Abstract
In this paper, we present a model that is based on near–far-field charged bubble formation and transportation in an underlying dielectric liquid. The bubbles are controlled by the dielectric liquid, which is influenced by an external electrical field. This allows us to control the shape and volume of the bubbles in the dielectric liquid, such as water. These simulations are important to close the gap between the formation of charged bubbles, which is a fine-scale model and their transport in the underlying liquid, which is a coarse-scale model. In the fine-scale model, the formation of the bubbles and their influence of the electric-stress is approached by a near-field model, which is done by the Young–Laplace equation plus additional force-terms. In the coarse-scale model, the transport of the bubbles is approached by a far-field model, which is done with a convection-diffusion equation. The models are coupled with a bubble in cell scheme, which interpolates between the fine and coarse scales of the different models. Such a scale-dependent approach allows us to apply optimal numerical solvers for the different fine and coarse time and space scales and help to foresee the fluctuations of the charged bubbles in the E-field. We discuss the modeling approaches, numerical solver methods and we present the numerical results for the near–far-field bubble formation and transport model in a dielectric carrier fluid.
Highlights
We are motivated to model bubble formation and transport in dielectric liquids, which are applied in controlled production of gas/plasma bubbles in chemical, petrochemical, plasma or biomedical processes, see [1,2,3,4].The benefit of additional particles or charged-bubbles in the dielectric carrier fluids are that they can influence their fluid behavior or have additional reactions in the fluid, see [5] or [6]
We concentrate on the first applications, we model the influence of the bubbles in a dielectric carrier fluid, such as water
We are able to use the additional influence of the electrical field to the dielectric liquid, which can be modeled with the Maxwell stress tensor, see [27]
Summary
We are motivated to model bubble formation and transport in dielectric liquids, which are applied in controlled production of gas/plasma bubbles in chemical, petrochemical, plasma or biomedical processes, see [1,2,3,4]. The macroscopic model is done with a transport model based on an advection equation, where the most standard solver approaches are: Volume-of-fluid (VOF) methods: the VOF function presents the fraction of the volume in the grid cells, which is occupied by one of the two fluids. This is modeled with an advection equation.
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