How to Evaluate the Efficiency of Single-use Mixing Systems

Mixing is one of the most critical process operations in biopharmaceutical production. It is essential for achieving homogenization, suspension, dispersion, and heat exchange. These unit operations are often necessary during media and buffer preparation, cell culture, fermentation processes, final formulation, and the filling of biologics. Specific mixing procedures may also be required to prevent precipitation and stratification or to facilitate temperature changes during harvesting, concentration, purification, formulation, and filling.

Traditional mixing equipment made of stainless steel is considered the gold standard in biopharmaceutical production. However, the increasing interest in single-use technologies within the biopharmaceutical industry—offering numerous advantages and fewer limitations compared to traditional stainless steel equipment—has spurred the development of single-use bag mixing systems. Currently, users can select from a diverse array of single-use bag mixing systems, which vary in scale, mixing principles, and levels of inherent cleanliness, instrumentation, and automation.

Mixing Processes: Definition and Description

The mixing process involves the distribution of solid or fluid components within a defined volume, where these components differ in at least one property. These properties may include concentration, aggregation, particle size and shape, droplet size and shape, temperature, viscosity, color, density, and more. The primary objective of mixing is to achieve a desired degree of homogeneity and to produce intermediates or final products. Furthermore, mixing is essential for certain subsequent processes and can enhance heat and mass transfer.

Mixing can be classified into three categories: distributive, dispersive, and diffusive. Distributive mixing leads to the adjustment of properties with spatial homogeneity among all components. Dispersive mixing is defined as the breakdown of agglomerates or clumps into the desired final particle size of solid particles or the domain size (droplets) of immiscible fluids, where existing stable clumps are disintegrated. In contrast, diffusive mixing, which is less applicable in industrial processes, is characterized by equilibrium concentrations that result from molecular diffusion. Laminar mixing, commonly observed in high-viscosity fluids, arises from longitudinal mixing, where fluid motion is primarily influenced by linear viscous forces. In this regime, fluid particles flow along parallel streamlines in a time-independent manner. To achieve homogeneity, additional radial mixing, which occurs perpendicular to the streamlines, is necessary. This can be accomplished through mechanisms such as shear, expansion, compression, and the utilization of backflow and spiral flow. Ultimately, turbulent mixing yields the most significant effects. This is because spatial and temporal flow fluctuations necessitate continuous reorientation of fluid particles along Lagrangian trajectories, leading to efficient turbulent mass transfer.

Mixing processes are typically characterized by statistical parameters, including mixture quality, mixing time, and residence time distribution. Additionally, the dimensionless Reynolds number and specific power input are crucial factors that influence mixing efficiency. All of these parameters are also relevant when scaling up or scaling down the mixing process.

Mixing Quality

Mixing quality is typically defined as the deviation of a measured property from the mean. Several indices are available to quantify mixing quality, and these vary depending on the application. Six recognized conditions for specific mixing quality include: perfectly unmixed system, ideal homogeneous mixing, stratified mixing, uniform random mixing, true mixing, and textured mixing. In a perfectly unmixed system, all components are locally separated. An ideal mixed system (also referred to as an ideal homogeneous system) resembles a lattice, where each component x is adjacent to the same number of component y. Stratification is characterized by the spatial separation of components, beginning at the walls of the adjacent system. A homogeneous random mixture represents a condition in which, after sufficient mixing time, there is an equal probability of encountering either component x or y. This outcome is expected, as mixing is inherently a random process. In practice, the actual mixing conditions in a mixed system fall somewhere between ideal homogeneous mixing and uniform random mixing. Textured mixing is rare in bioproduction.

Mixing Time

The mixing time is the second parameter used to quantify mixing efficiency and represents the duration required to achieve a specified level of mixing quality. A mixing degree of 95% is generally regarded as indicative of adequate performance for industrial mixing systems. However, more stringent requirements may exist in specialized applications.

Residence Time Distribution

The residence time distribution describes the probability that an element will remain in a continuously operating device for a specific duration. Consequently, the efficiency of spatial and temporal mixing can be assessed.

Reynolds Number

The Reynolds number, which describes the ratio of inertial forces to viscous forces, is used to analyze fluid flow patterns and is considered one of the most important parameters in fluid dynamics. For example, laminar flow occurs at low Reynolds numbers and is characterized by smooth and steady fluid motion. In contrast, turbulent flow develops at high Reynolds numbers. Unlike laminar flow, where viscous forces dominate, turbulent flow is characterized by inertial forces, which often lead to flow instabilities, such as random vortices.

Specific Power Input

Specific power input, defined as the amount of power per unit mass or volume introduced into a system by a mechanical, hydraulic, or pneumatic drive mechanism, is a crucial parameter for optimizing the design of mixing systems. It influences both their efficiency and scalability. Generally, a high specific power input leads to shorter mixing times. However, this can result in elevated shear stresses and increased temperatures within the mixing systems, both of which can be detrimental during the production of intermediates and final products, particularly when utilizing single-use bag mixing systems.

Although not all principles, designs, and dimensions are directly transferable, the operational principles of current single-use bag mixing systems closely resemble those of their reusable counterparts. Unsurprisingly, many of the operational principles of single-use bag mixing systems are also applicable to single-use bioreactors. Essential operations such as homogenization, suspension, gas-liquid dispersion, and heat exchange are critical for successful mixing processes and optimized culture procedures.

Over the past few years, single-use mixing systems have gained significant importance in bioproduction and are now widely accepted at all stages of the production process. The selection of the most suitable type of single-use bag mixing system primarily depends on the specific mixing task to be performed and the required level of cleanliness. Additionally, single-use bag mixing systems are generally easier and more convenient to handle and operate compared to their stainless steel counterparts.

As a leading single-use technology supplier, Duoning developed 2-20 L DuoMix® benchtop mixing systems, 50 -3,000 L floor-standing mixing systems and 3D single-use mixing bags with various volume and connection specifications designed for these systems.

DuoMix® floor-standing mixing system comprises a control cabinet, a tank, and a drive motor. The control cabinet is mounted on the tank, featuring an integrated design. The drive motor and magnetic head are located at the bottom of the tank, while the weighing module is positioned above the casters. This equipment is compatible with standard 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 accommodate various processes and procedures. The software interface for the DuoMix® benchtop and floor-standing mixing systems is user-friendly, supporting at least three levels of user authority. It includes features such as recipe editing, alarm functions, sensor calibration, data recording and export, audit tracking, and more.

In addition, to assist users in developing and scaling 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 parameters such as velocity fields, mixing performance, stirring power, pressure, vortex structures, shear rates, and gas-liquid distribution. Detailed reports can be obtained by contacting our product and technical team.