Literature Cited

Abramowitz M, Stegun I.A. Handbook of Mathematical Functions. Washington, DC: U.S. Department of Commerce, National Bureau of Standards; 1972.

Chester W, Breach D.R, Proudman I. On the flow past a sphere at low Reynolds number. Journal of Fluid Mechanism. 1969;37:751–760.

Conlisk A.T. Essentials of Micro- and Nanofluidics with Applications to the Biological and Chemical Sciences. Cambridge University Press; 2013.

Hele-Shaw H.S. Investigations of the Nature of Surface Resistance of Water and of Stream Line Motion Under Certain Experimental Conditions. Transaction of the Royal Institution Naval Arch. 1898;40:21–46.

Kaplun S. Low Reynolds number flow past a circular cylinder. Journal of Mathematical Mechanism. 1957;6:585–603.

Kirby B.J. Micro- and Nanoscale Fluid Mechanics. Cambridge University Press; 2010.

Kurup D.G, Koithyar A. New expansions of Bessel functions of first kind of complex argument. IEEE Transactions on Antennas and Propagation. 2013;61:2708–2713.

Millikan R.A. The isolation of an ion, a precision measurement of its charge, and the correction of Stokes’ law. Physical Review. 1911;32:349–397.

Oseen C.W. Über die Stokes’sche Formel, und über eine verwandte Aufgabe in der Hydrodynamik. Ark Mathematical Astrom Fysiol. 1910;6(No. 29).

Proudman I, Pearson J.R.A. Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder. Journal of Fluid Mechanism. 1957;2:237–262.

Sherman F.S. Viscous Flow. New York: McGraw-Hill; 1990.

Taylor G.I, Green A.E. Mechanism of the production of small eddies from large ones. Proceedings of the Royal Society of London A. 1937;Vol. 158:499–521.

White F.M. Viscous Fluid Flow. New York: McGraw-Hill; 2006.

Womersley J.R. Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known. Journal of Physiology. 1955;127:553–563.

Womersley J.R. Oscillatory motion of a viscous liquid in a thin-walled elastic tube. I. The linear approximation for long waves. Philosophical Magazine. 1955;46:199–221.

Yih C.-S. Fluid Mechanics. Ann Arbor: West River Press; 1979.

Supplemental Reading

Batchelor G.K. An Introduction to Fluid Dynamics. London: Cambridge University Press; 1967.

Lighthill M.J. An Informal Introduction to Theoretical Fluid Mechanics. Oxford, England: Clarendon Press; 1986.

Schlichting H. Boundary Layer Theory. New York: McGraw-Hill; 1979.

1 In spherical polar coordinates, the operator in the footnoted equations is actually −∇ × ∇ × ( ) or −curl curl ( ), which is different from the Laplace operator defined in Appendix B.

2 Equation (9.49) is the square of the operator, and not the biharmonic.

3 Developed from problem 2 on page 383 in Yih (1979).

4 Rephrased from White (2006) p. 211, problem 3.32.