The micro-probe particle technology has been used to measure hydrodynamic stress in various types of flows; including, turbulent jets, stirred tanks with various impellers, and cell culture bioreactors1,2. This micro-probe technology consists of poly (methyl methacrylate) (PMMA) nanoparticles that are diluted and aggregated in high salt solutions (above critical coagulation concentration) and then diluted further for use in the liquid system of process interest. PMMA nanoparticles consist of monomodal size distribution with mean diameter around 62 nm.2 These nanoparticles can form aggregates of uniform structure and size3 containing a very specific fracture strength. Upon dilution in the process fluid, the PMMA particles in the aggregates are only held together by van der Waals forces. These unique properties allow for accurate measurement of the resulting max stress they experience in a flowing liquid system by quantification of the aggregate break-up during processing. Firstly, a syringe pump is setup with a supply and receiving syringe connected by tubing intersected by a steel nozzle of known orifice. Aggregates are carefully added to process fluid and diluted to 50 ppm PMMA concentration. Previous researchers have demonstrated that the max stress exerted on the aggregates occurs in the laminar flow regime and as such, the max stress can be estimated through an analytical equation3. Samples of the aggregates from the syringes are characterized using static light scattering (SLS) to examine size change over time until a steady state is achieved at a given flow condition. Using characterization from steady state, data is analyzed to yield radius of gyration, <Rg>. <Rg> can be plotted against the calculated max stress to yield a calibration curve. This same batch of aggregates is then diluted in a liquid vessel to same concentration and recirculated through a peristaltic pump until steady state is achieved in terms of PMMA aggregate size. Data analysis described above yields <Rg> of aggregates from the pump system at a given flow condition and this can be used to estimate the max stress using the calibration curve with the premise that the PMMA aggregates will break the same in both systems only as a function of the max stress.
The FSI model couples a mechanical FEM model of the peristaltic pump and tubing undergoing pumping to a CFD model which captures the fluid flow. as the mechanical model, run within ABAQUS, captures the tubing compression and expansion that occurs in the pump head during operation. The CFD model is run using XFlow and a 1-way coupling is prescribed where the FEM tubing inner boundary conditions are the input to the CFD model. To properly capture the displacement of the tubing upon pumping, a separate mechanical FEM model was required to determine the material properties of the tubing. A reduced polynomial hyper-elastic material model was used and the coefficients of the material model were determined by compressing a section of tubing radially at a fixed velocity in a Mechanical Testing System. The force versus displacement curves were compared to the same geometry compressed via the FEM model. The material model coefficients were optimized to minimize difference between experiment and model. The CFD model was run assuming water as the fluid. A series of peristaltic pump experiments were run using 1/4” and 3/8” silicon tubing and flow rates of 0.25-3.4 L/min and the conditions were simulated using the CFD model by changing RPM of the pump. The flow field data output from the CFD model was then compared to the flow rates and max stress determined empirically in the pump trials as a means of verifying accuracy of the model predictions.
This work has generated robust protocols for use of the PMMA micro-probe technology from aggregation through data analysis. The reproducibility and accuracy of calibration curve generation has been established. Aging of aggregates has been shown to cause greater fracture at a given stress. Stress history was shown not to influence fracture behavior of the aggregates as long as prior stress events occurred at a max stress lower than the terminal stress studied. Very good agreement in flow rates were observed between the CFD model and experiments. As expected, the analysis of max stress from the model output shows a periodicity related to pulsation of liquid as tubing is compressed through rollers in pump head and fluid pushed forward. The quantified max stress using PMMA micro-probe technology was above 99% of fluid simulated. This finding provides confirmation that the pump model is simulating top stresses accurately and the PMMA aggregates are in fact fracturing only when exposed to critical fracture stress.
We see that this PMMA micro-probe methodology can have numerous applications to explore risk to product quality as a function of hydrodynamic stresses as well as verification and possibly validation work for other process models.
References
1: Srom, O. et al. Study of hydrodynamic stress in cell culture bioreactors via lattice-Boltzmann CFD simulations supported by micro-probe shear stress method. Biochemical Engineering Journal 208 (2024) 109337
2: Villiger, T.K. et al. Experimental Determination of Maxium Effective Hydrodynamic Stress in Multiphase Flow Using Shear Sensitive Aggregates. AiChE Journal, pg. 1735 – 1744. May 2015, Vol. 61, No. 5
3: Soos, M. et al. Aggregate Breakup in a Contracting Nozzle. Langmuir 2010, 26 (1), pg. 10-18