Time development of a cylindrical channel generated by spark discharge in water

Electrical discharges in liquids are on one side a parasitic phenomenon in high voltage techniques, where some liquids are used as an excellent isolating medium, on the other side they are demanded source of free radicals, shock waves, and strong visible and UV radiation. Besides that, electrical discharges in liquids are used for underwater cutting and welding, for biological applications (e.g. water sterilization), for decomposition of water pollutants, for synthesis of metamaterials (metaliquids), for production of carbon nanotubes and other nano- and micro- particles. Shock waves (after focusing) are used for extracorporeal lithotripsy, for grinding of rocks, and for cleaning or deforming of materials. Optimization of shock wave generation means to find conditions, on which the transformation of electrical energy deposited in the discharge into mechanical energy of expanding cylindrical channel (generated by spark discharge) is the most efficient. For description of this process, we use a difference method, when in each time-step the discharge channel is not only Ohmically heated (externally given, or experimentally measured source function), but also cooled by emitted radiation (Stefan-Boltzmann law), and by out-conducted heat (Fourier law); these last two processes simultaneously heat and evaporate the surrounding liquid. Moreover, the pressure gradient drives the spark channel boundary outside (Navier-Stokes equation), which results in channel expansion as well as in its further cooling. This model will be compared with earlier models developed by Naugolnykh and Roy, by Braginskii, and by Engel, and with resent experiments. (author)