The time-irreversible cell enlargement of plant cells at a constant temperature results from two independent physical processes, e.g. water absorption and cell wall yielding. In such a model cell growth starts with reduction in wall stress because of irreversible extension of the wall. The water absorption and physical expansion are spontaneous consequences of this initial modification of the cell wall (the juvenile cell vacuolate, takes up water and expands). In this model the irreversible aspect of growth arises from the extension of the cell wall. Such theory expressed quantitatively by time-dependent growth equation was elaborated by Lockhart in the 60's.The growth equation omit however a very important factor, namely the environmental temperature at which the plant cells grow. In this paper we put forward a simple phenomenological model which introduces into the growth equation the notion of temperature. Moreover, we introduce into the modified growth equation the possible influence of external growth stimulator or inhibitor (phytohormones or abiotic factors). In the presence of such external perturbations two possible theoretical solutions have been found: the linear reaction to the application of growth hormones/abiotic factors and the non-linear one. Both solutions reflect and predict two different experimental conditions, respectively (growth at constant or increasing concentration of stimulator/inhibitor). The non-linear solution reflects a common situation interesting from an environmental pollution point of view e.g. the influence of increasing (with time) concentration of toxins on plant growth. Having obtained temperature modified growth equations we can draw further qualitative and, especially, quantitative conclusions about the mechanical properties of the cell wall itself. This also concerns a new and interesting result obtained in our model: We have calculated the magnitude of the cell wall yielding coefficient (T) [m<sup>3</sup> J<sup>-1</sup>•s<sup>-1</sup>] in function of temperature which has acquired reasonable numerical value throughout.
Flux-limiting and non-linear solution techniques for simulation of transport in porous media
