Calculation of ternary <scp>liquid‐liquid</scp> equilibrium data using <scp>arc‐length</scp> continuation

Binous, Housam; Bellagi, A.

doi:10.1002/eng2.12296

Cited by 5 publications

(9 citation statements)

References 20 publications

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“…Given the limited solubility along with PFP − water immiscibility and EtOH−water miscibility, a ternary liquid-liquid phase diagram can be drawn as Supplementary Fig. 4 (type II mixture, similar to methanol-cyclohexane-water 35 ). Thus, at the composition of 49 wt% water, 49 wt% EtOH, and 2 wt% PFP, a two-phase equilibrium is reached with two extremes of pure PFP and 50 wt% EtOH/water, considering the curvature of the binodal curve.…”

Section: Resultsmentioning

confidence: 99%

Investigating water/oil interfaces with opto-thermophoresis

2022

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Charging of interfaces between water and hydrophobic media is a mysterious feature whose nature and origin have been under debate. Here, we investigate the fundamentals of the interfacial behaviors of water by employing opto-thermophoretic tweezers to study temperature-gradient-induced perturbation of dipole arrangement at water/oil interfaces. With surfactant-free perfluoropentane-in-water emulsions as a model interface, additional polar organic solvents are introduced to systematically modify the structural aspects of the interface. Through our experimental measurements on the thermophoretic behaviors of oil droplets under a light-generated temperature gradient, in combination with theoretical analysis, we propose that water molecules and mobile negative charges are present at the water/oil interfaces with specific dipole arrangement to hydrate oil droplets, and that this arrangement is highly susceptible to the thermal perturbation due to the mobility of the negative charges. These findings suggest a potential of opto-thermophoresis in probing aqueous interfaces and could enrich understanding of the interfacial behaviors of water.

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Section: Resultsmentioning

confidence: 99%

Investigating water/oil interfaces with opto-thermophoresis

2022

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“…Let us consider the following parametric system of N nonlinear equations, written in vector representation [9,18,41].…”

Section: Arc-length Continuation Methodsmentioning

confidence: 99%

“…The calculated binodal curves and tie lines [9] were obtained using the UNIQUAC model and PSO for the estimation of the binary interaction parameters. The results are depicted in Figure 11.…”

Section: N-hexane-methyl Cyclopentane-anilinementioning

confidence: 99%

“…In previous studies, the complex homotopy continuation method was the method of choice for analyzing LLE [21,41]. The simpler arc-length continuation technique has been applied rarely to LLE data computations [9].…”

Section: Introductionmentioning

confidence: 99%

“…Then, we introduce the reader to the arc-length continuation method and the particle swarm optimization (PSO) numerical techniques. In our discussion of the arc-length continuation technique, we draw on previous work in which the method has been used to solve various chemical engineering problems [9,10,13,13,20,23,27]. The last section of this paper contains the generated LLE data for seven industrially relevant mixtures that have been successfully benchmarked against corresponding experimental data.…”

Section: Introductionmentioning

confidence: 99%

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Application of graduate‐level numerical tools to teach phase equilibria of liquid ternary systems

Binous

Mejbri

Bellagi

2021

Comp Applic In Engineering

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The present paper describes a numerical technique to compute phase equilibria of ternary liquid systems. First, particle swarm optimization is used to estimate the binary interaction parameters of the NRTL (Non-Random Two Liquid) and UNIQUAC (Universal Quasi-Chemical) models. We show how the arc-length continuation method allows the calculation of the liquid-liquid equilibrium diagram for any ternary system. A total of seven case studies of industrially important mixtures are described. Both Type I systems (oleic acid-water-ethanol, water-1propanol-toluene, DEC-ethanol-water, water-propionic acid-n-hexane, and water-TMA-benzene) and Type II mixtures (water-1-butanol-nhexane) are discussed. In addition, a system with temperature-dependent behavior (n-hexane-methyl cyclopentane-aniline) is studied. The numerical techniques and the thermodynamic problem involved in this paper are suitable for a first-year graduate-level course in chemical engineering. All computer coding is based either on MATHEMATICA© or MATLAB®. This is an ideal opportunity to introduce graduate students to advanced commands and programming syntax of state-of-the-art mathematical software. K E Y W O R D Sarc-length continuation, graduate chemical engineering thermodynamics, liquid-liquid equilibrium data, MATHEMATICA© and MATLAB®, NRTL and UNIQUAC models

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Calculations of complex chemical reaction equilibria using stoichiometric and non‐stoichiometric approaches in combination with arc‐length continuation

Binous

Bellagi

2022

Engineering Reports

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Chemical equilibrium calculations—as they are required to evaluate the evolution limits of any reactive system—are fundamentally performed using either a reaction based stoichiometric (S) approach or a non‐stoichiometric (NS) method. One objective of the present paper is to check and discuss whether both methods lead to comparable solutions in the case of complex chemical equilibria encountered in high temperature and pressure combustion of hydrazine and propane and in steam gasification of glucose and cellulose. Within both calculation models various numerical methods can be used. We apply several techniques for each approach and discuss their easiness of implementation and usage, in particular when chemical equilibria are computed for reacting systems under a multitude of temperature and pressure conditions and feed compositions. In addition, we present a novel approach to perform sensitivity analyses based on a combination of S or NS methods and arc‐length continuation technique. For this purpose, three industrially relevant case studies are exposed: (1) synthesis of ammonia using the Haber process, (2) steam gasification of a typical biomass surrogate, glucose, and (3) steam gasification of cellulose. For all the above reacting systems, our results are benchmarked against their counterparts obtained either from the ubiquitous process simulator: ASPEN‐Plus® or from data available in the open literature.

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Calculation of ternary liquid‐liquid equilibrium data using arc‐length continuation

Cited by 5 publications

References 20 publications

Investigating water/oil interfaces with opto-thermophoresis

Investigating water/oil interfaces with opto-thermophoresis

Application of graduate‐level numerical tools to teach phase equilibria of liquid ternary systems

Calculations of complex chemical reaction equilibria using stoichiometric and non‐stoichiometric approaches in combination with arc‐length continuation

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