Cationic polyacrylamide (CPAM) emulsifier is widely applied in the wastewater treatment industry, mining industry, paper industry, cosmetic chemistry, etc. However, optimization of input parameters in the synthesis of CPAM by using the traditional approach (i.e., changing one factor while leaving the others fixed at a particular set of conditions) would require a long time and a high cost of input materials. Onsite mass production of CPAM requires fast optimization of input parameters (i.e., stirring speed, reaction temperature and time, the amount of initiator, etc.) to minimize the production cost of specific–molecular–weight CPAM. Therefore, in this study, we synthesized CPAM using reverse emulsion copolymerization, and proposed response surface models for predicting the average molecular weight and reaction yield based on those input parameters. This study offers a time–saving tool for onsite mass production of specific–molecular–weight CPAM. Based on our response surface models, we obtained the optimal conditions for the synthesis of CPAM emulsions, which yielded medium–molecular–weight polymers and high conversion, with a reaction temperature of 60–62 °C, stirring speed of 2500–2600 rpm, and reaction time of 7 h. Quadratic models showed a good fit for predicting molecular weight (Adj.R2 = 0.9888, coefficient of variation = 2.08%) and reaction yield (Adj.R2 = 0.9982, coefficient of variation = 0.50%). The models suggested by our study would benefit the cost–minimization of CPAM mass production, where one could find optimal conditions for synthesizing different molecular weights of CPAM more quickly than via the traditional approach.
Based on the refined theory, the edge stress state of an isotropic round plate of variable thickness under the influence of local load was considered. In constructing the mathematical model of the plate, three-dimensional equations of the theory of elasticity and the variation Lagrange principle were used. Displacements were represented in the form of polynomials along with the coordinate normal to the middle surface, which was two degrees higher than the classical theory of the Kirchhoff – Love type. The resolving system of equations includes eleven ordinary differential equations with variable coefficients. The solution of the formulated boundary-value problem was carried out by finite difference methods and matrix sweeps. The deformations and tangential stresses of the plate were determined from the corresponding geometric and physical equations of the elasticity theory. This article has been focused on identifying the stress state of the boundary layer type near rigidly and elastically fixed edges by the round plate where the destruction of thin-walled structural elements in machinery, including aviation and space technology, takes place.
The boundary treatment for modeling complex geometries in smoothed particle hydrodynamics (SPH) methods is always challenging, especially for objects with sharp corners. In this paper, we propose an improved boundary treatment technique to handle boundary conditions in the SPH method where objects are represented as implicit surfaces. The improved boundary treatment technique provides a full treatment for complicated geometries and can handle sharp edges without any special treatment. The boundary particles are uniformly distributed in compliance with the curvature of the objects, therefore taking into consideration the effect of the boundary. Several simulations are presented to validate and demonstrate the applicability and versatility of the proposed technique.
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