A number of viscosity and flow curve models can be used to numerically investigate the non-Newtonian behavior of fluids. Although particle size, grain size distribution and concentration play a crucial role in determining the viscosity and flow behavior of suspensions and colloidal systems, they are either ignored or considered indirectly in almost all models. We present a mathematical extension of the widely used Cross flow curve model to account for the effect of concentration and particle size in modeling viscosity and flow curves. In particular, this study takes into account a variable total number of individual particles in unit volume, which is assumed to be constant in other models. The proposed extension allows the flow curve to model suspensions that are typically shear-thinning but can also be Newtonian, or shear-thickening for at different shear rates and concentrations. These considerations provide insight into studying and designing suspensions, colloidal systems, and other complex fluid–solid interactions.
Due to climate change, the frequency and duration of meteorological drought have increased. In addition, local water supply capacity has not met water demand in many regions, which will eventually lead to serious water shortages. To mitigate the effects of drought on sustainable water use, it is necessary to understand how climate change affects regional water supply capacity and drought risk. To this end, this study evaluated the drought response capacity of regional water supply systems and assessed the comprehensive drought risk in terms of drought hazard, vulnerability, and response capacity. To avoid subjectivity in risk analysis, structural equation modeling was used to select primary indicators and probability and statistical methods were used to assign weights to the indicators. The changes in drought risk in different climate change scenarios were assessed using sensitivity analyses. The overall results indicate that the future drought risks in Gyeonggi, Gyeongsang, Chungcheong, Jeolla, and Gangwon are 18, 12, 13, 9, and 10% higher, respectively, than the current risk level. The sensitivity analyses showed that Jinju in Gyeongsang province, which has a high drought response capacity, had the largest decreasing rate in drought risk. The quantified changes in drought risk under future climate change scenarios will be useful for identifying areas with a high drought risk and making decisions about drought mitigation under climate change.


