The first US pattern for reheating of foodstuff in a multimode microwave oven was filed in 1945 [1]. Today’s domestic multimode microwave ovens use a free-running cavity-magnetron operating a frequency of f_o = 2.45 ± 0.05 GHz (free space wavelength, λ_o ~ 12.2 cm) as the energy source. At this frequency, the microwave photons have insufficient energy to break molecular bonds and for this reason the electromagnetic radiation is considered to be non-ionizing [2] [3] [4]. However, bio-materials (carbohydrate, protein, and vitamin and enzymes) placed within a microwave electromagnetic field undergo a rapidly changing complex permittivity (ε* = ε' −jε'') that is thought to induce translational and rotational motion effects [3] [4] [5]. Some of the earliest reports of domestic multimode microwave oven use for “non-thermal” microwave-assisted continuous flow treatment of bacteria by Kozempel et al. (1998) [6], Kozempel et al. (2000) [7], and Shazman et al. (2008) [8] in food processing and microbiology journals. Notably, researchers at the Department of Microbiology and Immunology, UBC, Canada have played a major role in the development of batch “non-thermal” microwave-assisted inactivation process, where ice and ice slurry baths are used to regulate the temperature of: bacteriophage Wang et al. (2001) [9], Baines (2005), Bryant et al. [10] (2007) [11] and; Gram-negative vegetative E. coli Barnett et al. (2006) [12], and Assay et al. (2008) [13]. However, the description of the microwave-assisted cooling baths was brief (66 to 213 words), and without diagrams, or photographs: making it difficult to understand the complexly of the volumetric heating process. In addition, in [6] - [13] microwave assisted treatments, the ambiguous term “non-thermal” or “athermal” began to be used in an attempt to differentiate dielectric volume heating and electrical conductive (Ohmic) heating [14] - [23], from possible direct microwave interaction with specific microorganisms. In the later two references, Hayes (2004) [22] and Hayes and Collins (2005) [23] changed the cooling medium from ice baths to forced air cooling of the outer surface of the reaction vessel in organic and biochemistry synthesis, where the technique is known as enhanced microwave synthesis (EMS), a method that produces higher yields and shorter processing times as compared to classic thermal treatment. The generally accepted view (but still controversial) is that within the microwave irradiation period itself, selective heating of polar and ionic molecules (lipids, proteins, carbohydrates, DNA) within microorganism cytoplasm and cell wall membrane reach a high local instantaneous temperature (T_i) causing specific heat transformations that lead to cell lysis. “Non-thermal” effects (bulk temperature (T_B) at < 40˚C) are claimed to be associated with direct microwave interaction that cause: electroporation [5] [7] [9] [10] [11] [12] [24], cell rupture [7] [9] [10] [11] [13] and disruption at the metabolic and genetic [3] [5] [7]. The obscuring or masking of the underlying “non-thermal” (where T_B ≪ T_i) by “thermal” effects, both in time and space are thought to occur particularly in continuous liquid flow experiments [6] [7] [8] and continuous aerosol flow [25] [26], or indeed in inorganic chemistry syntheses [3] [22] [23] [27] [28].

Wang et al. (2019) [29] demonstrated microwave inactivation of Gram-negative vegetative E. coli was more efficient in airborne environments as compared to liquid suspensions. In their conclusion it was considered that volumetric heating was the main mechanism in the liquid suspension phase, whereas microwave photon is able to react directly with vegetative E. coli, thereby indicating a “non-thermal” microwave effect.

From 2000, domestic and industrial microwave ovens were employed in batch microwave oven generated steam (MGS) decontamination of N95 respirators that were inoculated with influenza virus and bacteriophage MS2 [30] - [34]. With regard to these batch MGS decontamination studies, two studies by Law and Dowling (2021) [35] [36] were published on thermodynamics and dielectric analysis of the MGS decontamination process. Siddharta et al. (2016) [37] also reported on a microwave oven (rated at 800 W continuous wave (CW)) that was employed in the batch microwave-assisted inactivation of the hepatitis C virus (HCV) and human immune deficiency virus (HIV).

For volumetric heating of homogenous dielectric materials, Geedipalli et al. (2007) [38] used a physics-based model to map in 4-dimensions (x, y, z, and t) batch microwave oven heating uniformity of potato, and Yeong et al. (2017) [39] has also used COMSOL software studies for distilled water. Building on this work, Lee et al. (2020) [40] used OpenFoam software to reveal that under pulsed modulated conditions (T_on = 10 seconds and T_off = 20 seconds) an increase in the average water flow velocity in the initial T_on period then fluctuates downwards in the following T_off period. Similarly the temperature standard deviation rises in the first T_on period then steadies in the following T_off period. Over the next modulated 60 seconds, the temperature standard deviation increases in a step-like behavior while flow velocity falls in similar step-like behavior. The overall effect is to improve heat uniformity throughout the water volume when compared to CW mode of operation. Therefore, truncating the T_off period (t → 0) will induce the CW mode and breakdown heat uniformity. In effect, if heat uniformity is important to the user, the duty-cycle (D) should be used, although a longer microwave irradiation time will be required. From this perspective, pulse modulated operation may induce “non-thermal” microwave transformations in the T_off period.

In 2022, four microwave-assisted review articles, with a primary focus on the removal of harmful microorganisms in food processing and the environment were published. Kubo et al. (2022) [41] reviewed microwave (300 MHz to 300 GHz) and Ohmic heating of microorganism, food proteins, and enzymes. The authors rightly discuss the challenges in comparing mono-mode with multimode experiments, in particular temperature uniformity within multimode microwave ovens hot spots and temperature profile, and the measurement thereof whilst simultaneously removing heat during the irradiation process. It was noted that the complex heterogeneous nature of food (i.e. tomatoes, grapes, and juices etc.) have food elements of dimensional scale that influence the microwave electric field and hence mask “non-thermal” effects. From this perspective simple model systems need to be developed and experiments well documented for reliable conclusion on the expectance and extent of “non-thermal” effects. Similarly, Gut [42] wrote a letter to the editor of Food Chemistry with a Response to “non-thermal” conceptual and methodological problems [43]. In the letter he presents an optimistic and constructive approach to explore “non-thermal” effects in broader range of electric field frequencies and strengths, through experiments or simulations, and to collaborate with the advance of emerging technologies, such as Ohmic and PEF, in the food processing sector. Notable, Zhang et al. [44] discussed the possibility of destroying biofilms and antibiotic resistance bacteria by microwave irradiation.

In these publications [41] [42] [43] [44] there was no direct reference to the domestic microwave oven pulsed width modulated (PWM) waveform that controls the power time period (T_on) and power off (T_off) time periods of the cavity-magnetron, where increasing T_on results in a decrease in T_off. This is a key aspect of microwave-assisted processing as it provides macro control of the cavity-magnetron applied power that is suitable for heating of foodstuff and water, and less sensitive chemical procedures such as digestion and moisture analysis [23]. This oversight is unfortunate, as it well known that homogeneous microorganism populations follow a first-order rate law inactivation behavior, and a heterogeneous population invariably does not [45]. Given that many historical studies of microwave oven microwave-assisted disruption and inactivation studies of homogeneous bacteria and virus populations [9] - [20] [30] - [34], Law and Dowling (2022) [46] [47] data mined these studies to map the microorganism resilience to microwave stress on to a energy phase-space projection for a specific fomite. The range of fomites being: moist face towels, cotton swabs, kitchen sponge, and scrubbing pad, syringes, and cigarette filters and N95-like respirator. Their results found that in either linear-linear or log-linear projection, the process energy budget (measured in kJ) is plotted on the horizontal axis and the energy density (kJ·ml⁻¹) plotted on the vertical axis, while inactivation reduction is compressed to ≥4 log₁₀. Here, an inactivation reduction of ≥4 log₁₀ is used as a measure of resilience before the fomite-microorganism system moves into a different region of state space when subjected to stress, Carpenter et al. (2001) [48], and Cumming and Coiler (2005) [49]. Figure 1 shows the results for:

Gram-negative vegetative E. coli, Gram-positive B. cereus, Gram-positiveB.subtils, HCV, HIV, and H1N1 for different fomites of varying dielectric properties. The figure reveals that the majority of Gram-negative E. coli data points are clustered in the low 20 to 100 kJ process energy budget region, whereas the remaining data points lay along specific volume-trend lines.

Over lapping the publication time period of [46] [47], Su et al. (2022) [50] used the specific form of power absorption efficiency (PAE) that equates to the ratio of the power used to heat the material to the input power) to define energy utilization efficiency of microwave oven heating of dielectric porous materials, i.e. not-ready-to eat products. In addition, they showed that for binary dielectric materials, relative position and geometry may interfere with and shield the local electromagnetic fields. From this it is reasonable to assume that the baths thermal conduction rate may also be affected. It is self-evident that there are many areas in the research described in [46] [47] [50] overlap and would thus benefit in further development in medium and geometry.

In 2022, Bazana et al. [51] published a study on batch thermal microwave-assisted inactivation of Candida spp. in a 25 ml agar plated Petri dish. The study used an Electrolux ME28S microwave oven a (rated at 900 W CW, illuminating a 28 L oven cavity [52] ) and exposure time of 40 seconds. For this irradiation time, the process energy budget = 36 kJ and energy density = 1.44 kJ·ml⁻¹. This would indicate that Candida spp. in agar suspension has a similar microwave stress behavior to that of Gram-negative vegetative E. coli in liquid suspension.

The aim of this work is to bring to the attention of American Journal of Analytical Chemistry readers the complex thermal and microwave interaction within “non-thermal” microwave-assisted volumetric heating of ice and ice slurry bath that constitutes a binary dielectric mixture, within multimode microwave ovens. To achieve this objective, the reconstructed experiments are described here using detailed text description, diagrams, and photographs. A non-invasive acoustic recording of the time-modulated cavity-magnetron and its control relays with a 20 liter Bluesky; model BMG20-8, cavity, rated at a 2.45 GHz, 800 W CW is used. This approach enables researchers to characterize the microwave oven applied power with minimum electrical expertise. The measurement technique is combined with standard thermal temperature measurement and calorimetric analysis of “non-thermal” microwave-assisted heating of fixed quantity of tap-water under both internal and external cooling conditions. Section 3 describes the calorimetric and acoustic calibration of the microwave oven. In section 4, this knowledge is use to experimentally compare suspension time-dependent temperature profiles of “non-thermal” microwave-assisted experiments pertaining to bacteriophage [9] [10] [11] and Gram-negative vegetative E. coli [12] [13]. In these experiments, a standardized 10 ml of tap-water is used to represent a thermal equilibrated microorganism suspension that is cooled using either an internal ice bath, or external crushed ice or ice slurry bath whilst being microwave irradiated for process times from 0 to 40 s. To separate out thermal heat transfer (conduction) pathways to and from the suspension volume a further set of experiments using four separated water dummy-loads is performed. Section 5 provides an energy phase-space projection and electric field strength analysis of this work. Section 6 provides a summary of the reconstructed “non-thermal” microwave-assisted experimental results and their impact on the historical “non-thermal” microwave-assisted inactivation of microorganism experiments [9] - [13], and outlook for both experiments and simulation.

The domestic microwave oven is primarily designed to defrost and heat foodstuff using a free-running cavity-magnetron operating a frequency of f₀ = 2.45 ± 0.05 GHz [1] within a multimode cavity. In many cases of these relatively low cost (60 to 70 euro in 2022) appliances, the cavity-magnetron, and its cathode filament heater, normally employs a Feinberg voltage-doubler drive circuit [53] that is turn-on and turn-off at the step-up side of the microwave oven transformer (MOT) using a PWM circuit. Figure 2 depicts such a circuit with the position

of the PWM circuit board. For further details of this circuit and other cavity-magnetron drive circuits see [54].

The centrifuge tube-in-tube system was first used by Wang et al. [9] as a cooling mechanism in “non-thermal” microwave-assisted microorganism inactivation experiments; Baines [10] further developed this procedure. In these experiments the internal tube contained solid ice, with the annulus between the tubes containing the microorganism suspension. These systems, however, were found to produce inconsistent microorganism inactivation results due to small quotients of suspension volume and poor thermal contact between the coolant and suspension. Bryant et al. [11] and Barnett et al. [12] replaced the internal bath for an external crushed ice bath and increased the suspension size, in doing so improving thermal contact and measurement reproducibility. In the final series of experiments, Asay et al. [13] used an external ice water slurry bath to regulate the temperature of an intermediate water bath that was in contact with a Petri dish that contained the microorganism suspension. This complex arrangement is henceforth termed a “double bath system”. The five publications [9] - [13] hold a rich source of experimental data spread over three domestic microwave ovens. However as with most experiment parameters reported on similar subject matter by different authors, experimental conditions were not reported in a consistence manner. Table 2 lists the experimental parameters as reported by the five papers. The: * indicate secondary source information obtained from on-line manuals, and the ** indicates complete information is unavailable. The grey colored cells indicate the need for further experimental measurement investigation.

This section describes the use of energy phase-space projection to map the “non-thermal” microwave-assisted 10 ml pseudo-suspension experiments, thereby allowing a direct comparison with the thermal microwave-assisted microorganism inactivation (≥4 log₁₀) experiments present in Figure 1. The result of this mapping is given in Figure 9: with a horizontal-axis of 0 to 30 kJ, and a vertical-axis of 0 to 10 kJ·m⁻¹. The comparison thermal data corresponds to the 39 L Sharp microwave oven S630D rated at 1050 ± 50 W CW [16], and the 28 L Electrolux microwave oven ME28S rated at 900 W CW [51]. The ≥4 log₁₀ inactivation microorganisms are Gram-negative vegetative E. coli, bacteriophage MS2 [16] and Candida spp. agar plated Petri dish [51].

The first feature of note in Figure 9 is that the 10 ml “non-thermal” experiments data points are aligned on the 10 ml dotted trend-line, which is closely matched to the thermal microwave-assisted 10.93 m dashed trend-line. Within the “non-thermal” data set, the tube-in-tube system (x) outcome is positioned between the beaker-Petri dish with no dummy-load (+) and the beaker-Petri dish with dummy-load (o). The projection mapping also shows there is a clear experimental separation between the 10 ml and 10.93 and the 64 ml trend-line. This mapping resolution is sufficient to enable the 25 ml Candida spp. agar plated Petri dish data point to be displayed clearly.

The energy ranking for the “non-thermal” experiments may be rationalized by considering the geometry of the baths and dummy-load. Firstly the tube-in-tube system presents a narrow external vertical suspension column that is directly exposed to the microwave energy. This design feature is in contrast to the beaker-Petri dish systems where the suspension is surrounded by the crushed ice. Secondly the separated dummy-load (four 50 ml of crushed ice) that have lowest energy density values indicating that some of the applied 800 W is absorb directly by the dummy-loads themselves. These observations point to preferential volumetric heating of the suspension depending on whether an internal or external ice bath is employed. In the case of the internal ice bath, the suspension is directly illuminated, whereas the external ice bath suspension provides a shielding effect [50]. The absence of microwave irradiation in the duty cycle T_offperiod (where slow thermal conduction processes are present) induce a retardation of the suspension heating rate leading to a complex time-dependent suspension temperature profile, Rougier et al. (2014) [63], and Law and Dowling (2022) [46].

It is generally claimed that “non-thermal” microwave-assisted effects arise from the microwave electric field imposing a transmembrane electric potential. At low potentials hydrophobic nano diameter pores are reversibly generated that cause cell material leakage. Above a critical potential, however, membrane dielectric breakdown occurs causing an uncontrolled and irreversible cell material leakage, leading to cell lysis [5] [7] [9] [10] [11] [12] [24]. It is useful therefore to have an estimation of the instantaneous electric field strength (E, measured in V·m⁻¹) within the microwave oven. From a dielectric volume heating perspective, the instantaneous microwave electrical absorbed power per unit volume (P_v, measured in V·m⁻³) is proportional electric field within the sample volume, (2) [2] [38] [39] [40] [55] [63] [64].

P v ~ 2 π f o ε o ε ″ E r m s 2 (2)

where 2 π f o ε o ε ″ represents the effective dielectric conductivity (σ, measured in S·m⁻¹), ε_o is the permittivity of free space (8.8542 × 10⁻¹² F·m⁻¹), ε ″ is imaginary part of the complex permittivity of the load that decreases with temperature due to the increasing mobility of the water ionic component [36] [65] [66]. The E squared factor is derived that from the Ohms power Law (P = GV², where G is the inverse of R). Finally, the E_rms represents the root mean square of the electric field at the sample location. It is noted that there are a number variants of E in published literature, where the rms term is replaced by the effective square of the average electric field [2], or is removed and then dividing σby 2 [38], or replacing E_rmswith the E vector when spatiotemporal mapping of E [39] [40] [50] [55] and [63], and finally omitting the rmsvalue, as it does not take in to account electromagnetic focusing, or hot spots within a multimode microwave oven [64].

Equation (2) however does require a knowledge of the tap-water ε ″ value as a function of temperature, that may be found in published tables [64] and graphs [65]. In the case of graphs, digitalization software can be used to accurately reverse-engineer the visual information. For the “non-thermal” microwave-assisted Bluesky oven and thermal microwave-assisted Sharp oven data Figure 8, Table 6 provides the calculated ε ″ , σ, and E_rms values.

Figure 10 shows the suspension temperature (horizontal-axis) plotted against ε ″ (vertical-axis), where the 5 point trend-line equates to y = 0.461x + 8.799 with an R² = 0.9933. Using this strong linear association between suspension temperature and E, it is reasonable to extrapolate between the 800 and 1050 W data points to find the unknown suspension temperature and E in the Electrolux 900 W 25 ml Candida app. experiments. The first step in this extract process is to assume the 900 W parameters lay on the initial trend-line (without altering R²) and between the 800 and 1050 W dataset points. For a corresponding temperature range between 60˚C to 70˚C this yields an E_rms value of 36.8 to 41.2 V·ml⁻¹, see diamond points in Figure 10. The second step is to insert these values in to Equation (2) to obtain values for ε ″ and σ Table 7.

Historical (2001 to 2008) [9] - [13] multimode microwave oven “non-thermal” microwave-assisted inactivation of microorganism experiments have been revisited by reconstructing the experiments within a domestic microwave oven (Bluesky model BMG20-8). The outcome of reconstructed experiments are analyzed using thermodynamic and electrical engineering tools, and described with detailed text, diagrams, and photographs. A novel non-invasive acoustic measurement is used to access the ovens cavity-magnetron time-modulated waveform information (T_on, T_off, time-base, and duty cycle). Being non-invasive and using standard acoustic software, the measurement is easy to implement by non-electrical engineers. For an 800 W CW rated cavity-magnetron, the following experimental observations are noted:

1) The cavity-magnetron warm-up period (3 to 4 s) can influence output power within the initial base-time period, typically 30 s of the process time. For example, where a selected process time of 20 s [9] [10], or 40 s [11] [12] and [13] > twice the base-time, the cavity-magnetron CW rated power multiplied by the microwave illuminated time may provide a more accurate value when calculating the process energy budget, rather than averaged duty cycle power (supplied by the manufacture) multiplied by the process time.

2) It is noted that an internal ice bath [8] [10] result in the suspension being directly exposed to microwave illumination, whereas an external ice bath [11] [12] [13] provide a degree of shielding [50] that retards the time-dependent heating profile.

3) Separated water dummy-loads isolate and control thermal heat transfer (conduction) to and from the suspension, thereby diverting a portion of the cavity-magnetron rated power away from the suspension.

4) Dual water bath reconstruction experiments with a minimum of 200 g of ice with a ratio 1:1 to tap-water is sufficient to stabilize a 10 ml suspension temperature between 26˚C to 27˚C. The experiments reveal a complex heat pathway between the crushed ice and water within an ice slurry bath. In addition between the ice slurry bath and the intermediate water bath, where the main heat absorbing element, or dummy-load, is the crushed ice slurry bath.

5) Energy phase-space projection has been employed to analysis the “non-thermal” microwaves-assisted information. This approach enables the data to be directly compared with thermal microwave-assisted data. For close neighborhood data (800 to 1050 ± 50 W, and 10 ml to 64 ml suspension volumes, comparative values of E_rms have been calculated (22 to 41.2 V·m⁻¹).

6) It is noted that multiplying E_rmsby factor of 2.82 yields apeak-to-peak value. However, this would assume that the coherent sinusoidal wave in the cavity-magnetron TE₁₀-mode waveguide is the same in the ovens multimode cavity. This is not the case as the transverse electric (and magnetic) field structure becomes incoherent due to reflections from complex load and multiple reflections from the cavity wall influence the cavity auto-matching resonant frequency that is bounded by the free-running frequency bandwidth of the cavity-magnetron (2.45 ± 0.05 GHz).

The paper has highlighted number of dielectric volumetric heating issues that would benefit from further investigation.

1) For “non-thermal” microwave-assisted inactivation of homogenous microorganism populations require a process time of 20 to 40 s, it would be useful to have detailed recording measurements of T_on, T_off, time-base, and suspension parameters (volume and temperature) that can be matched to scanning electron microscope, transmission electron microscope, or atomic force microscope imaging plus cell leakage analysis.

1) The use of energy phase-space projections combined with 3-dimasional computer modeling of the electric field strength within a complex load, as a function process time (0 to 40 s) may reveal real and not yet studied microwave induced thermodynamic and electromagnetic effects.

3) Such a multidiscipline investigation would advance the understanding of microwave-assisted induced cell membrane disruption that leads to cell lysis.

The authors declare they have no conflicts of interest.

Law, V.J. and Dowling, D.P. (2023) Revisiting “Non-Thermal” Batch Microwave Oven Inactivation of Microorganisms. American Journal of Analytical Chemistry, 14, 28-54. https://doi.org/10.4236/ajac.2022.141003