On the effect of resonant microwave fields on temperature distribution in time and space

Abstract

Microwave assisted chemistry has become a popular research topic within the framework of process intensification. The physics of microwave heating are fundamentally different from those found in conventional processing systems. Heating occurs fast, but non-uniformly in hard-to-predict patterns. In this study it is shown that these complexities are caused by the resonant nature of the microwave fields present in heating devices. This is demonstrated by means of experiments and modeling concerning heating of water-filled vials in single mode resonant microwave equipment. The results evince highly non-uniform, transient and irregularly behaving heating processes.

Introduction

Over the past 25 years, many interesting phenomena have been observed and reported in studies on microwave enhanced chemistry. It is seen as a convenient, fast and contact-free method of heating. Furthermore, there is an ongoing debate about the existence of a direct (non-thermal) influence of the microwave field on chemical reactions that may potentially reduce processing times significantly; indeed, many studies show unexpectedly high conversions over short periods [1], [2], [3], [4], [5], [6]. The increased reaction speeds are often explained as a consequence of non-uniform heating. Under non-uniform temperature conditions, it is possible that the temperature measurement occurs in a relatively cold position. In such an event, the higher temperatures that drive conversion are not registered and it would appear that the microwave field causes higher conversion than was expected on the basis of the measured temperature. Cases are indeed known in which apparent microwave effects disappear when reaction mixtures are vigorously stirred [7], [8], [9], [10]. Not all systems can be (effectively) stirred though. Relevant examples include continuous flow (milli) reactors, packed beds, or polymerization systems that are too viscous to be stirred effectively. Durka et al. [11], [12], for example, have shown temperature variations in a catalytic bed of roughly 50 °C over an 8 mm distance. Although non-uniform microwave heating may perform satisfactory in many applications – think of the prolific spread of domestic microwave ovens –, the above mentioned processes would require the spatial distribution of the microwave field to be known and controlled. The same requirement holds for reliable fundamental studies on microwave-chemistry interactions.

The cause of heating and temperature non-uniformity is often mentioned to be the limited penetration depth of microwave fields. More specifically, the field intensity is said to attenuate exponentially over a relatively short distance, so the outer edge of the reactor would experience a heating rate that is much higher than the center. The concept of penetration depth, however, is relevant only to the propagation of an electromagnetic field over a broad interface deep into an object, where width and depth should be considered in relation to the wavelength. For the typically used frequency of 2.45 GHz, the wavelength is 122 mm in air and 13 mm in water, which is of the same order of magnitude as typical glassware used in microwave enhanced chemistry research, so the condition mentioned above does not hold.

Field non-uniformity should be explained on the basis of the resonant nature of the microwave field in microwave cavity applicators. Resonance in this context is defined as the situation in which, for arbitrary points in space, waves are incident from more than one direction at the same time. The separate wave fields interfere, i.e. they combine constructively and destructively in an alternating pattern, thus forming a standing wave field. The behavior of resonant field patterns is highly spatially dependent and sensitive to the dimensions and materials involved. It is asserted herein that the resonant nature of the fields in microwave heating devices, currently used in microwave assisted chemistry research, makes the exact spatial electromagnetic field distribution difficult to determine and impossible to control and optimize.

The characteristics of heating with a resonant microwave field are demonstrated in this study by heating vials containing water in a single mode cavity (Discover, CEM corporation) [13]. We investigate this process via experiments and simulation. The heating device is one of the many commercial off-the-shelf lab-scale systems that have been developed for microwave assisted chemistry. It is a popular device as it is capable of rapidly providing heat without the need of a heat transfer surface or heat transport fluids, such as (open) flames, steam or heating oil. Importantly, it employs a resonant microwave field to heat loads that are placed inside it; therefore, it represents any resonant microwave field heating system. In practical terms this would include all microwave cavity heating devices, be these single mode or multimode cavities

Usually fiber optic temperature probes are used to measure temperature in microwave fields. In our study, we combine fiber optic probes with the use of temperature sensitive dyes (thermal fax paper). These methods are complementary; the sensors yield temporal temperature transients in a limited discrete number of points, whereas the fax paper reveals the shape of the regions in which a certain temperature is exceeded over an entire cross section. Fax paper has been used before to characterize patterns of microwave fields over the volume of resonant microwave cavities [14]. Its application in this study is, to our knowledge, the first attempt to evaluate the microwave field inside a liquid volume.

The simulation includes all relevant physics in the heating process under consideration: electromagnetic interactions, electromagnetic heat generation, convective and conductive heat transfer, and the fluid dynamics entailed with convection. Aside from the field distribution, we also aim at predicting the net microwave energy transfer towards the load. Therefore, we take into account the electromagnetic interactions over the entire microwave circuit, including the magnetron itself. Simulation studies of microwave processing systems have been done in the past. Robinson et al. [15] present a numerical study of a load that is being heated in the Discover. Their study indeed reveals complex field distributions; however, the complex forward and backward interaction between the microwave circuit in the Discover and the magnetron microwave source was not taken into account. Another simulation study by Zhu et al. [16] of a microwave heated continuous flow system reveals complex interactions as well. The authors present a model of a tube with foodstuffs flowing through it that is exposed to a microwave field by means of a cylindrical applicator cavity at a frequency of 915 MHz. Their study shows that the distribution of heating rate “strongly depends on the dielectric properties of the fluid in the duct and the geometry of the microwave heating system.” The interaction with the microwave source was not considered though.

In the present work, the investigated system (Discover) experiences rising temperatures and thereby varying dielectric medium properties, which are coupled back to the microwave source via the microwave field. Therefore, to correctly predict the microwave energy transfer, the resonant forward and backward interaction in the microwave circuit has to be accounted for. We do this via microwave network analysis. To the best of our knowledge, this is the first study to address this interaction in a microwave enhanced processing framework. In this paper, the layout of the microwave circuit in the Discover is explained first followed by experimental and numerical findings. Based upon these results, final conclusions are drawn with respect to the nature and applicability of resonant microwave fields for heating in chemical processes.