Bubble splitting in 2D gas‐solid freely bubbling fluidized beds is experimentally investigated using digital image analysis. The quantitative results can be applied for the development of a new breakage model for bubbly fluidized beds, especially discrete bubble models. The variation of splitting frequency with bubble diameter, new resulting bubble volumes, positions, and also the assumptions of mass and momentum conservation for bubbles after breakage are studied in detail. Small bubbles are found to be more stable than large ones and nearly all mother bubbles split into two almost equally sized daughter bubbles. The momentum of gas bubbles in the vertical direction remains approximately constant after breakage, whereas that of bubbles in the horizontal direction changes with no clear trend. The effect of fluidizing gas velocity in breakage frequency is also examined.

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American option prices under jump-diffusion models are determined as solutions to partial integro-differential equations (PIDE). In this paper a new combination of a time and spatial discretization applied to a linear complementary formulation (LCP) of the free boundary PIDE is proposed. First a coordinate stretching transformation is performed to the asset price so that the computation of the prices can be focused on regions of real interest instead of on the whole solution domain. An implicit-explicit time discretization applied to the reformulated LCP on a uniform temporal grid is followed by a spatial discretization to get a fully discrete system. The radial basis function (RBF) finite difference method is a local method resulting in a sparse linear system in contrast to global RBF-methods which lead to ill-conditioned dense matrix systems. For the corresponding European option we prove consistency, stability and second-order convergence in a discrete L2-norm. We derive mild conditions for the model parameters under which these results hold. Numerical experiments are performed with European and American options, and a comparison with numerical results available in the literature illustrates the accuracy and efficiency of the proposed algorithm.