The results of two-dimensional modelling of positive streamer dynamics in 2 cm point-to-plane gap are presented, including the process of photoionization in a gas volume. The model of photoionization in air, developed by Zhelezniak, Mnatsakanian and Sizykh is considered in detail and a comparison with the experimental data of Penney and Hummert is presented. The model of photoionization in nitrogen, based on the data of Penney and Hummert is described. The simulations of streamers were performed for air and nitrogen-like gas. It is shown, that fundamental space scale of streamer - the width of space charge layer lρ (ionization domain) around its head is defined by the length of absorption of photoionizing radiation la. This length defines all other parameters: electron density, radius of streamer channel etc, so one may speak about standard streamer in air, whose properties depend only on pressure. Based on simulation results one may assume that streamer branching occurs in high field, when lρ exceeds la. The process of branching may be interpreted as an instability which transforms the non-standard streamer into a number of standard ones.

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The results of a two-dimensional simulation of a cylindrically symmetric positive streamer in atmospheric pressure air between parallel plate electrodes are reported. A hydrodynamic diffusion-drift model was used. The results show that the streamer radius and velocity grow exponentially in time. We have found that the main parameter which governs streamer propagation is the width of the space charge front R ρ . It is shown that: (i) the field at the tip of the streamer is equivalent to the field of a charged ball of radius R ρ ; and (ii) the streamer velocity is proportional to R ρ , as previously predicted by Loeb [1]. The mechanism of streamer propagation is discussed. It is shown that positive streamer advancement occurs due to avalanche multiplication of primary photoelectrons in the narrow layer of the width R ρ ahead of the streamer.The energy delivered by the power supply is calculated. This energy accumulates as electrostatic energy of the space charge envelope around streamer channel. The energy increases exponentially in time and reaches 10 2 J when the streamer radius is about 20 cm.

Model of water transport in a membrane electrode assembly of a polymer electrolyte fuel cell ͑PEFC͒ is developed. The model takes into account nonlinear diffusion of liquid water in the membrane. It is shown that nonlinearity leads to the formation of closely located dry and wet regions in the membrane. The model is incorporated into our quasi-3D model of a PEFC and recent experiments of Bu ¨chi and Scherer are simulated. The model qualitatively reproduces measured membrane resistance and the mean profile of water content across the membrane. Calculated two-dimensional distribution of water in the cell cross section is discussed.