(485d) The Hydrodynamics of Vials and Laboratory Bottles

Chemistry and pharmaceutical laboratories commonly utilize vials and small bottles for variety of purposes, including the evolution of the dissolution of different mixture constituents, the dispersion of hard-to-dissolve solids in liquids, the determination or rate precipitation of crystals in reaction precipitations, and many others. Often, it is often the case that only a minimum amount of an Active Pharmaceutical Ingredient (API) is available during pharmaceutical drug development, implying that experimentation in larger scale equipment is impossible. In these small systems, mixing and agitation in general is achieved with a stir bar placed inside the bottle and stirred by a magnetic stirrer underneath. In all these small containers, the hydrodynamics plays a critical role in the process, and it is critical to have information on how the flow field varies depending on geometry and operating conditions in order to better understand mixing processes and scale scaleup. However, little information is available in the literature on the hydrodynamic and mixing performance of small bottles. Therefore, the purpose of this work was to experimentally determine the hydrodynamics of magnetically stirred vials and bottles of different sizes using Particle Image Velocimetry (PIV) and provide some guidance for scaleup. For this purpose, a custom-made vial/bottle centering equipment was built to precisely center the containers and the stir bar with respect to the stirrer. Particle Image Velocimetry (PIV) was then used to quantify all three components of the velocity vectors on a vertical plane through the bottle centerline, as well as across horizontal cross-sections, for bottles ranging in size from 4 mL to 250 mL. Different magnetic bars/bottle combinations were studied, some of which are shown in Figure 1. Additionally, the hydrodynamics in bottles with different fill volumes was also investigated. In a preliminary phase of the project different combinations of bottle size, magnetic bar size and type (e.g., with or without central pivot), and agitation speed were tested for stability of the stirring bar motion. Only the hydrodynamics of stable configurations was studied in detail. The 250-mL bottle filled with a 200-mL fill volume was selected as the reference system. This system was studied at three agitation speeds (100, 200, and 300 rpm), ranging from minimal agitation to high agitation resulting in a vortex of significant depth. Then three velocities for all the other bottles/vials were selected using the following criteria: (1) geometric similarity: experiments in bottles with nominal volumes different from that of the reference bottle were conducted at velocities that produced (approximately) similar vortex profiles as in the reference bottle (Remark: exact geometric similarity was not possible since the vial bottle/bar diameter ratio changed with bottles/vials of different sizes), and (2) constant Froude Number. Vector plots similar to those obtained in Figure 2 were obtained for all systems. The following conclusions can be drawn from this work:

• Stir bar selection is critical to ensure stability of the velocity profiles. Only certain combinations of bottles/vials and bar geometry and size result in stable motion;
• All systems studied here are extremely sensitive to minimal changes in geometry and bottle/vial/bar location;
• Even removing and reinserting the same bottle in the same system with the same agitation speed can result in small flow variations;
• Correct placement of the bottle/vial on the magnetic plate is critical;
• Careful conduction of PIV experiments resulted in reproducible velocity profiles.
• Selection of the appropriate stirring speed for any given system is important to obtain similarity of velocity profiles;
• The same Froude number should be used when scaling up/down.