Optimizing Column Length and Particle Size in Preparative Batch Chromatography Using Enantiomeric Separations of Omeprazole and Etiracetam as Models: Feasibility of Taguchi Empirical Optimization

The overreaching purpose of this study is to evaluate new approaches for determining the optimal operational and column conditions in chromatography laboratories, i.e., how best to select a packing material of proper particle size and how to determine the proper length of the column bed after selecting particle size. As model compounds, we chose two chiral drugs for preparative separation: omeprazole and etiracetam. In each case, two maximum allowed pressure drops were assumed: 80 and 200 bar. The processes were numerically optimized (mechanistic modeling) with a general rate model using a global optimization method. The numerical predictions were experimentally verified at both analytical and pilot scales. The lower allowed pressure drop represents the use of standard equipment, while the higher allowed drop represents more modern equipment. For both compounds, maximum productivity was achieved using short columns packed with small-particle size packing materials. Increasing the allowed backpressure in the separation leads to an increased productivity and reduced solvent consumption. As advanced numerical calculations might not be available in the laboratory, we also investigated a statistically based approach, i.e., the Taguchi method (empirical modeling), for finding the optimal decision variables and compared it with advanced mechanistic modeling. The Taguchi method predicted that shorter columns packed with smaller particles would be preferred over longer columns packed with larger particles. We conclude that the simpler optimization tool, i.e., the Taguchi method, can be used to obtain “good enough” preparative separations, though for accurate processes, optimization, and to determine optimal operational conditions, classical numerical optimization is still necessary.     

Design and parameterization of a stochastic cellular automaton describing a chemical reaction

Although most of the work concerned with reaction kinetics concentrates on empirical findings, stochastic models, and differential equations, a growing number of researchers is exploring other methods to elucidate reaction kinetics. In this work, the parameterization of an utter discrete spatio-temporal model, more specifically, a cellular automaton (CA), describing the reaction of HCl with CaCO(3) , is suggested. Furthermore, a system of partial differential equations (PDE), deduced from a set of CA rules, is implemented to compare both modeling paradigms. In this article, the experimental setup to acquire time series of data is explained, a stochastic CA-based model and a continuous PDE-based model capable of describing the reaction are proposed, the models are parameterized using the experimental data and, finally, the relationship between a discrete time step of the CA-based model and the physical time is studied. Essentially, the parameterization of both models can be traced back to the quest for a solution of the inverse problem in which a (set of) rule(s), respectively a system of PDE, is deduced starting from the observed data. It is demonstrated that the proposed CA- and PDE-based models are capable of describing the considered chemical reaction with a high accuracy, which is confirmed by a root mean squared error between the simulated and observed data of 0.388 and 0.869 g CO(2) , respectively. Further, it is shown that an exponential or linear relationship can be used to link the physical time to a discrete time step of the CA-based model.     

Influence of empty hole on crack running in PMMA plate under dynamic loading

The influence of original prefabricated empty hole on dynamic crack propagation was studied. The dynamic behavior of crack propagation due to the impacting of drop hammer on the defective PMMA medium of manufactured hole defect (different extent of left shift, respectively, for L = 110 mm, L = 111.25 mm and L = 112.5 mm) was conducted using the test system of digital laser dynamic caustics (DLDC). The stress intensity factor and velocity at the running crack tip were analyzed. Moreover, the recently developed distinct lattice spring model (DLSM) was validated using the experimental data. It was found that the numerical modeling can reproduce the experimentally observed phenomena. Combining the experimental and numerical results, it can be concluded that the influence of empty hole defects of brittle materials on dynamic fracturing is great.     

Combined receptor and ligand-based approach to the universal pharmacophore model development for studies of drug blockade to the hERG1 pore domain

Long QT syndrome, LQTS, results in serious cardiovascular disorders, such as tachyarrhythmia and sudden cardiac death. A promiscuous binding of different drugs to the intracavitary binding site in the pore domain (PD) of human ether-a-go-go related gene (hERG) channels leads to a similar dysfunction, known as a drug-induced LQTS. Therefore, an assessment of the blocking ability for potent drugs is of great pragmatic value for molecular pharmacology and medicinal chemistry of hERGs. Thus, we attempted to create an in silico model aimed at blinded drug screening for their blocking ability to the hERG1 PD. Two distinct approaches to the drug blockage, ligand-based QSAR and receptor-based molecular docking methods, are combined for development of a universal pharmacophore model, which provides rapid assessment of drug blocking ability to the hERG1 channel. The best 3D-QSAR model (AAADR.7) from PHASE modeling was selected from a pool consisting of 44 initial candidates. The constructed model using 31 hERG blockers was validated with 9 test set compounds. The resulting model correctly predicted the pIC(50) values of test set compounds as true unknowns. To further evaluate the pharmacophore model, 14 hERG blockers with diverse hERG blocking potencies were selected from literature and they were used as additional external blind test sets. The resulting average deviation between in vitro and predicted pIC(50) values of external test set blockers is found as 0.29 suggesting that the model is able to accuretely predict the pIC(50) values as true unknowns. These pharmacophore models were merged with a previously developed atomistic receptor model for the hERG1 PD and exhibited a high consistency between ligand-based and receptor-based models. Therefore, the developed 3D-QSAR model provides a predictive tool for profiling candidate compounds before their synthesis. This model also indicated the key functional groups determining a high-affinity blockade of the hERG1 channel. To cross-validate consistency between the constructed hERG1 pore domain and the pharmacophore models, we performed docking studies using the homology model of hERG1. To understand how polar or nonpolar moieties of inhibitors stimulate channel inhibition, critical amino acid replacement (i.e., T623, S624, S649, Y652 and F656) at the hERG cavity was examined by in silico mutagenesis. The average docking score differences between wild type and mutated hERG channels was found to have the following order: F656A > Y652A > S624A > T623A > S649A. These results are in agreement with experimental data.     

Simultaneous measurement of contact angle and surface tension using axisymmetric drop-shape analysis-no apex (ADSA-NA)

Axisymmetric drop-shape analysis-no apex (ADSA-NA) is a recent drop-shape method that allows the simultaneous measurement of contact angles and surface tensions of drop configurations without an apex (i.e., a sessile drop with a capillary protruding into the drop). Although ADSA-NA significantly enhanced the accuracy of contact angle and surface tension measurements compared to that of original ADSA using a drop with an apex, it is still not as accurate as a surface tension measurement using a pendant drop suspended from a holder. In this article, the computational and experimental aspects of ADSA-NA were scrutinized to improve the accuracy of the simultaneous measurement of surface tensions and contact angles. It was found that the results are relatively insensitive to different optimization methods and edge detectors. The precision of contact angle measurement was enhanced by improving the location of the contact points of the liquid meniscus with the solid substrate to subpixel resolution. To optimize the experimental design, the capillary was replaced with an inverted sharp-edged pedestal, or holder, to control the drop height and to ensure the axisymmetry of the drops. It was shown that the drop height is the most important experimental parameter affecting the accuracy of the surface tension measurement, and larger drop heights yield lower surface tension errors. It is suggested that a minimum nondimensional drop height (drop height divided by capillary length) of 1.7 is required to reach an error of less than 0.2 mJ/m(2) for the measured surface tension. As an example, the surface tension of water was measured to be 72.46 ± 0.04 at 24 °C by ADSA-NA, compared to 72.39 ± 0.01 mJ/m(2) obtained with pendant drop experiments.     

Applying a Smart Technique for Accurate Determination of Flowing Oil-Water Pressure Gradient in Horizontal Pipelines

Two-phase flow of liquids in pipelines is crucial subject in many industries such as chemical and petroleum. Accurate prediction of pressure gradient will lead to a better design of an energy efficient transportation system. Although numerous studies for prediction of two-phase flowing pressure drop have been reported in the literature, the accurate prediction of this parameter has been a topic of debate in many research areas. In this article, a novel model based on least square support vector (LSSVM) was proposed for calculation of two-phase flowing pressure drop in horizontal pipes. The inputs of this model are oil and water superficial velocities, pipe diameter, pipe roughness, and oil viscosity. To develop and test the model, more than 700 experimental dataset from open literature were utilized. The results of proposed model were compared against the well-known empirical correlations. Statistical error analysis showed that the LSSVM model outperforms existing predictive models. Finally, an outlier diagnosis was performed to detect the doubtful experimental.      

Modeling and analytical simulation of rotating disk ultrafiltration module

An unsteady state mass transfer model has been developed for rotating disk ultrafiltration module. Starting from the basic physics of the system, analytical expression of back transport flux generated due to rotation-induced shear field is determined, which is subsequently incorporated in the fundamental material balance equation. In order to get an analytical solution of governing partial differential equation via Laplace transformation, pseudo steady state consideration is imposed both on permeate as well as back transport flux. Once the analytical form of concentration field is obtained using the expression permeate flux, membrane surface concentration are evaluated using polymer solution theory and irreversible thermodynamics. Finally an iterative scheme is designed to simulate the permeate flux and membrane surface concentration under specified set of operating parameters. The prediction from this model is found to be in good agreement with experimental data obtained from PEG-6000/water system using cellulose acetate membrane of 5000 Da molecular weight cut-off.     

Modeling composite emulsion polymerization kinetics

The conversion profiles of a number of factorial designed experiments used to study composite emulsion polymerization were modeled using a deterministic mathematical construct as well as an empirical neural network approach. In the deterministic modeling approach, existing mechanistic models for emulsion polymerization were employed for which estimates of rate constants were obtained from established literature sources as well as experiments. Fitting of the kinetic data was done using nonlinear fitting algorithms to adjust the estimated rate constants to provide the best fit of the conversion profiles. In the case of the empirical modeling using neural networks, the neural net inputs were in the form of the factor levels of the various experimental designs. Several nonrelated experimental designs could be combined in this way to serve as the input, whereas the conversion profiles were targeted as outputs. Following the successful implementation of both modeling strategies, a hybrid modeling approach was tested by combining the neural network predictive power to estimate values for rate constants while retaining the aforementioned mechanistic models to fit the data. © 2012 Wiley Periodicals, Inc. Int J Chem Kinet 45: 101–117, 2013     

An Integrated Two Phases Approach to Zn2+ Ions Electroreduction on Hg

The following two numerical models have been applied to zinc cations electroreduction in 1 M NaClO₄ water solution: a classical EE model describing the concentration of involved species in solution (semi infinitive diffusion region), an extended EE model describing both: the concentration of involved species in solution and the concentration of metallic zinc inside mercury drop (in limited area of diffusion). In the latter model the inner part of mercury drop and surrounding solution were treated as dynamic interrelated system. Both models were applied to experimental cyclic voltammetric CV data in 1 M NaClO₄, the results compared and discussed. The concentration profiles of all species including metallic zinc inside mercury drop were performed. The presented integrated model is essential for theoretical and analytical aspects of the electrochemistry of mercury soluble metal cations and amalgams.     

Sorptive elimination of fluoride from contaminated groundwater in a fixed bed column: A kinetic model validation based study

The current investigation involves a continuous adsorption experiment in a packed bed column for the sorptive elucidation of fluoride from contaminated groundwater using an activated soil-clay mixture. Through the combination of naturally accessible laterite soil with silica enriched clay (3:1 ratio), a low-cost Al–Si heterogeneous material has been developed. Following detailed characterization, the developed materials were employed in a long-time column process to achieve a high degree of fluoride separation from real-world groundwater. In a packed bed column investigation, the effect of bed height, initial fluoride concentration, and flow rate on the breakthrough properties of the adsorption system were investigated. By using a non-linear regression equation, three model kinetics, such as the Thomas Model, Adams-Bohart Model, and Yoon-Nelson Model, were fitted to validate the column-based experimental data, by analysing the breakthrough curves profiles, and distinct kinetic parameters. The Bed Depth Service Time Analysis (BDST) model was tested to express the effect of bed height on breakthrough curves, as well as to predict the time for breakthrough, and material depletion under optimal conditions. The Thomas and Yoon-Nelson models were identified to be the most appropriate ones for describing the entire breakthrough curve, whereas the Adams-Bohart model was only utilised to predict the first half of the dynamic process. With correlation coefficients (R²) 0.96, the experimental results were well suited to Thomas, Yoon-Nelson, and Adams-Bohart models. Finally, regeneration assessment was carried out where even after four cycles of operation, regenerated adsorbent showed a rejection efficacy of 78% to fluoride that proves the viability of the material and methodology.     

微分方程演化建模用于色谱保留时间的研究

利用演化算法的自适应、自组织、自学习的特性,设计了遗传程序设计与遗传算法相嵌套的混合演化建模算法,以遗传程序设计优化模型结构,以遗传算法优化模型参数,为化合物的液相色谱容量因子随流动相组成变化关系自动建立微分方程演化模型．通过对７个化合物的建模结果表明,演化模型的拟合和预测精度均明显高于常规的ＧＭ（１,１）模型和改进的ＧＭ（１,１）模型．     

Understanding (sessile/constrained) bubble and drop oscillations

The diffuse literature on drop oscillation is reviewed, with an emphasis on capillary wave oscillations of constrained drops. Based on the review, a unifying conceptual framework is presented for drop and bubble oscillations, which considers free and constrained drops/bubbles, oscillation of the surface or the bulk (i.e. center of mass) of the drop/bubble, as well as different types of restoring forces (surface tension, gravity, electromagnetic, etc). Experimental results (both from literature and from a new set of experiments studying sessile drops in cross flowing air) are used to test mathematical models from literature, using a novel whole profile analysis technique for the new experiments. The cause of oscillation (cross flowing air, vibrated surface, etc.) is seen not to affect oscillation frequency. In terms of models, simplified models are seen to poorly predict oscillation frequencies. The most advanced literature models are found to be relatively accurate at predicting frequency. However it is seen that no existing models are reliably accurate across a wide range of contact angles, indicating the need for advanced models/empirical relations especially for drops undergoing the lowest frequency mode of oscillation (the order 1 degree 1 non-axisymmetric ‘bending’ mode that corresponds to a lateral ‘rocking’ motion of the drop).     

Estimation-identification problem for diffusive transport in porous materials based on single reservoir test: results for silica hydrogel

In this paper the problems of selection of an appropriate model of diffusive transport in silica hydrogel and estimation of model parameters are considered. The analytical solutions and simulations of diffusive transport in a single reservoir test with equilibrium model of sorption are developed. The mathematical models refer to transport of solute from a porous material to water or in reverse direction assuming arbitrary initial concentrations and Dirichlet or mixed type of boundary conditions. In order to quantify the relative importance of the model parameters, logarithmic sensitivity analysis of solute concentration with respect to estimated parameters describing diffusion, sorption, and interfacial effects is performed. The application of the discussed models for estimation of transport parameters is discussed using experimental results for diffusion of sodium chloride in silica hydrogel.     

Modelling and graphic interpretation of response surface in chemical analysis

The complicated effects of several factors on an analytical signal can be studied comprehensively only by an experimental design in which the additive and non-additive effects of these factors are included in one experimental run, with simultaneous variation of the values of all factors. From the law of mass action, it is shown that systems in which the analytical signal is produced by a species formed during a chemical reaction (i.e., for spectrophotometry) can be described by a model based on quasi-linear regressions with squares and products of variables. The regression coefficients can be evaluated by means of factorial designs at three levels. Interpretation of results in the case of two or three independent variables is simplified by using a graphic method in which the complex effects of factors on the dependent variable are represented as an empirical response surface. In the case of regression with three independent variables, the response surface is four-dimensional; its dimensionality is reduced to three by several three-dimensional representations. The shapes of the response surfaces described by the response functions and the adequacy of the models are discussed.     

Film Drainage between Colliding Drops at Constant Approach Velocity: Experiments and Modeling

Experiments and modeling of the drainage of the thin liquid film between two deformable spherical drops approaching each other at constant velocity in another liquid are being presented. Two numerical models based on the lubrication theory have been developed considering the cases of immobile or mobile drop interfaces. The absolute film thickness and the thinning rate have been measured using laser interferometry for a wide range of capillary numbers. In all studied cases, the model with immobile interfaces was found to give the best predictions of the experimental time evolution of the film thickness and radial expansion. These results made it possible to derive a typical time scale of the drainage process. Copyright 2000 Academic Press.     

构建支持向量机-偏最小二乘法为药物构效关系建模

为研究药物构效关系积累样本数据的过程中,需为小样本建模。此时较易造成过拟合,影响模型的预测性能和稳定性。为此可用偏最小二乘(PLS)法从样本数据中成对地提取最优成分,消除自变量间的复共线性,并有效的降维,然后应用最小二乘支持向量机对成对成分进行非线性回归,并以基于误差修正的策略调整,使之更有效地表达自、因变量间的非线性关系。由此构建为EB-LSSVM-PLS算法,所建模型的预报精度高,稳定性良好。将其应用于新型黄烷酮类衍生物的QSAR建模,效果令人满意,其泛化性能优于其它方法。     

Self-excited drop oscillations in electrowetting

We studied millimeter-sized aqueous sessile drops in an ambient oil environment in a classical electrowetting configuration with a wire-shaped electrode placed at a variable height above the substrate. Within a certain range of height and above a certain threshold voltage, the drop oscillates periodically between two morphologies where it is either attached to the wire or detached from it. We determine the range of control parameters, wire height, and voltage in which oscillations occur and explain it by a simple capillary model. Furthermore, we analyze the dynamics of the oscillations using high-speed video microscopy and numerical fluid dynamics modeling. We develop a one-dimensional harmonic oscillator model that describes the dependence of the drop oscillations on the relevant intrinsic (surface tension, viscosity, density) and extrinsic (wire height, voltage) parameters.