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In industrial processes, monitoring of heterogeneous phases is crucial to the safety and operation of the engineering structures. Particularly, the visualization of voids and air bubbles is advantageous. As a result many studies have appeared in the literature that offer varying degrees of functionality. Electrical impedance tomography (EIT) has already been proved to be a hallmark for process monitoring and offers not only the visualization of the resistivity profile for a given flow mixture but is also used for detection of phase boundaries. Iterative image reconstruction algorithms, such as the modified Newton-Raphson (mNR) method, are commonly used as inverse solvers. However, their utility is problematic in a sense that they require the initial solution in close proximity of the ground truth. Furthermore, they also rely on the gradient information of the objective function to be minimized. Therefore, in this paper, we address all these issues by employing a direct search algorithm, namely the Hooke and Jeeves pattern search method, to estimate the phase boundaries that directly minimizes the cost function and does not require the gradient information. It is assumed that the resistivity profile is known a priori and therefore the unknown information will be the size and location of the object. The boundary coefficients are parameterized using truncated Fourier series and are estimated using the relationship between the measured voltages and injected currents. Through extensive simulation and experimental result and by comparison with mNR, we show that the Hooke and Jeeves pattern search method offers a promising prospect for process monitoring.

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A capacitance method is applied to measure the space-averaged void fraction in concentric annular flows. From the analytical solution of the governing electrical field equations, the expression for the capacitance in terms of a given void fraction is derived. Also, a closed form formula to predict the void fraction from the capacitance measurement is proposed. The relationship between the capacitance and the void fraction is successfully compared with static phantom experiments.