We present a theoretical analysis of calendering of Ellis fluid based on lubrication approximation. The equations governing the flow are nondimensionalized and solved to get closed form expressions of velocity and pressure gradient. Runge–Kutta algorithm is employed to compute the pressure distribution. The operating variables which are used in the calendering process, i.e. roll-separating force, power input to the rolls and exiting sheet thickness are calculated. The influence of the material parameters on the velocity profile, pressure gradient, pressure distribution and operating variables is shown graphically and discussed in detail.
GaskellRE. The calendering of plastic materials. J Appl Mech1950; 17: 334–336.
2.
McKelveyJM. Polymer processing, New York: John Wiley & Sons, 1962.
3.
BrazinskyICoswayHFValleCF. A theoretical study of liquid-film spread heights in the calendering of Newtonian and power law fluids. J Appl Polym Sci1970; 14: 2771–2784.
4.
AlstonWWAstillKN. An analysis for the calendering of non-Newtonian fluids. J Appl Polym Sci1973; 17: 3157–3174.
5.
MiddlemanS. Fundamentals of polymer processing, New York: McGraw-Hill, 1977.
6.
TadmorZGogosCG. Principles of polymer processing, Haifa, Israel: John Wiley Sons, 1979.
7.
ZhengRTannerRI. A numerical analysis of calendaring. J Non-Newtonian Fluid Mech1988; 28: 149–170.
8.
MitsoulisEVlachopoulosJMirzaFA. Calendering analysis without the lubrication approximation. Polym Eng Sci1985; 25: 6–18.
9.
LevineLCorvalanCMCampanellaOH. A model describing the two-dimensional calendering of finite width sheets. Chem Eng Sci2002; 57: 643–650.
10.
SofouSMitsoulisE. Calendering of pseudoplastic and viscoplastic sheets of finite thickness. J Plast Film Sheet2004; 20: 185–222.
11.
SofouSMitsoulisE. Calendering pseudoplastic and viscoplastic fluids with slip at the roll surface. J Appl Mech-Trans ASME2006; 73: 291–299.
12.
ArcosJCMéndezFBautistaO. Effect of temperature-dependent consistency index on the exiting sheet thickness in the calendering of power-law fluids. Int J Heat Mass Transf2011; 54: 3979–3986.
13.
ArcosJCBautistaOMéndezF. Theoretical analysis of the calendered exiting thickness of viscoelastic sheets. J Non-Newtonian Fluid Mech2012; 177–178: 29–36.
14.
SiddiquiAMZahidMRanaMA. Calendering analysis of third-order fluid. J Plast Film Sheet2014; 30: 345–368.
15.
ZahidMRanaMASiddiquiAM. Effect of magneto-hydrodynamics on Newtonian calendering. J Plast Film Sheet2013; 29: 347–364.
16.
ZahidMRanaMASiddiquiAM. Modeling of non-isothermal flow of a magnetohydrodynamic, viscoplastic fluid during calendaring. J Plast Film Sheet2015; 0: 1–24.
17.
AliNJavedMASajidM. Theoretical analysis of the exiting thickness of sheets in the calendering of FENE-P fluid. J Non-Newtonian Fluid Mech2015; 225: 28–36.
18.
CalcagnoBOHartKRCroneWC. Calendering of metal/polymer composites: An analytical formulation. Mech Mater2016; 93: 257–272.
19.
MorrisonFA. Understanding rheology, New York: Oxford University Press, 2001.
20.
StellerRT. Generalized slit flow of an Ellis fluid. Polym Eng Sci2001; 41: 1859–1870.
