Abstract
The motivation of this work is to propose a special dough mixer with chaotic advection to take advantage of high performance mixing in chaotic mixers and to develop typical dough mixers. In order to prevent common difficulties encountered due to the dynamic mesh, a mathematical model was employed based on neglecting the transient term of the momentum equation using conceptual features from creeping flow. Then, the numerical simulation was performed using the bird Carreau dough model of Dhanasekharan. The mathematical model was further developed to complete the numerical procedure in order to find the required material point trajectories for assessing the presence of chaotic advection in the proposed mixer. In this approach, Lyapunov exponents were also calculated which quantify the exponential divergence of the initially close state-space trajectories and identify chaotic behavior of the system as well. The results indicated that the flow field was a combination of both chaotic and non-chaotic zones.
Similar content being viewed by others
References
S. Prakash and J. L. Kokini, Estimation and prediction of shear rate distribution as a model mixer, Journal of Food Engineering, 44 (2000) 135–148.
S. Prakash, M. V. Karwe and J. L. Kokini, Measurement of velocity distribution in the brabender farinograph as a model mixer using laser-doppler anemometry, Journal of Food Process Engineering, 22 (1999) 435–454.
C. F. Wang and J. L. Kokini, Prediction of the nonlinear viscoelastic properties of gluten doughs, Journal of Food Engineering, 25 (1994) 297–309.
K. M. Dhanasekharan, H. Huang and J. L. Kokini, Comparison of observed rheological properties of hard wheat flour dough with predictions of the Giesekus-Leonov, White-Metzner and Phan-Thien Tanner Models, Journal of Texture Studies, 30 (1999) 603–623.
K. M. Dhanasekharan, C. F. Wang and J. L. Kokini, Use of nonlinear differential viscoelastic models to predict the rheological properties of gluten dough, Journal of Food Process Engineering, 24 (2001) 193–216.
C. Breuillet, E. Yildiz, B. Cuq and J. L. Kokini, Study of the anomalous capillary bagley factor behavior of three types of wheat flour doughs at two moistures, Journal of Texture Studies, 33 (2002) 315–340.
S. J. Dus and J. L. Kokini, Prediction of the nonlinear viscoelastic properties of a hard wheat flour dough using the Bird-Carreau constitutive mode, Journal of Rheology, 34(7) (1990) 1069–1084.
C. F. Wang and J. L. Kokini, Simulation of the nonlinear rheological properties of gluten dough using the wagner constitutive model, Journal of Rheology, 39 (1995) 1465–1482.
R. K. Connelly and J. L. Kokini, 2-D numerical simulation of differential viscoelastic fluids in a single-screw continuous mixer: Application of viscoelastic finite element methods, Advances in Polymer Technology, 2(1) (2003) 22–41.
S. Prakash and J. L. Kokini, Determination of mixing efficiency in a model food mixer, Advances in Polymer Technology, 18(3) (1999) 209–224.
K. Sujatha, D. Ding and M. F. Webster, Modelling of dough mixing with free surfaces in two and three dimensions. Sixth International Conference on Computational Modelling of Free and Moving Boundary Problems, Brebbia CA, Sarler B (eds). WIT: Lemnos, Greece (2001) 102–111.
K. S. Sujatha, M. F. Webster, D. M. Binding and M. A. Couch, Modeling and experimental studies of rotating flows in part-filled vessels: Wetting and peeling, Journal of Food Engineering, 57 (2003) 67–79.
A. Baloch, P. W. Grant and M. F. Webster, Parallel computation of two dimensional rotational flows of viscoelastic fluids in cylindrical vessels, Engineering Computations, 19(7) (2003) 820–853.
D. M. Binding, M. A. Couch, K. S. Sujatha and M. F. Webster, Experimental and numerical simulation of dough kneading in filled geometries, Journal of Food Engineering, 58 (2003) 111–123.
A. Balouch and M. F. Webster, Distributed parallel computation for complex rotational flows of non-newtonian fluids, International Journal for Numerical Methods in Fluids, 43 (2003) 1301–1328.
M. A. Couch and D. M. Binding, An experimental study of the peeling of dough from solid surfaces, Journal of Food Engineering, 58 (2003) 299–309.
A. H. Bloksma, Slow creep of wheat flour dough, Rheologica Acta, 2 (1962) 217–230.
J. E. Goodrich and R. S. Porter, A rheological interpretation of torque rheometer data, Polymer Engineering Science, 7 (1967) 45–51.
L. Blyler and J. R. Daane, An analysis of Brabender torque rheometer data, Polymer Engineering Science, 7 (1967) 178–181.
B. L. D’Appolonia and W. H. Kunerth, The farinograph handbook, Third Ed. American Association of Cereal Chemistry (1982).
K. M. Dhanasekharan and J. L. Kokini, Viscoelastic flow modeling in the extrusion of a dough-like fluid, Journal of Food Process Engineering, 23 (2000) 237–247.
K. M. Dhanasekharan and J. L. Kokini, Design and scaling of wheat dough extrusion by numerical, Journal of Food Engineering, 60 (2003) 421–430.
K. L. Mackey and R. Y. Ofoli, Rheology of low-to intermediate-moisture whole wheat flour doughs, Cereal Chemistry, 67(3) (1990 b) 221–226.
A. Naranjo, M. del Pilar Noriega, T. Osswald, A. Roldan-Alzate and J. Diego Sierra, Plastics testing and characterization: Industrial applications, Munich: Hanser Gardner (2008).
J. G. Oldroyd. On the formulation of rheological equations of state, Proc. R. Soc. Lond. A, 22(200) (1950) 523–541.
N. Phan-Thien and R. I. Tanner, A new constitutive equation derived from network theory, J. Non-Newt. Fluid Mech, 2(4) (1977) 353–366.
R. K. Connelly and J. L. Kokini, 3D numerical simulation of the flow of viscous newtonian and shear thinning fluids in a twin sigma blade mixer, Advances in Polymer Technology, 25(3) (2006) 182–194.
R. K. Connelly and J. L. Kokini, Examination of the mixing ability of single and twin screw mixers using 2D finite element method simulation with particle tracking, Journal of Food Engineering, 79 (2007) 956–969.
R. K. Connelly and J. L. Kokini, The effect of shear thinning and differential viscoelasticity on mixing in a model 2D mixer as determined using FEM with particle tracking, Journal of Non-Newtonian Fluid Mechanics, 123 (2004) 1–17.
H. Aref, Stirring by Chaotic Advection, Journal of Fluid Mechanics, 143 (1984) 1–21.
C. Chagny, C. Castelain and H. Peerhossaini, Chaotic heat transfer for heat exchanger design and comparison with a regular regime for a large range of Reynolds numbers, Applied Thermal Engineering, 20 (2001) 1615–1648.
J. M. Ottino, The kinematics of mixing: stretching, chaos and transport, Cambridge University Press, Cambridge (1989).
M. M. Alvarez-Hernandez, T. Shinbrot, J. Zalc and F. J. Muzzio, Practical chaotic mixing, Chemical Engineering Science, 57 (2002) 3749–3753.
R. H. Liu, M. A. Stremler, K. V. Sharp, M. G. Olsen, J. G. Santiago, R. J. Adrian, H. Aref and D. J. Beebe, Passive mixing in a three-dimensional serpentine microchannel, journal of microelectromechanical systems, 9 (2000)190–197.
T. Y. Hwu, Chaotic stirring in a new type of mixer with rotating rigid blades, European Journal of Mechanics B/Fluid, 27 (2008) 239–250.
S. J. Park, J. K. Kim, J. Park, S. Chung, C. Chung and J. K. Chang, Rapid three dimensional passive rotation micromixer using the breakup process, Journal of Micromechanics and Microengineering, 14 (2004) 6–14.
T. C. Niederkorn and J. M. Ottino, Mixing of a viscoelastic fluid in a time-periodic flow, Journal of Fluid Mechanics, 256 (1993) 243–268.
P. D. Swanson and J. M. Ottino, A comparative computational and experimental study of chaotic mixing of viscous fluids, Journal of Fluid Mechanics, 213 (1990) 227–249.
S. Kumar and G. M. Homsy, Chaotic advection in creeping flow of viscoelastic fluids between slowly modulated eccentric cylinders, Journal of Physics and Fluids, 8(7) (1996) 1774–1787.
T. C. Niederkorn and J. M. Ottino, Chaotic mixing of shear-thinning fluids, AIChE Journal, 40 (1994) 1782–1793.
A. M. Cocero, The rheology and phase transitions of wheat glutenin, PhD thesis Rutgers University, New Brunswick, NJ, USA (1993).
D. M. Hobbs and F. J. Muzzio, the Kenics static mixer: a three-dimensional flow, Chemical Engineering Journal, 67 (1997) 153–166.
A. Yamagishi, T. Inaba and Y. Yamaguchi, Chaotic analysis of mixing enhancement in steady laminar flows through multiple pipe bends, International Journal of Heat and Mass Transfer, 50 (2007) 1238–1247.
Author information
Authors and Affiliations
Corresponding author
Additional information
Recommended by Associate Editor Yang Na
Seyed Mostaf Hosseinalipour is the professor of mechanical engineering of IUST (Iran University of Science and Technology). His main interest research subjects are experimental and numerical works in transport phenomena, Energy systems and food engineering.
Rights and permissions
About this article
Cite this article
Hosseinalipour, S.M., Tohidi, A., Shokrpour, M. et al. Introduction of a chaotic dough mixer, part A: mathematical modeling and numerical simulation. J Mech Sci Technol 27, 1329–1339 (2013). https://doi.org/10.1007/s12206-012-0895-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12206-012-0895-4