Derivation and Analysis of the Disk Movement Equation for a Vertically Reciprocating Mixer
Online First: 18/08/2026
Corressponding author's email:
tinhtt@hcmute.edu.vnDOI:
https://doi.org/10.54644/jte.2026.2014Keywords:
Reciprocating Mixer, Agitator, Approximation, Disk Movement, High OrderAbstract
Mixing plays a crucial role in a wide range of applications from biology, pharmaceutical to chemical and food industry. Vertically reciprocating mixers, which operate based on the up-and-down motion of a disk impeller, are particularly effective for mixing high-viscosity or highly sensitive materials. A thorough understanding of the disk’s motion equation, including its derivation and analysis, is essential for evaluating the performance of this type of mixer. In this study, the movement of a disk impeller connected to a flywheel via a connecting rod is systematically derived. The effects of higher-order approximations and the ratio between the flywheel radius (R) and the connecting-rod length (L) are investigated. When R is smaller than L, the position and velocity equations describing the reciprocating motion of the disk impeller are obtained. The results indicate that higher-order approximations have negligible influence on the motion equation. Furthermore, the study sheds light the impact of the R/L ratio on the position and velocity profiles. These findings provide solid foundation for further research on this field, especially power consumption, flow and mixing characteristics.
Downloads: 0
References
L. C. Li and B. Xu, “Numerical simulation of hydrodynamics characteristics in a tank with an up-down reciprocating agitator,” Journal of Applied Fluid Mechanics, vol. 16, no. 7, pp. 1455-1466, 2023. DOI: https://doi.org/10.47176/jafm.16.07.1721
T. T. Tran, E. G. Lee, I. S. Lee, N. S. Woo, S. M. Han, Y. J. Kim, and W. R. Hwang, “Hydrodynamic extensional stress during the bubble bursting process for bioreactor system design,” Korea-Australia Rheology Journal, vol. 28, no. 4, pp. 315-326, 2016. DOI: https://doi.org/10.1007/s13367-016-0032-5
Y. Komoda, Y. Inoue, and Y. Hirata, “Mixing performance by reciprocating disk in cylindrical vessel,” Journal of Chemical Engineering of Japan, vol. 33, no. 6, pp. 879-885, 2000. DOI: https://doi.org/10.1252/jcej.33.879
Y. Hirata, private communication, Nov 2013.
Y. Hirata, Y. Dote, T. Yoshioka, Y. Komoda, and Y. Inoue, “Performance of chaotic mixing caused by reciprocating a disk in a cylindrical vessel,” Chemical Engineering Research and Design, vol. 85, pp. 576-582, 2007. DOI: https://doi.org/10.1205/cherd06173
Y. Hirata, T. Dote, and Y. Inoue, “Contribution of suspended particles to fluid mixing in recipro-mixing with a disk impeller,” Chemical Engineering Research and Design, vol. 87, pp. 430-436, 2009. DOI: https://doi.org/10.1016/j.cherd.2008.12.022
J. Kamienski and R. Wójtowicz, “Dispersion of liquid-liquid systems in a mixer with a reciprocating agitator,” Chemical Engineering and Processing, vol. 42, pp. 1007-1017, 2003. DOI: https://doi.org/10.1016/S0255-2701(02)00214-3
M. Fan, J. Xu, H. Sun, S. Wang, X. Zhang, H. Wang, and W. Yin, “Enhancement of chaotic mixing performance in laminar flow with reciprocating and rotating coupled agitator,” Chemical Engineering Science, vol. 280, no. 118988, pp. 1-15, 2023. DOI: https://doi.org/10.1016/j.ces.2023.118988
M.H.I. Baird and N.V.R. Rao, “The reciprocating plate column – development and applications,” Chem. Eng. Comm., vol. 116, pp. 67-88, 1992. DOI: https://doi.org/10.1080/00986449208936044
S. Masiuk and R. Rakoczy, “Power consumption, mixing time, heat and mass transfer measurements for liquid vessels that are mixed using reciprocating multiplates agitators,” Chemical Engineering and Processing, vol. 46, pp. 89-98, 2007. DOI: https://doi.org/10.1016/j.cep.2006.05.002
S. Masiuk, R. Rakoczy, and M. Kordas, “Comparison density of maximal energy for mixing process using the same agitator in rotational and reciprocating movements,” Chemical Engineering and Processing, vol. 47, pp. 1252-1260, 2008. DOI: https://doi.org/10.1016/j.cep.2007.04.004
Y. Murakami, T. Hirose, T. Yamato, and H. Fujiwara, “Improvement in mixing of high viscosity liquid by additional up-and-down motion of a rotating impeller,” J. of Chemical Engineering of Japan, vol. 13, pp. 318-323, 1979. DOI: https://doi.org/10.1252/jcej.13.318
G.W. Stevens and M.H.I. Baird, “A model for axial mixing in reciprocating plate columns,” Chemical Engineering Science, vol. 45, pp. 457-465, 1990. DOI: https://doi.org/10.1016/0009-2509(90)87032-N
V.B. Veljkovic, I.B. Bankovic, and D.U. Skala, “Reciprocating plate column – fundamental research and application in Serbia from 1970 to 2020,” Hem. Ind., vol. 78, pp. 187-203, 2024. DOI: https://doi.org/10.2298/HEMIND230320028V
R. Wójtowicz, “Flow pattern and power consumption in a vibromixer,” Chemical Engineering Science, vol. 172, pp. 622-635, 2017. DOI: https://doi.org/10.1016/j.ces.2017.07.010
P.M. Orlewski, Y. Wang, M.S. Hosseinalipour, D. Kryscio, M. Iggland, and M. Mazzotti, “Characterization of a vibromixer: Experimental and modeling study of mixing in a batch reactor,” Chemical Engineering Research and Design, vol. 137, pp. 534-543, 2018. DOI: https://doi.org/10.1016/j.cherd.2018.08.003
Downloads
Published
How to Cite
Issue
Section
Categories
License
Copyright (c) 2026 Journal of Technical Education Science
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Copyright © JTE.
