From Raindrops in 1940 to Drug Dissolution in 2005

Third M.I.T. Conference on Computational Fluid and Solid Mechanics

Niall M. McMahon*, Martin Crane, Heather J. Ruskin, Lawrence J. Crane, School of Computing, Dublin City University, Glasnevin, Dublin 9, Ireland

Abstract

In 1940, G.I. Taylor presented Notes on Possible Equipment and Technique for Experiments on Icing on Aircraft [1] in which he outlined, with great clarity of thought, a methodology for determining the two-dimensional equations of motion of raindrops moving in curved airstreams. This work was to facilitate the design of a suitable wind tunnel for carrying out de-icing experiments. In this paper, Taylor presents the exact solution for raindrops moving close to a stagnation point when Stokes' law of resistance is assumed to apply. In general, these equations of motion must be solved numerically, a daunting prospect in 1940. Nevertheless, an undaunted Muriel Glauert, wife of Hermann Glauert, hand computed two-dimensional paths for raindrops of various sizes moving around simple shapes [2]. The authors regard the work of Taylor and Glauert as an excellent introduction to particle tracking in a fluid. In the first part of our presentation, we will describe simple numerical computer implementations of Taylor's special case of raindrops close to a stagnation point and Glauert's paths around cylinders and airfoils.

These elementary particle-tracking techniques are still relevant today. In the second part of our presentation, we will discuss how we are using similar, state of the art techniques to model the dissolution of a tablet in a pharmaceutical testing device*. Such in vitro tests are important in developing pharmaceutical products, yet their dynamics are poorly understood [3]. Like Taylor's work with regard to wind tunnel design, mathematical simulation can provide insight into the physics of these dissolution devices. In addition, sophisticated simulations could reduce the need for experimental testing and the associated costs [4]. We will present results from our simulations.

* United States Pharmacopeia Apparatus II Dissolution Test

Acknowledgements

The authors are very grateful to Francis Muir and, in particular, Audrey Glauert.

References

[1] Taylor, G.I. 15th January 1940. Notes on Possible Equipment and Technique for Experiments on Icing on Aircraft. Aeronautical Research Committee Reports and Memoranda 2024.

[2] Glauert, M. 10th November 1940. A Method of Constructing the Paths of Raindrops of Different Diameters moving in the neighbourhood of (1) a Circular Cylinder, (2) an Airfoil, placed in a Uniform Stream of Air ; and a Determination of the Rate of Deposit of Drops on the Surface and the Percentage of Drops Caught. Aeronautical Research Committee Reports and Memoranda 2025.

[3] Baxter, J.L. Kukura, J. Muzzio, F.J. 2005. Hydrodynamics-induced Variability in the USP Apparatus II Dissolution Test. Int J Pharm 292, 17-28.

[4] Crane, M. Crane, L. Healy, A. M. Corrigan, O.I. Gallagher, K.M. McCarthy L.G. 2004. A Pohlhausen Solution for the Mass Flux From a Multi-layered Compact in the USP Drug Dissolution Apparatus. Simul Model Pract Th, 12 (6), 397-411.

*Correspondence to: Niall McMahon, School of Computing, Dublin City University, Glasnevin, Dublin 9, Ireland.
E-mail: nmcmahon@computing.dcu.ie

This research is supported by the National Institute for Cellular Biotechnology.

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