## 1 Introduction  
It has been reported that glycyrrhizic acid (GA) is a major active constituent in the traditional medicines called _Glycyrrhizic__uralensis_, which has been used as a medicinal herb in worldwide [1]. Glycyrrhizic acid has been recognized as exhibiting many important pharmacological activities such as antiviral, anticancer, anti-HIV, antiulcer, anti-inflammatory, antioxidant [2; 3], and so on. Besides medicinal usage as an ingredient in pharmaceutical preparations, glycyrrhizic acid is also used extensively as a sweetener or functional additive in food, tobacco, and confectionery products all over the world [4; 5].  
In recent years, glycyrrhizic acid is generally extracted from various natural plants by several extraction techniques such as supercritical CO\({}_{2}\) extraction [6], aqueous two phase extraction [7], solvent extraction [5; 8], third-phase extraction [9], microwave-assisted extraction [10], ultrasound-assisted extraction [11], and so on. Among the different existing techniques, UAE has been widely recognized as a safe, effective, inexpensive, and environment-friendly technology. When it is applied in the solid-liquid extraction process, it has been proven to be capable of reducing the consumption of solvent, shortening the extraction time, and improving extraction yields [12; 13; 14; 15]. This is mainly attributed to the ultrasonic cavitation, which can generate cavitation bubbles in liquid medium and result in macro-turbulence, high-velocity flow, and perturbation in micro-particles of the biomass [16]. The collapse of these bubbles can facilitate the disruption of cell wall and allow the penetration of solvent into raw materials, thus increasing the contact surface area of solid particle and enhancing mass transfer across cell membrane [17]. Moreover, the conventional extraction methods for extraction of glycyrrhizic acid from _Glycyrrhizic uralensis_ suffer from various disadvantages such as more extraction time, large solvent requirement, higher extraction temperature, and lower yield. Thus, ultrasound will be applied for the extraction of glycyrrhizic acid in this work.  
In order to better predict the UAE process and also understand the effects of various extraction factors on the extraction process, it is very important for use a mathematical tool to model the extraction mechanism and determine the kinetic parameters. In recent years, [PERSON] and [PERSON] [11] have investigated the kinetic model for the extraction of glycyrrhizic acid based on the second order rate equation, in which they established the kinetic model of the temperature and solvent to solute ratio. However, the establishment of a kinetic model for ultrasonic power and ultrasonic frequency had not been studied. In fact, ultrasonic power and ultrasonic frequency are two important process parameters for the extraction of glycyrrhizic acid. [PERSON], et al. [18] reported that the extraction efficiency of glycyrrhizic acid increased dramatically with the increase of ultrasonic power from 50 to 200 W. [PERSON] and [PERSON] presented that there was a higher glycyrrhizic acid yield at ultrasonic frequency of 25 kHz. A similar result was reported in previous literatures [19]. Therefore, the optimization of extraction process using ultrasound and its establishment of kinetic model for ultrasonic power and ultrasonic frequency is worthy of further study.  
The objective of this work is to investigate the effects of process parameters on the extraction of glycyrrhizic acid from _Glycyrrhizic uralensis_ and to obtain optimum process parameters which will give higher yields compared to conventional extraction methods. The second objective is to understand the kinetics and to develop the extraction model for this extraction process under optimum process parameters to predict equilibrium concentration and integrated influence coefficient.