Shape reconstruction of axisymmetric Taylor bubbles using conductivity probes through a scheme of combined experiment and theory

A simple measurement scheme is proposed to reconstruct the geometry of an axisymmetric void propagating through a conducting liquid using a pair of parallel wire conductivity probes. An experimental study allows for obtaining the time variation of the resistance of the film surrounding the void. Analytical modeling and numerical simulation has been adopted to correlate the resistance between the wire electrodes and the film thickness. Finally, the shape of the void can be estimated by combining the predicted resistance-film thickness relationship and the measured time variation of resistance. For validation, this scheme has been used to reconstruct the shape of a rising Taylor bubble. There is a fair match between the reconstructed shape of the bubble and its photographic image. The probable errors in the measurement scheme have been discussed and assessed mathematically.