A fractional differential equation for a MEMS viscometer used in the oil industry

Journal of Computational and Applied Mathematics

Volumn 229, Issue 2, 2009, Pages 373-381

  Fitt, A D ^a   Goodwin, A R H ^b   Ronaldson, K A ^a   Wakeham, W A ^a  

^a UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

^b SCHLUMBERGER   (United States)

Author keywords

Densimeter; Fractional differential equation; MEMS device; Viscometer

Indexed keywords

CENTRAL DIFFERENCE SCHEMES; CLOSED FORMS; DENSIMETER; FRACTIONAL DIFFERENTIAL EQUATION; GOVERNING EQUATIONS; MEMS DEVICE; MICRO-ELECTRO MECHANICAL SYSTEMS; MODE OF OPERATIONS; NONLINEAR SPRINGS; NUMERICAL SCHEMES; NUMERICAL SOLUTIONS; OIL INDUSTRIES; OIL WELL EXPLORATIONS;

COMPOSITE MICROMECHANICS; MEMS; OIL WELLS; PETROLEUM ENGINEERING; PETROLEUM PROSPECTING; PETROLEUM REFINERIES; VISCOMETERS; VISCOSITY MEASUREMENT;

MICROELECTROMECHANICAL DEVICES;

EID: 67349206588     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2008.04.018     Document Type: Article

References (9)

1. Bagley R.L., and Torvik P.J. On the appearance of the fractional derivative in the behavior of real materials. J. Appl. Mech. 51 (1984) 294-298
2. Goodwin A.R.H., Donzier E.P., Vancauwenberghe O., Fitt A.D., Ronaldson K.A., Wakeham W.A., de Lara M.M., Marty F., and Mercier B. A vibrating edge supported plate, fabricated by the methods of micro electro mechanical system for the simultaneous measurement of density and viscosity: Results for methylbenzene and octane at temperatures between (323 and 423) K and pressures in the range (0.1-68) MPa. J. Chem. Eng. Data 51 (2006) 190-208
3. Goodwin A.R.H., Fitt A.D., Ronaldson K.A., and Wakeham W.A. A vibrating plate fabricated by the methods of microelectromechanical systems (MEMS) for the simultaneous measurement of density and viscosity: Results for argon at temperatures between 323 and 423 K at pressures up to 68 MPa. Int. J. Thermophys. 27 (2006) 1650-1676
4. Kilbas A.A., Srivastava H.M., and Trujillo J.J. Theory and Applications of Fractional Differential Equations (2006), Elsevier Science pp. 272-277
5. Luchko Y.F., and Srivastava H.M. The exact solution of certain differential equations of fractional order by using operational calculus. Comput. Math. Appl. 29 (1995) 73-85
6. Mainardi F., and Gorenflo R. On Mittag-Leffler-type functions in fractional evolution processes. J. Comp. Appl. Math. 118 (2000) 283-299
7. Podlubny I. Fractional Differential Equations (1999), Academic Press, San Diego
8. Ronaldson K.A., Fitt A.D., Goodwin A.R.H., and Wakeham W.A. Transversely oscillating MEMS viscometer: The "Spider". Int. J. Thermophys. 27 (2006) 1677-1695
9. Whittaker E.T., and Watson G.N. Modern Analysis. fourth edition (1940), Cambridge University Press (Chapter 12)