Simulation studies of nearest-neighbor distribution functions and related structural properties for hard-sphere systems

Molecular dynamics simulations have been carried out to investigate nearest-neighbor distribution functions and closely related quantities for the system of hard-spheres. The nearest-neighbor distribution function and the exclusion probability function were computed to examine the density dependence on the structural ‘void’ and ‘particle’ properties. Simulation results were used to access the applicabilities of various theoretical predictions based on the scaled-particle theory, the Percus-Yevick equation, and the Carnahan-Starling approximation. For lower density systems the three different approximations give the nearest-neighbor distribution functions which are very close to one another and also to the resulting simulation data. Among those theoretical predictions, the Carnahan-Starling approximation gives remarkably good agreement with the simulation data even for higher density systems. Also calculated is the nth moment of the nearest-neighbor distribution functions, in which the corresponding length scale is directly related to the measurement of the characteristic pore-size distribution.     

A modified Nukiyama-Tanasawa distribution function and a Rosin-Rammler model for the particle-size-distribution analysis

No fundamental mechanism or model enables a theory on particle-size distribution to be built. Consequently, a wide variety of empirical models or equations have been proposed to characterize experimental particle-size distributions, such as the Rosin-Rammler model. Because the Nukiyama-Tanasawa equation uses four parameters to simulate differential distribution frequencies for particle-size diameters, the distribution function is not easy to apply in order to fit experimental data. In this paper, a modification of the Nukiyama-Tanasawa model with only two parameters has been proposed to fit the data on a particle-size distribution (PSD). The proposed normalized distribution function has been applied successfully to the PSD analysis (cork granulate and spray atomization droplets).     

A novel feasibility analysis method for black‐box processes using a radial basis function adaptive sampling approach

Feasibility analysis is used to determine the feasible region of a multivariate process. This can be difficult when the process models include black‐box constraints or the simulation is computationally expensive. To address such difficulties, surrogate models can be built as an inexpensive approximation to the original model and help identify the feasible region. An adaptive sampling method is used to efficiently sample new points toward feasible region boundaries and regions where prediction uncertainty is high. In this article, cubic Radial Basis Function (RBF) is used as the surrogate model. An error indicator for cubic RBF is proposed to indicate the prediction uncertainty and is used in adaptive sampling. In all case studies, the proposed RBF‐based method shows better performance than a previously published Kriging‐based method. © 2016 American Institute of Chemical Engineers AIChE J, 63: 532–550, 2017     

A nonlinear inverse problem in simultaneously estimating the heat and mass production rates for a chemically reacting fluid

An Iterative Regularization Method based inverse algorithm is applied in the present study in simultaneously determining the unknown temperature and concentration-dependent heat and mass production rates for a chemically reacting fluid by using interior measurements of temperature and concentration.It is assumed that no prior information is available on the functional form of the unknown production rates in the present study. Thus, it can be classified as function estimation for the inverse calculations.The accuracy of this inverse heat and mass transfer problem is examined by using the simulated exact and inexact temperature and concentration measurements in the numerical experiments. Results show that the estimation of the temperature and concentration-dependent production rates can be obtained within a very short CPU time on a Pentium IV personal computer.     

A new method for the reconstruction of the particle radius distribution function from the sedimentation curve

A new method for the reconstruction of the particle radius distribution function from the sedimentation curve is proposed. This method permits us to obtain a continuous smooth distribution function. Two approaches are compared. The first approach is based on the calculation of the second derivative from the sedimentation curve. The second one is based on the solution of the original integral equation which describes a sedimentation process. Both of these approaches can be reduced to the problem of the solution of the Fredholm integral equation of the first kind. From the theory of integral equations, it is known that this problem is ill-posed. The usual methods lead to unstable solutions and we are forced to use special regularizing algorithms. In this paper, the Tikhonov regularization method is used to stabilize the solution of the integral equation. It is shown that the accuracy of both methods is higher than the accuracy of the graphical method, but the approach based on the solution of the original integral equation gives a more stable solution than that based on the derivative. The accuracy of the new method permits us to reconstruct the fine structure of the particle radius distribution function. Such an analysis cannot be carried out with the rough bar diagram obtained from the graphical method. The new method is absolutely indispensable in technology for controlling the degree of powder fineness.