In plasma technology, the plasma-liquid interaction is a significant issue. In this work, finite element methods are used to simulate a 2D dielectric barrier discharge and an arc discharge to investigate the simulation of discharge in spherical bubbles in the water that formed plasma-activated water. Different periods are examined to determine how the electron density changes with voltage, frequency, dielectric thickness, and bubble radius. The results demonstrated that increasing voltage, frequency, bubble radius, and decreasing dielectric thickness increase electron density linearly. The increasing rate of electron density by time evolution is investigated while voltage is constant in the generation of arc discharge. High plasma density indicates sufficient plasma-water interaction.topics: plasma-liquid interaction, plasma bubble discharge, arc discharge simulation
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