## Abstract

This study investigated the gas flow mechanism through microchannels in a flexible single-use packaging system composed of multilayer plastic film. The relationship was studied between the gas flow rate and several parameters, which included the differential pressure as an external parameter and channel geometries as internal parameters. Based on the results of this study, empirical formulas were derived that show the different dependency of the parameters for each gas flow regime. It was found that these formulas are suitable for calculating the size of a leak in a defective product directly from the corresponding flow rate. The test samples used were 50 mm patches of an ethylene vinyl acetate multilayer film (300 μm and 360 µm thick) and a polyethylene multilayer film (400 μm thick). Artificial leaks in a range of sizes from 2 μm to 100 μm were laser drilled into the center of each patch. The patches were assembled in a filter holder to form a leak-tight seal and were mounted on the test setup. The test setup included the flow measurement device and the pressure controller that used compressed air to produce a certain differential pressure. Various differential pressures were applied to each test unit to cover the whole range of desired use-case conditions. To understand and interpret the effect of the physics and geometry of the microchannels on flow rate measurement, the microscopic investigations performed in our previous study were used. All measurements were carried out under laboratory temperature conditions of 20°C.

- SUS
- Single-use system
- SUSI
- Single-use system integrity
- Gas flow rate through microchannels
- MALL
- Maximum allowable leakage limit

## Introduction

Microbial barrier integrity of all product packages, especially parental pharmaceuticals, is critical in quality assurance. Any defect through which bacteria can enter the system can be a threat to a patient’s health.

Therefore, high quality standards of container closure systems and single-use systems (SUSs) are required. For example, <USP 1207> (1) provides guidance in which the details of container closure integrity testing are explained, and ASTM E3244 adapted the same concept for SUSs (2). In particular, the use of deterministic methods to detect leaks at the product’s maximum allowable leakage limit (MALL) is discussed. <USP 1207> states that “MALL is the greatest leakage rate (or leak size) tolerable for a given product-package that poses no risk to product safety and no or inconsequential impact on product quality.” ASTM E3244 extends this definition to other typical barrier properties of SUSs, for example, to ensure environmental and operator safety.

The leak test method has a detection limit. This detection limit of the leak test method is reported either as a leakage rate or a leak size with different measurement units. To compare the test results of various methods, the relationship between the leak size and the leakage rate is required. If the limit of detection for a leak test method is in the range of the MALL, this leak test is considered an integrity test.

<USP 1207> contains a table showing the relation between a perfect hole of negligible length and the air flow rate passing through this hole at a pressure difference of 1 atm and a temperature of 25°C. As mentioned there, the relation is based on theoretical approximations and is not definitive. In the field of integrity of rigid containers, this table is used to convert the flow rate to the detected leak size.

In the first study conducted by our team (3), we defined the MALL for a SUS made of ethylene vinyl acetate (EVA) or polyethylene (PE) using microbial ingress testing. In that study, we reported the MALL as a leak diameter using the <USP 1207> flow rate table, despite knowing that the relation between flow rate and leak diameter for SUSs had not yet been studied.

In the second investigation, we studied the liquid leakage mechanism of SUSs (4). We realized in this study that two leaks having the same flow rate can behave differently. Because liquid leakage is a physical phenomenon, there must be other factors like the geometry of an individual microchannel that account for such differences. We have shown that, in real-case conditions, leaks are not perfectly shaped pinholes. For example, in the case of our SUS made of plastic material, a film thickness of 300 µm to 400 µm results in leaks that resemble microchannels rather than pinholes. On the other hand, the flow measurement does not give any information about the leak geometry. In our two previous studies, laser drilling was used to introduce artificial leaks. To our knowledge, laser drilling is the only known method used to drill a leak size <20 µm into flexible material with a thickness >200 µm. It is expected that the laser holes thus created will be approximately round with no tears or flaps (5). However, we have shown in our second study (4) that the laser-drilling process does not always result in a perfectly shaped microchannel.

Light microscopy images of the laser-drilled microchannels showed two outlets with different geometries, yet with the same flow rate. In addition, the difference between the size of the inlet and of the outlet for the laser-drilled leaks causes them to behave more like conical microchannels than cylindrical ones. Hence, we decided to explore the idea of measuring the gas flow rate of laser-drilled microchannels in SUSs to accomplish the following: first, find the relation between the gas flow rate and the leak diameter for our internal validation process of integrity testing for SUSs, and second, check whether this relation between flow rate and leak size for flexible materials is similar to the relation applicable to rigid materials. The present study is also intended to demonstrate that giving the leak size only in terms of the flow rate will not provide adequate information about the nature of a leak. Therefore, we investigated whether it would be more accurate to express the MALL in micrometers instead of in other units, as this would better meet market demands and increase the understanding of the concept and size of the MALL.

As single-use biomanufacturing increases, improvements in product robustness and process integrity are required to ensure safety, availability, process performance, and cost effectiveness. As an example, for large viral vaccines that cannot be sterile-filtered, all processing containers and transfer sets have to reliably maintain their inherent integrity throughout their entire life cycle. Consequently, SUS integrity (SUSI) is subject to increasing regulatory and industry scrutiny. Besides the application of quality by design (QbD) principles, all aspects related to integrity sciences described in the previous paragraphs are essential for improving SUSI in drug manufacturing. This is achieved by developing high-sensitive integrity testing technologies that provide the highest level of integrity assurance.

## Materials and Methods

A flow measurement setup (Figure 1) was used to measure the air flow through polymeric film patches at various differential pressure. These patches were intentionality compromised with artificially created defects of different sizes.

### Test Unit Assembly

The test samples used in the present study are identical to those of our past two studies (3–4) on the integrity of Flexboy, Celsius, and Flexsafe bags (Sartorius Stedim Biotech). These were EVA multilayer films (300 μm and 360 μm thick) and a PE multilayer film (400 μm thick), each cut into 50 mm diameter patches.

To simulate a pinhole leak, the patches were laser drilled in the center with different microhole sizes ranging from a nominal size of 2 μm to 100 µm by the German interdisciplinary institute Laser Zentrum Hannover e.V (LZH). The leak size of laser–drilled holes was calibrated by the same institute using microscopic image analysis. The leak was quantified as a diameter based on the calculation of the measured hole area. Because of the drilling process and the test sample material, the orifice size on the upstream side (inlet) of the patch is larger than on the downstream side (outlet). We defined the smaller downstream one as the nominal leak size.

A polypropylene patch holder secured the film patch in a stable position that was vertical to the flow direction, with the nominal leak size located at the outlet. A silicon gasket and a spacer on both sides of the patch directed air through the pinhole to the flow measuring device. To permit particles to block the pinhole, a 0.2 µm filter was installed between the stainless-steel tank and the holder. This test unit with a laser-drilled defect is representative of actual full-size bags with an artificial defect. Different aspects of this similarity and representativeness have been previously tested and confirmed.

### Test Medium

Dry air with a temperature between 20°C and 25°C was used as a test medium. With the aid of a pressure controller, compressed air was adjusted to produce a certain differential pressure. The actual atmospheric pressure served as a reference for differential pressure. To stabilize the selected pressure, the air volume was increased by using the stainless-steel tank connected to the test apparatus.

### Measuring Device

The measuring method used a system based on the Hagen-Poiseuille equation. The system consisted of a laminar flow element FCO96 (LFE) and a transmitter FCO560 (both supplied by Furness Controls). The LFE is structured so that the flow generated was laminar. To cover the flow range based on the defined leak sizes and differential pressures (50–1000 mbar), LFEs with the ranges of 2 mL/min, 20 mL/min, and 200 mL/min were used. The pressure drop along a defined distance was measured and transmitted as a flow rate by the transmitter. The standard flow rate chosen was referenced to an atmospheric pressure of 1013 mbar at a temperature of 20°C. Conditions deviating from this standard rate were compensated in the calculation of the flow value.

### Test Plan

In order to design the number of experiments needed to be performed, all variables that could affect flow measurement were considered, such as the film type and/or thickness, pressure, defect size, and channel geometry.

A total of 171 different film patches were tested in 2055 different runs. In each run, the air flow was measured through a film patch that had a defined leak size (diameter or area) and at a certain pressure. Among the total number of runs, 1515 runs had the relevant flow direction in which 975 different measurements, each with a unique set of conditions, were performed and 540 were test repetitions; the remaining 540 tests were done under the reverse direction of flow and not considered for the correlation. The reported flow rate was the average of 30 individual measurements within 15 s.

## Results and Discussion

The theory shows that many factors, especially the channel geometry, influencing each other are defining a flow through a microchannel. The specific leak geometry combined with a wide range of use case conditions leads to three different empirical correlations for different conditions. With specific impacts of the differential pressure, channel geometry and smallest leak size, the respective flow rate can be calculated/predicted.

### Theoretical Background

As the SUS under study is made of several layers, with a total thickness of about 300 μm to 400 μm, any leak in the film material is not a simple pinhole but a microchannel; at best, this leak will have a cylindrical or conical shape (Figure 2). Therefore, the gas flow rate through microchannels needs to be studied. In the theory of gas flow, three different types of flow can occur based on flow characteristics and on the material and geometry of a channel. The flow parameters considered here are gas viscosity, temperature, and pressure. For all measurements we used air under laboratory conditions; therefore, the viscosity and temperature remain nearly constant as well as the atmospheric pressure as reference. Additionally, the temperature and reference pressure effect was compensated in the calculation of the flow result. However, the effect of differential pressures through the channels is crucial for this study. Because the plastic film materials used for SUS have similar properties, we do not consider them as two different materials. The following parameters are regarded for the channel geometry: 1) the film thickness representing the channel length; 2) the leak size, that is the channel cross-sectional diameter at the exit point designated as the outlet; and 3) the channel cross-section diameter at the entrance, called the inlet. We will show later how the ratio of the inlet to the outlet of the channel can affect the flow rate. Finally, the parameters determining each type of flow are the following: the mean free path of the gas in relation to the characteristic length of the tube, the velocity of the flow for the given cross dimensions of the tube, and the internal friction of the gas.

The Knudsen number and the Reynolds number are two known dimensionless numbers quantifying these different parameters. The Knudsen number, the ratio of the mean free path of the gas molecules to the characteristic length of the tube, introduces three different conditions based on the level of interaction between gas particles and the walls of the tube as shown next:

Molecular flow

Transitional or Knudsen flow

Viscous flow

In viscous flow, the ratio between the inertia of mass and the viscous force within a fluid that is subjected to relative internal movement due to different fluid velocities is defined as the Reynolds number. This number characterizes the type of flow as laminar if it is <2300 or as turbulent if it is >4000. The area between 2300 and 4000 is considered a transitional area (6). Figure 2 shows the contour plot of the Knudsen number and the Reynolds number as a function of leak size for several pressures applied. Different areas in Figure 2a show that for most of the leak size and pressure combinations we encounter viscous flow, and a transitional or Knudsen flow can occur only for leak sizes <10 µm. A laminar to turbulent transition for viscous flow can take place for leak size and pressure combinations that have a Reynolds number >2300 (orange area in Figure 2b).

For a certain tube geometry and a known gas, one can determine the type of flow through the tube under specific pressure differences. The flow rate of a gas, which is defined as transported gas per time through the channels, can be calculated by a representative formula for each type of flow. For a very long tube (l ≫ d), that is, laminar flow in a viscous regime, the Hagen-Poiseuille law can be used to calculate the flow rate only if the ratio of the length to the radius of the tube is greater than one forty-eighth of the Reynolds number (7).

In the current situation, this inequality applies to all leaks <40 µm as long as differential pressures stay <1000 mbar.

If the tube length is short compared with the diameter, the wall friction is negligible, and the tube can behave like an orifice. Many variables influence the calculation of flow rates of gases through orifices. Therefore, finding a single formula that can cover all different conditions is difficult. Lenox Laser Company uses an empirical formula to predict the gas flow through an orifice made by laser drilling through different materials. However, this formula can be used if an orifice has been previously flow-calibrated under certain conditions (8). The Lenox Laser formula uses proportional factors, which introduce the impact of basic changes, such as inlet pressure, outlet pressure, temperature, and molecular weight of gases. Besides that, a specific factor in the formula differs based on the ratio of the pressure difference to the inlet pressure. According to our knowledge, Lenox Laser uses different sizes of laser-drilled orifices through aluminum foil with a thickness of 125 µm for flow rate calibration.

There are various formulas to calculate the rate of gas flow through a tube with a gradually narrowing cross section (6). The flow behavior defined by the formulas is based on different ranges of the outlet to inlet pressure. For an orifice, it has been shown that the flow rate reaches a maximum level if the outlet-to-inlet pressure ratio is around 0.5. However, all other factors must remain unchanged. Additional studies also discuss the role of friction on the flow of gases through microchannels (9⇓–11).

Many factors affect the value of friction in microchannels. These include the channel length and diameter, microchannel fabrication method, and roughness geometry. However, for long microchannels, the slip flow condition is considered, and analytical formulas or iteration methods are used to calculate the slip velocity through microchannels (12⇓–14). Several analytical formulas have been found to calculate the flow rate at certain conditions due to the differences between microchannels of different materials. Such formulas need to be customized for other materials and conditions.

As the current study considers a wide range of leak sizes and pressures, several flow rate regimes are distinguishable. For each regime, we need to consider the relevant formula to calculate the flow rate.

Additionally, we need to take into account that laser-drilled leaks through flexible material are imperfect conical channels. This condition can introduce some extra parameters that can affect the gas flow rate. For example, if the ratio of inlet to outlet pressure varies, gas velocity through conical channels can vary.

Therefore, the gas flow rate calculated theoretically with an existing formula for each flow regime shows a pronounced deviation in experimental measurements. This intensifies the need for new empirical formulas that can relate the gas flow rate through leaks appearing in SUS to leak parameters, such as leak area, for a wide range of applications. In the next section, three empirical formulas for each separate flow regime are introduced by the authors.

### Experimental Results

A total number of 171 film patches were evaluated in different runs of the gas flow measurements.

Table I lists the results of flow measurements performed with PE and EVA film patches that had a leak size between 2 µm and 100 µm and were subjected to a pressure difference between 50 mbar and 1000 mbar, respectively. The general behavioral dependency of the measured gas flow rate through different leaks at various differential pressures is logical.

Figure 3 shows the flow rate through the leaks as a function of nominal leak size at a differential pressure of 50 mbar and for all three film thicknesses. The semilogarithmic scale indicates a minimum of three orders of magnitude for flow rates. At a leak size of around 30 µm, the divergence in the behavior of the flow rate indicates that the film thickness may affect the flow rate in different ways.

To find the appropriate formula that can relate the gas flow rate to a leak size under current test conditions, the role of different parameters, like inlet and outlet diameter and the ratio between the inlet and outlet pressure, was studied and considered besides the prior knowledge available on gas flow. To find the best fit with experimental data, the main parameters found in the first steps were optimized by using appropriate mathematical tools. The formulas found in this approach are listed following for each individual flow regime. See eqs 1–3.

**Knudsen Flow**
(1)

**Viscous Flow, Tube**
(2)

**Viscous Flow, Orifice**
(3)where
1

Figure 2 shows the top and side views of the film patch schematically. The center ring in the middle depicts the position of the laser-drilled leak through the film. As a result of laser drilling through the film with the thickness of l, a microchannel with an inner radius of and an outer radius of is formed.

As mentioned in the last section, based on the calculation of the Knudsen number for the leak size and pressure combinations considered in this study, two different flow behaviors are distinguishable: Knudsen flow and viscous flow (Figure 3). The respective data were analyzed accordingly.

Based on the formulas, the three main factors affecting the flow rate are differential pressure, leak size, and leak geometry. Additional factors like temperature, material, and fluid characteristics were kept constant.

### The Impact of Differential Pressure

The differential pressure can influence the flow rate by increasing the speed of molecules passing through the leak channel. The dependency of the differential pressure and speed of molecules is given in the formula as a ratio between the inlet pressure *p _{1}* applied and the respective atmospheric pressure

*p*, multiplied by the speed

_{2}*c*. This dependency is linear for Knudsen flow and exponential for viscous flow. The term

*z*, which includes the ratio between the channel length and the average of leak diameters, serves as a parameter representing how the geometry can change the impact of the differential pressure on the flow rate. The smaller the ratio is between the channel lengths and the average leak diameter, the more the leak will resemble an orifice and the more the dependency will change from linear to exponential.

### The Impact of Leak Size

As indicated by the authors, the leak size is defined by the outlet diameter and influences the flow rate by the power of two. However, as various leak geometries need to be considered, different tendencies are observed, especially for viscous flow (Figure 4).

### The Impact of Leak Geometry

The impact of geometry is apparent in the specific ratio between the diameter of the inlet and that of the outlet. The behavior of Knudsen flow depends only on a fraction of the power of the inlet to outlet ratio. However, for viscous flow, the ratio between the channel length and the average of the inlet and outlet needs to be additionally considered. In a viscous flow regime, if the ratio of the channel length to the average leak size is <4, the leak will behave more like that through an orifice; however, if this ratio is >5, the flow behavior will be similar to the flow behavior in a tube. The transitional area in which the ratio between the channel length and the average of leak size remains between 4 and 5 has shown irregular flow behavior. According to our understanding, the magnitude of the inlet-to-outlet ratio is constant for the target leak size (outlet) based on the setting parameters for laser drilling and/or the material which is laser-drilled. The Appendix shows the average ratio for our film materials and laser-drilling parameters used by LZH. To check how the conical shape of the microchannel can affect the flow rate, the gas flow in both directions was measured. The significant change in the flow rate observed here is due to the known funnel effect, so we will not discuss it further.

## Conclusion

To reliably improve the integrity assurance level of SUSs, it is important to understand microbial ingress mechanisms (3) as well as the liquid leakage mechanism (4) and determine the MALL under use-case conditions. Usually, these investigations report the MALL as a defect size, mainly in micrometers. Therefore, to develop physical integrity testing methods using gas flow as a unit of measure, as well as their specifications, it is essential to understand the relation between gas flow and the size and geometry of a leak.

The gas flow rate through laser-drilled microchannels in flexible single-use packaging systems is studied in the present article. The test method is applied to PE and EVA multilayer film patches under different use–case conditions to establish a relationship between the gas flow rate as a measure of loss of package integrity for SUSs made of these materials and the corresponding leak size. The gas flow rate measurements are performed for film patches that had various leak sizes, as well as at different pressures applied. It is known from gas flow studies that many variables affect the flow rate through microchannels. In the current study, the wide range chosen for pressures and leak sizes, together with channel geometries and gas properties, results in different flow rate regimes.

To distinguish between different flow regimes, Knudsen and Reynolds numbers were calculated. For each combination of leak parameters and differential pressure, the appropriate regimes are considered. The conical shape of the channels, together with flexible film properties, prevents us from using the existing formula to compare the experimental data with the calculated theoretical numbers. Therefore, we established three empirical formulas each for the specific flow regime to gain insights into the flow rate behavior of our specific system and to relate it to the size of leak that may occur throughout the lifetime of our SUS products. To summarize, it is understood that besides the linear effect of the outlet area, the flow rate for small leaks (< 5 µm) behaves linearly with differential pressures, regardless of the channel length, that is, film thickness. For larger leaks (>5 µm), the ratio between the outlet diameter and the channel length separates the flow rate regimes into friction or no-friction categories. In both cases, the flow rate behaves nonlinearly with respect to the differential pressure and the channel length, that is, film thickness, and this needed to be considered. The geometry in the form of the fractional power of the ratio between the diameter of the inlet and that of the outlet contributes its own variable for each individual area.

The empirical formulas established by the authors in the present paper can be used as an internal calibration tool to relate the measured flow rate through the leaks that are laser drilled in our SUSs. The results of this study are essential for the validation of physical integrity testing methods of SUSs.

## Conflict of Interest Declaration

The authors declare that they have no competing interests.

## Appendix

Laser drilling is used to make the artificial leaks needed in this study. This is one of the few techniques for producing through-holes with a high aspect ratio of depth to diameter. However, the cylindrical shape of microchannels expected after drilling is not always created by this technology. Light microscopy of the laser-drilled samples from Lenox Laser and LZH showed that the orifice size on the upstream side (inlet) of the patch is larger than that on the downstream side (outlet). The ratio of the inlet to the outlet becomes larger if the laser is set to drill a hole of a few microns. Table A-I shows the average characteristic ratios of the inlet to the outlet diameter. These data are valid and applicable to our film materials. For other materials and more accurate calculation and correlation, the real inlet and outlet diameters need to be considered.

## Footnotes

↵1 It is a constant derived from the kinetic theory of gases, and for air at 20°C is 463 m/s.

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