The Effective Permittivity of Reacting Mixture Solutions for Multiphysics Calculations
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The Effective Permittivity of Reacting Mixture Solutions for Multiphysics Calculations Hua-Cheng Zhu • Xiao-Qing Yang • Ka-Ma Huang
Received: 26 January 2011 / Accepted: 8 December 2011 / Published online: 16 October 2012 Ó Springer Science+Business Media New York 2012
Abstract Huang and Yang (PIER Lett. 5: 99–107, 2008) proposed a method based on experimental results to calculate the effective permittivity of liquid reacting mixture solutions. The method cannot be directly applied to multiphysics calculations for microwave heating on chemical reactions, because the derived formula of effective permittivity is a function of the reaction time. In this paper, we improve the method to obtain the effective permittivity as a function of the reactants’ concentrations and temperature by numerical fitting. Thus, the formula can be directly used for multiphysics calculation. Three measured effective permittivity curves for the iodination of acetone reaction under constant temperature were used to calculate the corresponding coefficients of the method at both 915–2,450 MHz. The results calculated by the coefficients are in satisfactory agreement and approach the measured results. Keywords Effective permittivity Chemical reactions Microwave heating Multiphysics calculation
1 Introduction Microwave heating as a new technique for chemical reactions has developed rapidly since the 1980s [1, 2]. Unfortunately, some difficulties limit the application of high-power microwaves in the chemical industry [3]. The main problem is that the reflection and absorption of microwaves by the reactants change nonlinearly with time during the reaction [4]. When high-power microwaves are applied, the reactants may be burned out and the microwave chemical reactor may be destroyed. To solve this problem, multiphysics calculations for microwave heating on chemical reaction should be further studied. Therefore, knowledge of the effective permittivity of the reacting mixture solution as functions of the reactants’ concentration and temperature is preliminary and necessary. H.-C. Zhu X.-Q. Yang K.-M. Huang (&) College of Electronics and Information Engineering, Sichuan University, Chengdu 610064, People’s Republic of China e-mail: [email protected]
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J Solution Chem (2012) 41:1729–1737
We proposed a method in Ref. [5] to calculate the effective permittivity of the reacting mixture solution, by using three measured curves of the variation of effective permittivity with time at three constant temperatures to produce a new curve for any constant temperature in this range. In multiphysics calculations, we need to model the effective permittivity of the reacting mixture solution as functions of the reactants’ concentrations and temperature. Then, the formulae, as functions of time and temperature, can be directly applied to multiphysics calculations. In this paper, the formula in Ref. [5] has been improved to give the effective permittivity changes with the reactants’ concentrations and temperature. In order to corroborate the method
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