Modeling the Batch Sedimentation of Calcium Carbonate Particles in Laboratory Experiments-A Systematic Approach

The design of continuous thickeners and clarifiers is commonly based on the solid flux theory. Batch sedimentation experiments conducted with solid concentrations still provide useful information for their application. The construction of models for the velocity of settling allows the estimation of the flux of solids throughout time, which can, in turn, be used to find the area of the units required to achieve a given solid concentration in the clarified stream. This paper addresses the numerical treatment of data obtained from batch sedimentation experiments of calcium carbonate particles. We propose a systematic framework to fit a model that is capable of representing the process features that involve (i) the numerical differentiation of data to generate initial estimates for the instantaneous velocity of settling; (ii) the integration of a differential equation to fit the model for the velocity of settling; and (iii) the assessment of the quality of the fit using common statistical indicators. The model used for demonstration has a theoretical basis combined with an empirical component to account for the effect of the particle concentrations and their state of aggregation. The values of the numerical parameters obtained are related to the characteristic dimensions of the aggregates and their mass-length fractal dimensions.

On the Design of Aqueous Emulsions of Colophony Resin

Companies regularly face market pressure to develop products faster but they also need to simultaneously incorporate technological constraints, sustainability trends, and customer requirements into their designs, which requires the use of systematic procedures. Firms that exploit natural resources and convert them into high-value products are among them. However, the literature on the application of such systematic approaches to products of this type remains scarce, as they often requrire extensive experimental plans involving the testing and optimization of multiple formulations. Here, we propose a systematic approach to the design of pine-resin-in-water emulsions, which can be used to fabricate pressure-sensitive adhesives. The strategy is customer-centric in the sense that the customers’ specifications are integrated into the decision-making tool used to assess the quality of the formulations obtained through experiments. This tool uses loss functions to assess satisfaction with individual quality characteristics and multi-attribute decision-making methods to integrate them into an overall quality metric. Our framework is aligned with industrial practices and consists of three sequential stages: (i) screening of primary factors; (ii) optimization of secondary factors; and (iii) assessment of the experimental repeatability of the formulations. In each of these stages, the decision-making tool is used to “drive” the process of finding the optimal formulation.

Using rheological monitoring to determine the gelation kinetics of chitosan-based systems

The modeling of polymeric reactions is a topic of large interest. The gelation reactions that may result from self-crosslinking or hybrid (agent based-) crosslinking are examples with interest specially in biomaterials applications. The composition of polymer entities during the reaction is hard to follow, and their concentration is not a good measure of the system dynamics. One alternative is monitoring the rheological behavior of the reacting mass, and relate the elastic modulus of the mixture with the rheological degree of conversion. In this paper we use rheological data to fit Malkin and Kulichikin (1996) [1] based models to describe the crosslinking of chitosan. First, the self-crosslinking of chitosan is considered. Then, the agent-based crosslinking reaction promoted by genipin is addressed. We use dynamical rheological data to fit the reaction models. The model fitting problem generated using Maximum Likelihood principle with heteroscedastic prediction error variance is formulated as a Dynamic Optimization problem and subsequently solved with a sequential approach. Parametric confidence regions are computed using the linear approximation of the covariance matrix at the optimum. Further, the parameters correlation matrix is also determined and used to qualitatively infer about the practical identifiability. The reaction order obtained for self-crosslinking kinetics is 1.3375 ± (0.0151) - approximately of first order -, and is 2.2402 ± (0.0373) for hybrid crosslinking (approximately of second order). In both cases we prove the error variance model is heteroskedastic and the model is identifiable. The approach proposed herein can be extended to other polymer systems.

Optimal design of multiple-objective Lot Quality Assurance Sampling (LQAS) plans

Lot Quality Assurance Sampling (LQAS) plans are widely used for health monitoring purposes. We propose a systematic approach to design multiple-objective LQAS plans that meet user-specified type 1 and 2 error rates and targets for selected diagnostic accuracy metrics. These metrics may include sensitivity, specificity, positive predictive value, and negative predictive value in high or low anticipated prevalence rate populations. We use Mixed Integer Nonlinear Programming (MINLP) tools to implement our design methodology. Our approach is flexible in that it can directly generate classic LQAS plans that control error rates only and find optimal LQAS plans that meet multiple objectives in terms of diagnostic metrics. We give examples, compare results with the classic LQAS and provide an application using a malaria outcome indicator survey in Mozambique.

Wide-range and accurate modeling of linear alkylbenzene sulfonate (LAS) adsorption/desorption on agricultural soil

In this paper, rigorous data and adequate models about linear alkylbenzene sulfonate (LAS) adsorption/desorption on agricultural soil are presented, contributing with a substantial improvement over available adsorption works. The kinetics of the adsorption/desorption phenomenon and the adsorption/desorption equilibrium isotherms were determined through batch studies for total LAS amount and also for each homologue series: C10, C11, C12 and C13. The proposed multiple pseudo-first order kinetic model provides the best fit to the kinetic data, indicating the presence of two adsorption/desorption processes in the general phenomenon. Equilibrium adsorption and desorption data have been properly fitted by a model consisting of a Langmuir plus quadratic term, which provides a good integrated description of the experimental data over a wide range of concentrations. At low concentrations, the Langmuir term explains the adsorption of LAS on soil sites which are highly selective of the n-alkyl groups and cover a very small fraction of the soil surface area, whereas the quadratic term describes adsorption on the much larger part of the soil surface and on LAS retained at moderate to high concentrations. Since adsorption/desorption phenomenon plays a major role in the LAS behavior in soils, relevant conclusions can be drawn from the obtained results.

Evaluation of Linear Alkylbenzene Sulfonate (LAS) behaviour in agricultural soil through laboratory continuous studies

The behaviour of Linear Alkylbenzene Sulfonate (LAS) in agricultural soil is investigated in the laboratory using continuous-flow soil column studies in order to simultaneously analyze the three main underlying phenomena (adsorption/desorption, degradation and transport). The continuous-flow soil column experiments generated the breakthrough curves for each LAS homologue, C10, C11, C12 and C13, and by adding them up, for total LAS, from which the relevant retention, degradation and transport parameters could be estimated, after proposing adequate models. Several transport equations were considered, including the degradation of the sorbate in solution and its retention by soil, under equilibrium and non-equilibrium conditions between the sorbent and the sorbate. In general, the results obtained for the estimates of those parameters that were common to the various models studied (such as the isotherm slope, first order degradation rate coefficient and the hydrodynamic dispersion coefficient) were rather consistent, meaning that mass transfer limitations are not playing a major role in the experiments. These three parameters increase with the length of the LAS homologue chain. The study will provide the underlying conceptual framework and fundamental parameters to understand, simulate and predict the environmental behaviour of LAS compounds in agricultural soils.

A Semi-Infinite Programming based algorithm for determining T-optimum designs for model discrimination

T-optimum designs for model discrimination are notoriously difficult to find because of the computational difficulty involved in solving an optimization problem that involves two layers of optimization. Only a handful of analytical T-optimal designs are available for the simplest problems; the rest in the literature are found using specialized numerical procedures for a specific problem. We propose a potentially more systematic and general way for finding T-optimal designs using a Semi-Infinite Programming (SIP) approach. The strategy requires that we first reformulate the original minimax or maximin optimization problem into an equivalent semi-infinite program and solve it using an exchange-based method where lower and upper bounds produced by solving the outer and the inner programs, are iterated to convergence. A global Nonlinear Programming (NLP) solver is used to handle the subproblems, thus finding the optimal design and the least favorable parametric configuration that minimizes the residual sum of squares from the alternative or test models. We also use a nonlinear program to check the global optimality of the SIP-generated design and automate the construction of globally optimal designs. The algorithm is successfully used to produce results that coincide with several T-optimal designs reported in the literature for various types of model discrimination problems with normally distributed errors. However, our method is more general, merely requiring that the parameters of the model be estimated by a numerical optimization.

Finding Bayesian Optimal Designs for Nonlinear Models: A Semidefinite Programming-Based Approach

This paper uses semidefinite programming (SDP) to construct Bayesian optimal design for nonlinear regression models. The setup here extends the formulation of the optimal designs problem as an SDP problem from linear to nonlinear models. Gaussian quadrature formulas (GQF) are used to compute the expectation in the Bayesian design criterion, such as D-, A- or E-optimality. As an illustrative example, we demonstrate the approach using the power-logistic model and compare results in the literature. Additionally, we investigate how the optimal design is impacted by different discretising schemes for the design space, different amounts of uncertainty in the parameter values, different choices of GQF and different prior distributions for the vector of model parameters, including normal priors with and without correlated components. Further applications to find Bayesian D-optimal designs with two regressors for a logistic model and a two-variable generalised linear model with a gamma distributed response are discussed, and some limitations of our approach are noted.