The shape, size, density, and porosity of fluidized nanoparticle agglomerates (FNPAs) at the bottom of a fluidized bed were studied, the internal microscopic structures were revealed by the transmission electron microscopy observation of slices of the solidified FNPAs, and the drag coefficients were measured by the settling experiments. The results show that the distributions of diameter, density, and porosity all follow the Gaussian distribution. They have a similar hierarchical structure to FNPAs in the middle and upper parts of the bed. Primary nanoparticles connect to form aggregates of a few hundred nanometers, which then form simple agglomerates of several micrometers. The total porosities of FNPAs are in the range of 0.92−0.99, and the porosities between simple agglomerates, ε s,out , are in the range of 0.44−0.93. The values of the drag ratio, Ω, are larger than 1, around 1, and lower than 1 when values of ε s,out are in the ranges of ≤0.58, 0.58−0.77, and >0.77, respectively.
Microfinance institutions (MFIs) have attracted great attention, due to their significant role in poverty reduction. Given the features of MFIs, this paper proposes a novel hybrid model of soft set theory, and an improved order preference by similarity to ideal solution (HMSIT) to evaluate the sustainability of MFIs, considering accounting ratios, corporate governance factors, and macro-environmental factors, from a cross-country perspective. This setting enables the examination of the role of macro-environmental factors in the sustainability of MFIs. For this purpose, soft set theory is adopted to select optimal criteria. An improved order preference by similarity to ideal solution method, in which the weight of each criterion is determined by soft set theory, is proposed to rank the sustainability of MFIs. This algorithm enables HMSIT to make full use of various types of information. The case study uses cross-country samples. Results indicate that macro-environmental factors are significant in evaluating the sustainability of MFIs from a cross-country perspective. Particularly, they can play a key role in distinguishing MFIs with low sustainability. The results also indicate that HMSIT has strong robustness. Ranked results, produced from the proposed HMSIT are reliable enough to provide some managerial suggestions for MFIs and help stakeholders make decisions.
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