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Plants, algae, and fungi are essential for nearly all life on earth. Through photosynthesis, plants and algae convert solar energy to chemical energy in the form of organic compounds that sustains essentially all life on earth. In addition, plants and algae convert the carbon dioxide produced by respiring organisms to oxygen that is needed for respiration. Fungi decompose complex organic compounds produced by respiring organisms so that molecules can be recycled in photosynthesis and respiration. Plants, algae, and fungi have one important feature in common, their cells have walls. Expansive growth and its regulation are central to the life and development of plant, algal, and fungal cells, i.e. cells with walls. In recent decades there has been an explosion of information relevant to expansive growth of cells with walls. Mathematical models have been constructed in an attempt to organize and evaluate this information, to gain insight, to evaluate hypotheses, and to assist in the selection and development of new experimental studies. In this article some of the mathematical models constructed to study expansive growth of cells with walls are reviewed. It is nearly impossible to review all relevant research conducted in this area. Instead, the review focuses on the development of mathematical equations that have been used to model expansive growth, morphogenesis, and growth rate regulation of cells with walls. Also, relevant experimental findings are reviewed, conceptual models are presented, and suggestions for future research are proposed. The authors have attempted to provide an overview that is accessible to researchers that are not working in this field.

A planar simulation of film boiling and bubble formation in water at 373°C, 219 bar on an isothermal horizontal surface was performed by using a volume of fluid (VOF) based interface tracking method. The complete Navier-Stokes equations and thermal energy equations were solved in conjunction with a interface mass transfer model. The numerical method takes into account the effect of temperature on the transportive thermal properties (thermal conductivity and specific heat) of vapor, effects of surface tension, the interface mass transfer and the corresponding latent heat. The computations provided a good insight into film boiling yielding quantitative information on unsteady periodic bubble release patterns and on the spatially and temporally varying film thickness. The computations also predicted the transport coefficients on the horizontal surface, which were greatly influenced by the variations in fluid properties, compared to calculations with constant properties.

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