Factors Affecting Mixing Efficiency in Biopharmaceuticals and Considerations for Scaling Up

The fluid dynamics of mixers utilized in various biopharmaceutical process unit operations significantly influence many critical process and product attributes. Consequently, reliable process development and scale-up necessitate thorough characterization of mixing performance, which can be impacted by fluid properties, operating parameters, and vessel geometry.

Mixing generally refers to the process of combining substances to create a homogeneous system through mechanical agitation. This process can be applied to both single-component and multi-component mixtures of solids, liquids, and gases. Various aspects of fluid dynamics influence mixing, affecting heat and mass transfer phenomena as well as phase dispersion properties. Several factors impact fluid dynamics, including vessel geometry (e.g., size, aspect ratio), internal geometry (e.g., impellers, baffles, piping), and the physical and chemical properties of the fluid (e.g., density and viscosity). Additionally, operating parameters such as stirring rate, liquid filling volume, and liquid feed rate or position play a crucial role. A robust process design and scale-up rely on a thorough understanding and control of fluid dynamics, which in turn affects quality attributes, including uniformity and physical properties.

The tendency of biomolecules to aggregate or denature at high shear rates and gas-liquid interfaces is a critical design consideration in bioprocesses. These processes are often influenced by gases such as oxygen, leading to a two-phase gas-liquid system. Furthermore, intense agitation can cause gases to be entrained from the headspace of the mixer into the system, making it essential to understand shear and interface effects in a well-designed process. Numerous methods and tools are available to facilitate the reliable scale-up of various unit operations, ranging from simple empirical correlations to first-principles modeling combined with model-guided experiments.

Mixing Fundamentals and Key Considerations for Scaling Up

Turbulence: Increasing fluid turbulence can enhance mixing performance. The average measurement of turbulence is expressed as the Reynolds number, which is defined as the dimensionless ratio of inertial resistance to viscous resistance in a fluid. The Reynolds number is related to the impeller diameter, rotational speed, liquid density and viscosity. It can be used to predict the transition between laminar flow (characterized by minimal lateral mixing) and turbulence (which manifests as transverse flow and eddy currents). Laminar flow occurs in systems with low Reynolds numbers, where viscous resistance predominates. In contrast, turbulence arises in systems with high Reynolds numbers, where inertial forces govern fluid motion. Laminar flow systems are the most challenging to mix, so conservatively low Reynolds numbers are often selected to assess poor mixing performance.

For applications involving the mixing of low-viscosity liquids, inertial forces can generate sufficient turbulence to homogenize the fluid without the need for an external mixing device. However, in most cases, mixing is enhanced by the use of stirring and/or baffling devices. Mixing is most effective when it allows the fluid to circulate throughout the entire container within a timeframe relevant to the process, while also directing the fluid to all areas of the container, thereby minimizing "dead zones." The design of impellers is a critical factor in determining mixing efficiency.

Impeller: The design of impellers can be categorized into two types: small blade impellers that rotate at high speeds, suitable for mixing low to medium viscosity liquids, and impellers with a large blade area that rotate at low speeds, which are effective for high viscosity and shear-thickening liquids. While there have been studies that provide general guidelines for selecting appropriate impellers under typical conditions, they often lack process-specific information. Therefore, these guidelines can serve as a starting point for designing well-mixed systems.

Platform Approach and Scaling Based on Empirical Relevance: From a production perspective, there is a strong desire to establish a standardized hybrid process platform that can be applied across multiple products and various batch sizes. While this is feasible for shear-insensitive materials, it may not be practical for shear-sensitive applications. In shear-insensitive systems, agitation can be conservatively designed to achieve homogenization without risking product degradation, making it suitable for platform method. However, in shear-sensitive systems, where excessive agitation can compromise product quality, a platform approach may not be appropriate. A straightforward empirical method that identifies the most extreme conditions can assist in selecting the optimal mixing speed and duration. The "worst case" conditions determined based on scientific principles allow for conservative estimates of appropriate mixing conditions.

Robust and scalable pharmaceutical manufacturing processes should avoid mixing conditions that lead to foaming and splashing, as proteins denature at the gas-liquid interface. The combination of conditions is applied to the target system, and the mixing speed is gradually increased while monitoring the mixing performance. By visually assessing the mixing speed at which splashing or foaming occurs under these adverse conditions, an appropriate upper limit for mixing speed can be established. Conversely, the maximum mixing time can be determined by considering the worst-case scenario, which involves using the highest batch-to-volume ratio, the highest viscosity and density, the highest excipient concentration, and the lowest temperature to replace the solution. This combination of parameters represents the most challenging conditions for mixing time.

Empirical correlations can be utilized to determine the appropriate mixing conditions for scaling processes up or down across different equipment, as well as to adjust mixing based on the volume of liquid in the container. However, correlations may not always account for significant variations in container geometry and internal configuration, which can greatly influence fluid dynamics. Consequently, this method is most effective in scenarios where geometric similarities exist between the process equipment being scaled. In straightforward cases, this approach can be employed to establish an acceptable stirring rate and a range of mixing times—essentially defining the design space necessary to achieve adequate homogenization based on the volume of liquid loaded or during scaling operations.

There are several dimensionless numbers commonly used to characterize the fluid dynamics of biological liquids. These numbers are defined in relation to the properties and geometry of the liquid and include the following: the Reynolds number, which is the ratio of inertial to viscous forces; the impeller power number, which is used to calculate the power and torque output of the impeller; and the number of impeller pumps, which is used to determine the pumping capacity of the impeller. Common correlation-based scaling rules for geometrically similar vessels include the Reynolds number, tip speed, and power input. Scaling based on power input is most frequently employed in bioprocess scale-up calculation because it provides a conservative basis for scaling up process performance.

The correlations extensively described in the literature can be utilized to establish an operating range for the relationship between mixing time and stirring rate. Standard stirring systems typically adhere to several common geometric ratios, including the diameter of the impeller, the height of the liquid level in the tank, and the width of the baffle, all in a standard ratio to the diameter of the tank. Additionally, the clearance of the impeller, the width of the impeller blade, and the length of the impeller are maintained in standard ratios relative to the diameter of the impeller.

Average Shear Rate: Shear stress and shear rate are tensors that depend on time, spatial position, and size. However, correlation can be employed to calculate the average shear rate, which is a crucial factor for proteins. Viscosity measures a fluid's resistance to deformation under shear stress. Due to viscosity, fluid layers move at varying speeds. The fluid thickness is a form of shear stress between layers that resists any applied force. The true shear stress exerted on a fluid element is a tensor and is influenced by the local environment. In the mixing process, shear stress arises from the complex velocity gradient and phase interface. This shear, along with interface effects, can potentially damage biomolecules. The overall shear rate in an unbaffled vessel is related to the overall velocity and the tank's diameter, while the blade tip shear rate is associated with the impeller's diameter and its rotational speed.

Correlation-based mixing and shearing evaluations can be employed to scale up mixing times and shearing rates between geometrically similar containers. However, the characteristics of laboratory, pilot, and commercial-scale vessels, impellers, and internal configurations often lack geometric similarity or do not conform to standard mixing system designs. In such instances, correlation-based scaling criteria may be insufficient; computational fluid dynamics (CFD) modeling offers a robust alternative for effectively scaling up processes in non-standard systems.

Mechanical agitation is an effective method for achieving dissolution and uniformity, it’s crucial in the operation of individual units within the pharmaceutical product process. This agitation exposes the active molecules to shear forces generated by headspace gases being drawn into the solution and the gas-liquid interface. Consequently, a small-scale experimental evaluation is recommended to assess the impact of these conditions on product quality. It is essential that these small-scale experiments are meticulously designed to accurately capture shear forces and gas exposure during the scaling process.

Biomolecules exhibit varying sensitivities to shear forces during processing. For instance, monoclonal antibodies (mAbs) are especially susceptible to mechanical stress. While agitation during filling is typically regarded as low shear, localized high shear rates are often observed near the impeller and around the baffle. Furthermore, the shearing effect caused by bubbles, which can lead to damage, may occur at significantly lower impeller speeds under sparging conditions. Consequently, the agitation employed for mixing biomolecules must minimize shear force while still ensuring effective mixing of the components.

In cases where sensitivity to shear from mixing is critical, computational fluid dynamics (CFD) serves as a valuable tool for ensuring reliable scale-up and consistent product properties. A thorough understanding and control of fluid dynamics are essential for robust process design and scale-up. The primary parameter that characterizes the fluid dynamics of the system is the turbulent kinetic energy dissipation rate, which quantifies the loss of turbulent kinetic energy due to viscous forces in turbulence. In any mixing system, the turbulent kinetic energy dissipation rate exhibits time-space heterogeneity. This dissipation rate influences the dynamics of various potential processes, including heat and mass transfer, fragmentation and agglomeration, and phase dispersion.

While the mixing properties related to energy dissipation rates are challenging to measure experimentally, single-phase CFD simulations can offer insights into properties that cannot be obtained through experimental methods. Furthermore, standard impeller power numbers and correlations do not account for variations in the size of potentially unconventional reactor and impeller configurations. CFD provided the foundational understanding of the governing equations that describe the transfer of momentum, mass, and energy. Consequently, CFD is utilized to simulate the time-space distribution of flow patterns, turbulence, temperature, and substance concentrations, all of which are critical in determining overall equipment and process performance.

In the production of biomolecular pharmaceutical products, both insufficient and excessive mixing can adversely affect quality attributes in various ways. Inadequate mixing can lead to inconsistencies within batches, ultimately resulting in unstable drug product analysis outcomes and jeopardizing patient safety. Furthermore, effective mixing is essential for the dissolution of excipient components, which is necessary to achieve a completely uniform mixture. Conversely, overly vigorous mixing can apply excessive shear force, potentially causing proteins to denature and form polymers. In summary, mixing must be adequate to ensure uniformity while avoiding excessive damage to shear-sensitive products.

CFD-based studies typically have three main objectives: (1) evaluating the mixing parameters and batch size of the mixing process, (2) assessing the effect of high shear stress conditions on product stability using a scale-down model, and (3) examining the mixing rate of the excipient solution and the time required for complete dissolution before use. This integrated modeling and experimental approach aims to provide a comprehensive assessment of a reasonable range of operational conditions and their impact on key quality attributes.

In addition, monoclonal antibodies are often susceptible to oxidative degradation, which can impact quality attributes of the product, such as potency, stability, and/or color. Conducting meticulous small-scale laboratory experiments is essential for assessing the oxygen sensitivity of biomolecules during unit operations, including dissolution, pooling, and filling of pharmaceutical products. Dissolved oxygen (DO) probes can be employed to quantify the oxygen content in biomolecular solutions exposed to varying levels of oxygen. The effects of oxidative degradation can be quantitatively evaluated by measuring quality properties that are known to be sensitive to oxygen for each solution.

In the case of shear-sensitive biomolecules, it is essential to understand the fluid dynamics under process-related conditions to ensure the reliable scale-up of oxygen-sensitive processes. Both positive and negative deviations from optimized mixing conditions can have varying detrimental effects on product quality. Overmixing may result in the entrapment of significant amounts of gas from the container's headspace, which can lead to oxidative degradation. Conversely, undermixing can cause product inconsistency and prolong processing time. Therefore, comprehending the fluid dynamics of oxygen-sensitive systems is critical. When gases trapped in the headspace of the stirring vessel threaten product quality attributes, the following three hydrodynamic characteristics can inform the scale-up of the process: (1) The gas distribution within the stirring vessel serves as an indicator of the uneven gas content throughout the entire process fluid. (2) Gas holdup measures the total gas volume fraction in the container. (3) The gas-liquid mass transfer rate (KLa) and its distribution indicate the local gas transfer to the liquid phase.

Measuring these parameters on a large scale or predicting them from laboratory-scale experiments based on correlations can be quite challenging and costly in terms of time and resource investment. However, CFD modeling tools can provide valuable insights to inform process scale-up. Single-phase CFD modeling is a well-established platform that is computationally less expensive compared to multiphase simulations and can be used to infer various behaviors of two-phase mixtures. In certain applications, multiphase simulation may be the most effective tool for accurately characterizing the fluid dynamics of a specific system. When scaling up processes that are sensitive to oxygen, it is advisable to maintain the KLa constant throughout the scale-up. Laboratory-scale experiments can be employed to identify a KLa that does not lead to product degradation at the laboratory scale. Subsequently, the filling level and stirring rate can be adjusted for scale-up while ensuring that the KLa remains consistent throughout the process.

Conclusion

The performance of any unit operation and the quality of the product are often significantly influenced by the fluid dynamics within mixers. In some instances, standard empirical correlations may serve as a preliminary framework for understanding suitable mixing conditions. However, in most cases, these simple correlations fail to adequately capture the complexities of processes that impact biomolecular mass transfer. Many containers commonly utilized in industry do not conform to standard designs and require scaling up to accommodate different geometric shapes. In such cases, correlations may not sufficiently represent critical hydrodynamic properties. Additionally, biomolecules are generally sensitive to shear forces and interfacial effects. While adequate mixing is essential for homogenizing the product, excessive shear and gas entrapment can adversely affect product quality. For these applications, a combination of first-principles modeling and model-guided experiments can yield the most reliable information for effective scale-up. Computational fluid dynamics (CFD) modeling is a dependable method for understanding fluid dynamic properties that cannot be fully captured through experiments alone. Properly executed CFD modeling, in conjunction with model-guided experiments, can provide a comprehensive understanding of the fluid dynamics of a specific process, thereby facilitating reliable process scale-up.

The 2L-20L DuoMix® benchtop mixing system, the 50L-3000L DuoMix® floor-standing mixing system, and the accompanying 3D single-use mixing bags developed by Duoning provide a comprehensive solution for liquid mixing, suitable for various scenarios ranging from process development to large-scale production. The DuoMix® benchtop magnetic-coupling mixing system consists of three components: a control system, a base equipped with a magnetic drive motor and a weighing module, along with a supporting holder. The controller can connect to three mixing bases, allowing three mixing units to operate simultaneously, thereby maximizing efficiency. The drive unit and the mixing bag transmit power through magnetic coupling, which is both simple and user-friendly. Additional modules, including pH and conductivity sensors, temperature sensors, and auxiliary pumps, are also available.

The DuoMix® floor-standing magnetic mixing system comprises a control cabinet, a tank body, and a drive motor. The control cabinet is integrated and mounted on the tank. The drive motor and magnetic head are positioned at the bottom of the tank, while the weighing module is located above the casters. This equipment is compatible with common impellers available on the market and can be used with optional modules, including pH and conductivity sensors, temperature sensors, temperature control units, and peristaltic pumps. Additionally, the size and shape of the system can be highly customized to meet various process requirements. The software interface for the DuoMix® benchtop and floor-standing magnetic mixing systems is user-friendly and supports at least three levels of authorization, it also includes features such as recipe editing, alarms, sensor calibration, data recording and export, audit trail and more.

In addition, to assist users in developing and scaling their mixing processes, we offer comprehensive computational fluid dynamics reports for systems with various container sizes, geometric configurations, and impeller designs. These reports include analyses of the velocity field, mixing performance, mixing power, pressure, wake vortex structure, shear, gas-liquid distribution, and other parameters. Detailed reports can be obtained by contacting our product and technical team.

Example of computational fluid dynamics of 2,000 L mixing system.