase in particle velocity.

To collect at any given stage a particle must have sufficient inertia to escape the prevailing air stream. Particle inertia is a function of mass and velocity which is why changes in air flow translate into changes in stage cut-off diameter. Particles travelling at low velocity need a relatively large mass to achieve the inertia associated with impaction. Smaller particles only acquire sufficient inertia to escape the air stream and impact on collection surfaces at higher velocities.

This behaviour has some critical implications for flow control for cascade impactor measurements:

1. Knowing stage-cut off values relies on accurately knowing test flow rate.
2. Intra-analysis variability in test flow rate will erode the ‘sharpness’ of stage cut off values.
3. Inter-analysis variability in test flow rate will erode the repeatability and reproducibility of measurements.

The bottom line? Precise air flow rate control at an accurately known value is essential for reliable APSD measurements.

Choosing a test flow rate

However, test flow rate is not just important from the perspective of cascade impactor performance. As discussed in an earlier blog air flow rate can also impact OIP performance. This is why test flow rates for cascade impactor measurements vary according to OIP type. Differences are attributable to the way in which each class of OIPs works, with the pharmacopoeias specifying, in summary:

• 28.3 or 30 L/min for metered dose inhalers (MDIs), depending on impactor choice.
• 15 L/min for nebulisers.
• The flow rate associated with a pressure drop of 4 kPa across the device for DPIs, up to a maximum of 100 L/min.

The passive nature of most DPIs makes them especially susceptible to variability in test flow rate, intensifying the need for flow rate stability. This leads to the requirement for ‘critical flow’ conditions across the device during testing.

Critical flow occurs when the pressure downstream of a valve falls below ~50% of upstream pressure. At this point air flow through the valve reaches sonic velocity producing a choking effect; beyond it further decreases in downstream pressure have no effect. Under critical flow conditions flow rate therefore becomes a function of upstream pressure rather than pressure drop across the valve. This is an excellent condition for flow stability since it eliminates downstream pressure as a source of variability.

Controlling flow rate

The USP and Ph. Eur. indicate that test flow should lie within +/-5% of the target flow for OIP testing. This is a ‘composite’ accuracy including all errors from setting, determining, and controlling flow rather than simply flow meter accuracy.

A range of different flow control ancillaries are available to help analysts meet this requirement with different test set-ups. For DPIs, for example, the need to maintain a critical flow condition is met using a critical flow controller. This vital ancillary ensures maintenance of the required pressure drop and by extension good flow stability.

Flow meters are essential for all OIPs with laminar flow/differential pressure element, mass flow and rotameter devices, all commercially available. Since these each work on different operating principles most labs prefer to stick to a single type, but each can work well.

That said, successfully using flow meters for APSD measurement calls for attention to certain specific issues, such as:

• The pharmacopoeial requirement to calibrate air flow at the exit of the flowmeter, the inlet to the impactor. Common practice is rather to calibrate for inlet flow but USP <601> provides an equation to correct for this should you need one.
• Variations in temperature and atmospheric pressure, relative to calibration conditions, which can distort flow meter readings. Mathematically correcting for this is also vital.
• The need to convert measured values to volumetric flow rate, for mass flow meters. More sophisticated flow meters will do this automatically which is helpful.
• The size of connecting tubing, with larger bores preferable, within the constraints of the system, to reduce pressure drop.
• Leaks, since these introduce an error between the flow rate measurement and actual flow through the impactor. For the NGI, for example, the recommendation is for a rise rate of <100 Pa/s at a vacuum of 2.5 kPa. This equates to a leak rate of <0.5% of total flow to the impactor at the lowest calibrated flow rate.

In summary

In APSD measurement air flow rate may influence cascade impactor performance, OIP performance or both. This makes it a significant source of variability, necessarily subject to precise control.

Optimal ancillaries, routine calibration, and good operating practice are key for robustly maintaining a target flow rate. And for compendial methods that target flow rate is clear. Software that enables the input of actual test flow rate further enhances data accuracy by factoring any permitted variance into APSD calculations.

Beyond compendial methods the use of more patient relevant flow profiles, as required for ‘Realistic APSD’, is becoming increasingly popular. This bring new challenges with respect to flow control but there are solutions in place for those that need them. If this is an area of interest for you then check out future blogs. On the other hand, you’ll find more on the basics of flow control here.