Modelling  – the proximity effect

When experimenting with positioning of food items such as small potatoes, carrots, onions and meatballs in ready meal containers, it is not uncommon to experience so strong heating in the small contacting regions of such items that these may dry out or even burn. Two examples obtained by modelling are shown here. Spherical items with 16 mm diameter are exposed by a plane wave. The chosen diameter will provide a compromise between large and small surface areas being close.
The figures show two examples, with 1 mm distance between spheres with
ε =52–j20 (left) and 16–j4 (right). The amplitude settings are at the magenta boundaries, and the maximum level increases with decreasing distance between the items. There are thus two effects: a general increase of the power density with closer contact, and a sometimes drastic increase of the power density in the closest regions.
The heating in the closest regions must be caused by a concentration of the displacement current, due to the requirement on its continuity in the region. Ít can be shown that there is an effective capacitor surface area of the dielectric bodies – in the cases here of about  4×4 mm. The current-carrying capacitance will become almost 8 times smaller in the airspace than in the bodies with  ε = 52–j20 (left images). Thus, a distance in air of only ½ mm has the same capacitance as 4 mm inside the load. With ½ mm airspace between the dielectric surfaces there will then very roughly be a comparable heating effect in the body in general and locally by the additional capacitive coupling.
If the permittivity
ε of the spheres is instead 16–j4 (right images), the coupling phenomena would occur for larger distances between the items. This is also the case, as seen in the images.
The capacitance concept with unchanged capacitor area of the dielectric body would result in only about a doubling of the distance from the same effect. But a larger part of the lower-
ε bodies participate in the effect as indicated by the size of the affected regions. One may therefore conclude that the effective coupling distances are approximately inversely proportional to the permittivity, at least for typical small objects of spherical shape.
The heating of small regions may become very strong. They will then dry out and the capacitance will decrease and by that the effect – a negative feedback may occur. Even if burns or Maillard reaction discolouring may occur, fires will very rarely, if at all, start by the close contact effect. For that to happen, arcs between quite sharp edges or points of food substances containing parts with high fat or sugar content are needed.
It is stated in some literature that this and other phenomena are caused by an internal total reflection effect related to the internal standing waves and resonant patterns. However, the wavelength of the microwaves is comparable to the characteristic sizes of food items and these are furthermore so curved that geometric optics concepts are not applicable. The quasistatic capacitance concept provides sufficient coupling data for most practical purposes.