Abstract
We investigate the effects of non-Newtonian parameters on the exiting sheet thickness in the calendering of Oldroyd 4-constant fluid. The governing equations are first converted into dimensionless form and then simplified under lubrication approximation theory. A complete numerical approach is developed based on Matlab built-in routine “bvp4c” in order to obtain stream function and pressure gradient. The pressure is computed using Runge-Kutta method. The effects of involved material parameters on various quantities of interest are highlighted through graphs. The results indicate that Oldroyd 4-constant model predicts lower pressure in the nip region than that of the Newtonian model. The force and power for Oldroyd 4-constant model are also lower than their counterparts for Newtonian model. Moreover, the leave-off distance is nearly independent of the material parameters of the Oldroyd 4-constant model for larger value of the entering sheet thickness.
Conflict of interest statement: The authors have no conflict of interests regarding this manuscript.
References
[1] Gaskell RE. J. Appl. Mech. 1950, 17, 334–336.10.1115/1.4010136Search in Google Scholar
[2] McKelvey JM. Polymer Processing. John Wiley and Sons: New York, 1962.Search in Google Scholar
[3] Brazinsky I, Cosway HF, Valle CF, Clark R, Jones R, Story V. J. Appl. Polym. Sci. 1970, 14, 2771–2784.10.1002/app.1970.070141111Search in Google Scholar
[4] Alston WW, Astill KN. J. Appl. Polym. Sci. 1973, 17, 3157–3174.10.1002/app.1973.070171018Search in Google Scholar
[5] Middleman S. Fundamentals of Polymer Processing. McGraw-Hill: New York, 1977.Search in Google Scholar
[6] Tadmor Z, Gogos CG. Principles of Polymer Processing. John Wiley and Sons: Haifa, Israel, 1979.Search in Google Scholar
[7] Zheng R, Tanner RI. J. Non-Newton. Fluid Mech. 1988, 28, 149–170.10.1016/0377-0257(88)85037-7Search in Google Scholar
[8] Luther S, Mewes D. Polym. Eng. Sci. 2004, 44, 1642–1647.10.1002/pen.20162Search in Google Scholar
[9] Sofou S, Mitsoulis E. J. Plast. Film Sheet. 2004, 20, 185–222.10.1177/8756087904047660Search in Google Scholar
[10] Sofou S, Mitsoulis E. J. Polym. Eng. 2004, 24, 505–522.10.1515/POLYENG.2004.24.5.505Search in Google Scholar
[11] Mitsoulis E, Sofou S. J. Appl. Mech. 2006, 73, 291–299.10.1115/1.2083847Search in Google Scholar
[12] Mitsoulis E. J. Non-Newton. Fluid Mech. 2008, 154, 77–88.10.1016/j.jnnfm.2008.03.001Search in Google Scholar
[13] Mitsoulis E. J. Plast. Film Sheet. 2010, 26, 141–161.10.1177/8756087910376144Search in Google Scholar
[14] Polychronopoulos ND, Loannis ES, Papathanasiou TD. Polym. Eng. Sci. 2014, 54, 1712–1722.10.1002/pen.23719Search in Google Scholar
[15] Arcos JC, Bautista HO, Méndez F, Bautista EG. J Non-Newton. Fluid Mech. 2012, 177–178, 29–36.10.1016/j.jnnfm.2012.04.004Search in Google Scholar
[16] Ali N, Javed MA, Sajid M. J Non-Newton. Fluid Mech. 2015, 225, 28–36.10.1016/j.jnnfm.2015.09.005Search in Google Scholar
[17] Sajid M, Ali N, Javed MA. J. Plast. Film Sheet. 2017, 33, 124–141.10.1177/8756087916635855Search in Google Scholar
[18] Sajid M, Siddique H, Ali N, Javed MA. J. Polym. Eng. 2018, 38, 83–93.10.1515/polyeng-2016-0294Search in Google Scholar
[19] Javed MA, Ali N, Sajid M. J. Plast. Film Sheet. 2017, 33, 207–226.10.1177/8756087916647998Search in Google Scholar
[20] Ali N, Javed MA, Atif HM. J. Plast. Film Sheet. 2017. doi: 10.1177/8756087917746454.10.1177/8756087917746454Search in Google Scholar
[21] Ali N, Atif HM, Javed MA, Sajid M. Polym. Eng. Sci. 2018. 58 327–334.10.1002/pen.24578Search in Google Scholar
[22] Lee Y. PhD thesis, The Pennsylvania State University, Department of Mathematics, 2004.Search in Google Scholar
[23] Carreau PJ. PhD thesis, University of Wisconsin-Madison, 1968.Search in Google Scholar
[24] Maxwell JC. Philos. Trans. R. Soc. London A. 1866, 157, 26–78.Search in Google Scholar
[25] Bird RB, Armstrong RC, Hassager O. Dynamics of Polymer Liquid. Vol. 1 Wiley: New York, 1977.Search in Google Scholar
[26] Ali N, Wang Y, Hayat T, Oberlack M. Biorheology 2008, 45, 611–628.10.3233/BIR-2008-0510Search in Google Scholar
[27] Baris S. Turkish J. Eng. Env. Sci. 2001, 25, 587–594.10.1111/j.1745-4514.2001.tb00816.xSearch in Google Scholar
[28] Quintana GC, Cheh HY. J. Non-Newton. Fluid Mech. 1987, 22, 253–270.10.1016/0377-0257(87)85019-XSearch in Google Scholar
[29] Ali N, Atif HM, Javed MA, Sajid M. J. Plast. Film Sheet. 2018, 34, 43–59.10.1177/8756087917694934Search in Google Scholar
[30] Atif HM, Ali N, Javed MA, Abbas F. J. Plast. Film Sheet. 2018, doi: 10.1177/8756087918769345.10.1177/8756087918769345Search in Google Scholar
[31] Baumgaertal M, Winter HH. Rheol. Acta 1989, 28, 511–519.10.1007/BF01332922Search in Google Scholar
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Articles in the same Issue
- Frontmatter
- Material properties
- Steady shear and dynamic strain thickening of halloysite nanotubes and fumed silica shear thickening composite
- Diffusivity of solvents in semi-crystalline polyethylene using the Vrentas-Duda free-volume theory
- Toughening effect and mechanism of polyamide 12 and modified montmorillonite in polybenzoxazine resin
- The effects of cross-linked/uncross-linked electrospun fibrinogen/polycaprolactone nanofibers on the proliferation of normal human epidermal keratinocytes
- Frequency independent AC electrical conductivity and dielectric properties of polyaniline-based conductive thermosetting composite
- Preparation and assembly
- Study on the preparation and drug release property of soybean selenoprotein/carboxymethyl chitosan composite hydrogel
- Engineering and processing
- Interaction of nanofillers in injection-molded graphene/carbon nanotube reinforced PA66 hybrid nanocomposites
- Prediction of the yellowing of styrene-stat-acrylonitrile and acrylonitrile-butadiene-styrene during processing in an internal mixer
- Milling process optimization for the best surface coat adhesion of the rigid polyurethane foam
- A numerical analysis of calendering of Oldroyd 4-constant fluid