Abstract
Shear forces are a significant concern in biopharmaceutical production, particularly for monoclonal antibodies (mAbs), as they can lead to protein degradation, aggregation, and loss of biological activity. Various stages of manufacturing, including cell culture, purification, and formulation, expose proteins to shear stress. The ability to predict and mitigate shear effects is essential to ensuring product quality and therapeutic efficacy. This paper presents a comprehensive review of quantitative mathematical models designed to evaluate shear rates across different bioprocessing equipment. These models provide a practical approach for estimating shear in pipelines, pipe bends, peristaltic pumps, piston pumps, rotary lobe pumps, filtration systems, and impeller-agitated mixing tanks. By applying these models, engineers can optimize process parameters, design low-shear processes, and troubleshoot deviations related to shear-induced damage. The insights gained from these calculations contribute to improving protein stability and overall process robustness in biopharmaceutical manufacturing.
1.0 Introduction
Shear forces play a critical role in influencing the stability, quality, and functionality of monoclonal antibodies (mAbs) during biopharmaceutical production. These forces can occur at various stages, including upstream cell culture, downstream purification, and formulation processes. To ensure the production of high-quality therapeutic proteins, researchers have extensively studied shear effects and developed strategies to mitigate them.
This paper provides a review of simple, quantitative mathematical models to evaluate shear in fluid flow across various equipment commonly used in biologics manufacturing. These include pipelines, pipe bends, peristaltic pumps, piston pumps, rotary lobe pumps, filtration systems, and packed column operations. The straightforward calculations presented offer engineers practical tools to design low-shear processes that preserve protein quality. Additionally, these models can be invaluable for investigations where shear is suspected to contribute to protein degradation or aggregation deviations.
2.0 Shear Impact on Therapeutic Protein
The impact of shear stress on therapeutic proteins, particularly monoclonal antibodies (mAbs), is a critical consideration in biopharmaceutical manufacturing and delivery. Shear stress can lead to fragmentation, aggregation, and loss of biological activity of these proteins, which can compromise their therapeutic efficacy and safety.
Fragmentation and Aggregation: Shear forces can induce fragmentation of mAbs, resulting in smaller protein fragments that may not retain their biological function. The mechanical stress associated with shear can disrupt the tertiary and quaternary structures of proteins, exposing hydrophobic regions and aggregation-prone residues (APRs) to the solvent, which facilitates intermolecular interactions and aggregation [1, 2]. For instance, studies have shown that shear rates as low as 10,000 s⁻¹ can lead to significant aggregation of mAbs, while higher rates can exacerbate this effect [3, 4]. The formation of aggregates is not merely a result of shear stress; interfacial phenomena and cavitation also play significant roles in this process [5, 6].
Moreover, the aggregation behavior of mAbs is highly dependent on the specific flow conditions they experience. For example, extensional flow has been shown to trigger aggregation in various IgG1 molecules, indicating that the flow field and the protein's structural characteristics are crucial in determining the extent of aggregation [7, 8]. The presence of air-liquid interfaces during processing can further exacerbate aggregation due to hydrodynamic stresses that proteins experience at these interfaces [9, 10].
Loss of Biological Activity: The aggregation of mAbs not only affects their physical stability but also leads to a loss of biological activity. Aggregates can mask the active sites of antibodies, preventing them from binding to their target antigens effectively [11, 12]. This loss of activity is particularly concerning in therapeutic applications, as aggregates can also elicit immune responses, potentially leading to adverse effects in patients [12]. The structural integrity of mAbs is essential for their function, and any disruption caused by shear can result in the formation of aggregates that are not only inactive but may also be immunogenic [13].
3.0 Sources of shear in biopharmaceutical manufacturing
Shear forces in biopharmaceutical manufacturing arise from various sources, each posing a potential risk to protein stability. High-speed impellers used in mixing tanks generate turbulence and localized shear forces that can destabilize proteins. Fluid transfers through pipelines, particularly at high flow rates, create velocity gradients that contribute to shear, which is further exacerbated by abrupt changes in flow direction at pipe bends, leading to localized high-shear zones. Peristaltic pumps, rotary lobe pumps and piston pumps commonly used for fluid handling, introduce shear as they compress and release fluid, with higher flow rates intensifying the effect. Tangential flow filtration (TFF) systems contribute to shear as fluids pass through membrane pores. Similarly, sterile filters, with their narrow pore sizes and high-pressure differentials, generate significant shear forces that can compromise protein stability. These sources of shear must be carefully managed to preserve product quality in biopharmaceutical processes.
4.0 Shear from flow through straight and 90⁰ bend pipes
To calculate the shear rate in pipe flow, it is crucial to understand the relationship between shear stress, viscosity, and flow characteristics. The shear rate (γ) can be determined from the velocity gradient of the fluid as it flows through the pipe. For a Newtonian fluid, the shear rate is defined as shown in Eq (1) [14 ]:
Where, du is the velocity change and dy is the distance from the wall to the pipe's centerline. This relationship is especially simple under laminar flow conditions, where the velocity profile is parabolic. In such cases, the maximum shear rate occurs at the pipe wall and is expressed as shown in Eq (2) [14]: where Q is the volumetric flow rate and D is the pipe radius
To calculate the shear rate in fluid flow through a 90-degree pipe bend, we focus on the velocity gradient in the fluid, particularly near the pipe walls. Shear rate (γ) is influenced by the curvature of the bend, flow velocity, and fluid properties as shown in Eq (3) [15].
Here, the Reynolds number (Re) is calculated as Eq (4). In a 90-degree bend, velocity increases on the outer curve and decreases on the inner curve due to centrifugal effects. For simplicity, the maximum velocity near the wall (𝜐max) can be approximated as 𝜐max ≈ 1.5 𝜐avg.
5.0 Shear from Peristaltic Pumps
Shear rate in peristaltic pumps is an essential parameter to evaluate, especially when handling shear-sensitive materials such as biological fluids, proteins, or cells. The shear rate arises from the deformation of the fluid as the tubing is compressed and relaxed under the rollers. We'll approximate the shear rate as the rate of strain experienced by the fluid during compression and decompression as a function of number of rollers in the pump (Nᵣ), rotational speed of the pump (in revolutions per minute, RPM), compression percentage (C), expressed as a decimal (e.g., 50% compression = 0.5), and internal diameter of the tubing (d) (when fully uncompressed).
The shear rate due to roller compression is inversely related to the time of compression and the thickness of the compressed fluid layer is expressed as shown Eq (5)[16]:
Where: Velocity of the roller contact point in (m/s) is calculated as 𝜐 = Nᵣ ×π×d×f/ 60, and effective thickness of the fluid layer after compression is calculated as h = (1 - C)×d, substituting the roller velocity and thick of fluid layer under compression in Eq (5) will yield Eq (6) [16].
6.0 Quattro flow pump
The Quattroflow pump is a quaternary diaphragm pump designed for gentle fluid handling, making it ideal for sensitive biological products such as proteins and cell cultures. It operates using four diaphragms connected to a central shaft, which move in a reciprocating motion driven by an eccentric shaft linked to a motor. This phased diaphragm movement ensures smooth and continuous flow, as one diaphragm expands (suction stroke) while another contracts (discharge stroke). Each diaphragm is housed in a chamber equipped with check valves that control the fluid’s direction, preventing backflow and maintaining consistent flow from the inlet to the outlet. The pump’s design creates a peristaltic-like effect, producing low-shear, pulsation-free flow that protects shear-sensitive materials. The hermetically sealed construction eliminates the risk of contamination, making it suitable for biopharmaceutical applications such as cell culture transfers, chromatography, and filtration processes. With adjustable flow rates and compatibility with single-use systems, the Quattroflow pump is versatile and scalable for various stages of biomanufacturing [17].
Step | Equation | Description |
1. Calculate Effective Diaphragm Area | A = π ⋅ D² / 4 | A = Diaphragm area (m²)D = Diaphragm diameter (m)
|
2. Calculate Flow Rate per Diaphragm | Qdiaphragm = f ⋅ A ⋅ s
| Qdiaphragm = Flow per diaphragm (m³/s)f = Frequency (Hz)s = Stroke length (m)
|
3. Calculate Total Flow Rate | Qtotal = n ⋅ Qdiaphragm
| Qtotal = Total flow rate (m³/s)n = Number of diaphragms
|
4. Calculate Outlet Area | AOutlet = π ⋅ Do² / 4 | AOutlet = Outlet cross-sectional area (m²)DO = Outlet diameter (m)
|
5. Calculate Flow Velocity | γ = Qtotal ÷ AOutlet | v = Flow velocity (m/s) |
6. Calculate Shear Rate | 𝛾= (8 𝑣 /A Outlet) | γ = Shear rate (s⁻¹)
|
7.0 Shear from Rotary lobe Pumps
Shear in lobe pumps is primarily generated in the clearance gap between the lobes and the casing as fluid is compressed and transferred. The shear rate depends on factors such as the pump's rotational speed (N), clearance gap (C), lobe diameter (D) and the number of lobes (n), making them ideal for applications requiring low shear to protect the integrity of delicate products like proteins and cells.
8.0 Shear from Piston Pumps
Piston pumps function by using a piston's motion to draw liquid into a cylinder and then expel it with precision. When the piston retracts, it creates a vacuum that pulls liquid into the cylinder. As the piston advances, it forces the liquid out through the cylinder and into the filling nozzle. This mechanism ensures accurate and consistent liquid dispensing, making piston pumps highly suitable for applications requiring precise volume control and reliability.
To calculate shear in piston pumps, consider the fluid flow dynamics and mechanical interactions. Shear arises primarily from the fluid passing through narrow passages, such as inlet and outlet valves, and from its interaction with the cylinder wall during piston movement.
Shear rate near the piston wall is calculated as shown in Eq (8), Here, Ap is the cross-sectional area of the piston and C is the clearance between piston and cylindrical wall.
For shear in the valve openings, calculate it as shown in Eq (9). Here, d is the valve diameter.
The total shear rate (γT), by combining the wall shear rate and valve shear rate as shown in
Eq (10).
9.0 Shear from Tangential Flow Filtration Systems
The shear rate (γ) in a tangential flow filtration (TFF) system is a measure of the velocity gradient at the membrane surface. This parameter is critical for understanding the effect of flow dynamics on shear-sensitive materials and filtration performance. The following outlines the steps to calculate the shear rate in a TFF system. The shear rate is calculated using the Eq (11)[18].
Where, Q is the Volumetric flow rate (μm³/s or L/min), A is the cross-sectional area of the flow channel (μm²), h is the Characteristic height of the flow channel (μm). The cross-sectional area is determined as: A = w · h. Where: w is the width of the flow channel (in meters or millimeters) and the characteristic height of the flow channel.
10.0 Shear from Flow through membrane Filtration Systems
The forces exerted on fluid during filtration through a 0.2-micron membrane filter can be estimated by considering flow dynamics within the pores, focusing on parameters such as pore size (dp ), flow rate (Q), filter area (Af), and porosity (ϵ). These estimations provide insight into filtration-induced shear effects. The porosity of membrane filters also plays a vital role in their performance. Durapore® polyvinylidene fluoride (PVDF) membranes exhibit a porosity of approximately 70% [19].
11.0 Shear from impeller agitated mixing tanks
In impeller-agitated mixing tank systems, the maximum shear rate (𝛾max) typically occurs at the tip of the impeller, where the fluid experiences the highest velocity gradient. This shear rate is determined by the impeller tip speed (𝜐T) and the thickness of the boundary layer (𝛿) near the impeller blades. The impeller tip speed is expressed as 𝜐T = π.Di.N/60, where Di is the impeller diameter, and N is the impeller rotational speed in revolutions per minute (RPM). The boundary layer thickness is approximated as 𝛿 ≈ [KV / (2πN/60)]1/2, with KV representing the kinematic viscosity of the fluid. The angular velocity, defined as ω = 2πN, further characterizes the rotational motion influencing the boundary layer behavior. Together, these relationships provide a framework for estimating the maximum shear rate at the impeller tip as shown in Eq (13) [20, 21].
12.0 Conclusion
Understanding and mitigating shear forces is paramount to maintaining the stability, quality, and functionality of monoclonal antibodies (mAbs) throughout biopharmaceutical production. By providing a review of simple and quantitative mathematical models, this paper equips engineers and researchers with practical tools to evaluate and minimize shear effects across various critical equipment, including pipelines, pumps, filtration systems, and packed columns.
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