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The shape and rising behavior of the horizontally arranged twin bubbles in a steady liquid are experimentally studied employing high-speed photography and digital image processing, and numerically studied by the Volume-Of-Fluid (VOF) method, in combination with a momentum equation coupled with a surface tension model. The movement trajectory and the velocity variation in horizontal and vertical directions of the horizontally arranged twin bubbles rising side by side, as observed in experiments, are described. According to the results, when two bubbles rise side by side, their horizontal velocity changes by the simple harmonic law; there is a cyclical process of two bubbles repeatedly attracted to and bounced against each other, rather than at constant distance between each other, and the bubbles swing up and down periodically in the water. The mathematical model and its numerical implementation are presented in detail. The validation of the model is confirmed by comparing the numerical and experimental results, which are in good agreement with each other; the numerical simulation can accurately reproduce the deformation, attraction, and repulsion of the bubble pairs. The phenomenon of attraction and repulsion is comprehensively analyzed from the viewpoint of a flow field. It is considered that the interaction between the bubbles is mainly influenced by the changes of the flow field due to vortex counteraction and wake merging effects.

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Based on the design of the general Chebyshev bandpass filter with finite transmission zeros the filter simulation model has been established according to the calculated couple matrix. Combining EM software with an optimization method, the size of the duplexer has been optimized and designed by using the group delay fitting method.The test results show that the insertion loss of the proposed duplexer is less than 1.5dB, the VSWR is less than 1.5, the band-stop-rejection is greater than 85dB. The measured curves agree well with the design specifications and the correctness of this method has been verified.

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