RHEOLOGICAL MODELLING OF WORMLIKE MICELLES SYSTEMS USING FRACTIONAL VISCOELASTIC MODEL
Abstract
Rheological constitutive equations with operators of fractional integration or differentiation play an increasing role at the phenomenological description of polymeric materials. The wormlike micelles system is formed by mixing Cetyltrimethylammonium bromide (CTAB) and sodium nitrate (NaNO3). Two wormlike micelle systems belonging to the low and high salt regime are prepared. The effects of copolymer on the rheological behavior of the two worm like micelles system are investigated by rheological measurements. A fractional rheological description is obtained by replacing the first order time derivatives with fractional derivatives of order q and μ. The Friedrich-Braun model relating stress to strain is used to fit the experimental results on these wormlike micelle systems. The comparison between the experimental results and theoretical predictions showed good agreement.
References
Bagely, R.L., and Torvik, P.T. (1983). A theoretical basis for the application of fractional calculus to viscoelasticity. J. Rheol., 27(3):201-210.
Binks, B.P., Espert, A., and Fletcher, P.D. (2003). Phase behaviour of microemulsions stabilized by double chain cationic surfactants and alcohol co-surfactants. Colloid and Surfaces, 212(A): 135-145.
Cappelaere, E., and Cressely, R. (1998). Rheological behavior of an elongated micellar solution at low and high salt concentrations. Colloid Polymer Sci., 276:1,050-1,056.
Christensen, R.M. (1982). Theory of viscoelasticity, An introduction. Academic Press, New York, p. 1-63.
Eldred, L.B., Baker, W.P., and Palazotto A.N. (1996). Numerical application of fractional derivative model constitutive relations for viscoelastic materials. Computers and Structure, 60(6):875-882.
Friedrich, Chr. (1992). Rheological material functions for associating comb-shaped or H-shaped polymers: a fractional calculus approach, Phil. Mag. Lett., 66(6): 287-292.
Friedrich, Chr., Braun, H., and Weese, J. (1995). Determination of relaxation time spectra by analytical inversion using a linear viscoelastic model with fractional derivatives. Polym. Eng. and Sci., 35(21):1,661-1,669.
Hartman, V., and Cressely, R. (1998). Linear and non linear rheology of a wormlike micellar system in presence of sodium tosylate. Colloid Polymer Sci., 276:169-175.
Herb, C.A., and Prud’homme, R.K. (1994). Structure and flow in surfactant solutions. American Chemical Society, Washington, DC., p. 1-63.
Oldham, K.B., and Spainer, J. (1974). The fractional calculus. Academic Press, New York, p. 1-27.
Palade, L., Attane, P., Huligol, R., and Mena, B. (1999). Anomalous stability behavior of a properly invariant constitutive equation which generalizes fractional derivative models. Int. J. Eng. Sci., 37:315-329.
Podlubny, I. (1999). Fractional differential equations. Academic Press, p. 1-77.
Samko, S.G., Kilbas, A.A., and Marichev, O.I. (1993). Fractional integrals and derivatives: theory and application. Gordon and Breach, Amsterdam, p. 1-31.
Schiessel, H., and Blumen, A. (1993). Hierarchical analogous to fractional relaxation equations. J. Phys. A: Math. Gen., 26:5,057-5,096.
Schiessel, H., Friedrich, Chr., and Blumen, A. (2000). In: Applications to problem in polymer physics and rheology. In: Applications of fractional calculus in physics. Hilfer, R. (ed). World Scientific press, Singapore, p. 331-376.
Siong, K.C., Isa, S.M., Ghazali, Z., and Radiman, S. (2001). Rheology of wormlike micelles in the presence of copolymer. Proceeding of National Physics Conference; (PERFIK 2001). Crystal Crown Hotel, Kuala Lumpur, p. 89-92.
