Modeling of bubble detachment in reduced gravity under the influence of electric fields and experimental verification

A simple model for predicting bubble volume and shape at detachment in reduced gravity under the influence of electric fields is described in the paper. The model is based on relatively simple thermodynamic arguments and relies on and combines several models described in the literature. It accounts for the level of gravity and the magnitude of the electric field. For certain conditions of bubble development the properties of the bubble source are also considered. Computations were carried out for a uniform unperturbed electric field for a range of model parameters, and the significance of model assumptions and simplifications is discussed for the particular method of bubble formation. Experiments were conducted in terrestrial conditions and reduced gravity (during parabolic flights in NASAs KC-135 aircraft) by injecting air bubbles through an orifice into the electrically insulating working fluid, PF5052. Bubble shapes visualized experimentally were compared with model predictions. Measured data and model predictions show good agreement. The results suggest that the model can provide quick engineering estimates concerning bubble formation for a range of conditions (both for formation at an orifice and boiling) and such a model reduces the need for complex and expensive numerical simulations for certain applications. a Major axis of spheroid (m) - a _m Measured bubble height (m) - b Minor axis of spheroid (m) - b _m Measured bubble width (m) - A, B, C, F Parameters of the Kumar-Kuloor model - a/b Computed aspect ratio - a _m /b _m Measured aspect ratio - D Orifice diameter (m) - E Magnitude of the electric field (V/m) - g Gravitational acceleration (m/s²) - g _t Terrestrial gravity (g _t = 9.81 m/s²) - N _w Electrical Weber number - p Pressure (Pa) - Q Volume flow rate (m³/s) - r Radius of the spherical bubble (m) - R Radius of curvature at the tip of the bubble (m) - t Time (s) - t Time interval (s) - T Temperature (°C) - U Electrical potential (V) - u Velocity (m/s) - V Volume (m³) - x, y Dimensionless coordinates of the Cartesian coordinate system - x, y Scaled coordinates, Cheng-Chaddock model - X, Y Dimensional coordinates of the Cartesian coordinate system - Characteristic wave number (m^–1) - Eötvös number - Absolute dielectric permittivity (F/m) - Contact angle (deg.) - Gibbs free energy (J) - Surface tension (N/m) - Dynamic viscosity (Pa s) - Density (kg/m³) - cr Critical value - d Detachment - eq Equilibrium - g Gas - K Refers to the Kumar-Kuloor model - l Liquid - m Measured value - t Terrestrial