A so-called “slug-flow” capillary microreactor has been proposed for the investigation of mass-transfer-limited liquid−liquid reactions. Internal circulation within the slug leads to an intensified and tunable mass transfer. Understanding the development of the circulatory flows and the influence of operating parameters upon them is thus crucial. In this study, experiments were carried out to visualize the internal circulations using particle image velocimetry (PIV) technique. State-of-the-art computational fluid dynamics (CFD) simulations were used to predict the internal circulation within the liquid slugs and a CFD particle tracing algorithm employed to visualize them. Each slug was modeled as a distinct single-phase flow domain. The effect of the flow velocity and slug length on the velocity profile and stagnant zones of the internal circulations for a slug with and without a wall film is discussed. The internal circulations could be qualitatively and quantitatively characterized with the help of the ...

/pdf/internal-circulation-within-the-liquid-slugs-of-a-liquid-4ecu3wqcrl.pdf

Internal Circulation within the Liquid Slugs of a Liquid-Liquid Slug-Flow Capillary Microreactor

The widely used separation process of liquid−liquid extraction is performed in a variety of contactors. The interfacial area in these conventional contactors is often poorly defined, because of the...

Liquid−Liquid Slug Flow in a Capillary: An Alternative to Suspended Drop or Film Contactors

The effect of thermal conductivity of the packing material on transient heat transfer in a fixed bed

This paper represents a survey of the recent literature in the area of process identification and parameter estimation techniques applicable to lumped-parameter, deterministic, dynamical systems. Methods reviewed include statistical estimation techniques, direct and indirect methods based on optimal control theory, functional expansion, impulse response, frequency response and a number of other specific methods. Each method is presented in a consistent format which includes an outline of the general characteristics, calculational techniques, experimental techniques, reliability estimates and applications. The overall objective is to provide a basis for comparison of the methods and a guide to particular applications which will assist the reader in selecting the best method for his specific problem Comments and additions are solicited: see page 263.

A review of process identification and parameter estimation techniques

A comparative study of short cut procedures for parameter estimation in differential equations

Given a set of observed data for a particular physical phenomenon, the problem of computing the “best fit” parameters for the mathematical model describing the phenomenon is a common problem in process or reaction mechanism identification. If the mathematical model comprises a set of non-linear ordinary differential equations, this leads to a non-linear boundary value problem. A very powerful way of attacking this class of problem uses an adaptation of the Newton-Raphson-Kantorovich procedure, called quasilinearization, which regards the non-linear problem as the limit of a sequence of linear problems. Starting from an initial trial solution, convergence if it does occur, occurs rapidly; further, convergence is assured if the initial guess is “close enough” to the true solution. The difficulty of making a good initial guess, a serious limitation of the method in the past, can in principle be overcome by the algorithm proposed. When a given vector may not be within the domain of convergence of the original problem, it must be within the domain of convergence of some other derived problem. The latter may then be perturbed towards the original problem in a finite number of steps. In the case of process identification, new data points are derived; these are subsequently adjusted until they coincide with the original data. The algorithm has been successfully applied to several examples from recent chemical engineering literature.



Si l'on a en main une serie de resultats d'observation pour un phenomene physique particulier, un probleme courant est de calculer les parametres qui conviennent le mieux au modele mathematique qui serf a decrire le phenomene, lors de l'identification du mecanisme d'un procede ou d'une reaction. Si le modele mathematique comprend une serie d'equationg differentielles ordinaires et non-lineaires, il s'agit d'un probleme de valeur-limite non-lineaire et l'un des meilleurs moyens de l'attaquer est la quasi-linearisation, une adaptation du procede de Newton, Raphson et Kantorovich, ou l'on considere le probleme non-lineaire comme la limite d'une serie de probleme lineaires. Si l'on part d'une solution initiate d'essai, la convergence, si elle se produit, survient rapidement; en outre, la convergence est certaine, si l'estimation initiale est assez proche de la solution reelle. On peut surmonter par l'algorithme propose la difficulte eprouvee a faire une bonne estimation initiale, ce qui a limite serieusement l'emploi de la methode dans le passe. Lorsqu'un vecteur d'essai donne n'entre pas dans le domaine de convergence du probleme original, il doit entrer dans celui d'un autre probleme qui en derive; on peut alors ramener ce dernier au probleme original dans un nombre d'etapes defini. Dans le cas de l'identification d'un procede, on en deduit de nouveaux points de repere, qu'on ajuste subsequemment jusqu'a ce qu'ils coincident avec les resultats originaux. On a applique l'algorithme avec succes a plusieurs exemples provenant des travaux recents en genie chimique.

Identification of parameters in systems of ordinary differential equations using quasilinearization and data perturbation

A mathematical model of a packed bed reactor was developed to include radial and axial diffusion within the reactor as well as film and pore resistances to both heat and mass flows. The non-linear partial differential equations which are coupled by a generalized reaction rate expression were finite-differenced and integrated in the time domain. The performance of the detailed model was compared with those predicted for two simpler models: a homogeneous reactor model and a surface resistance reactor model. The range of variables over which these considerations are important is also indicated.



On a mis au point un modele mathematique d'un reacteur a lit garni destine a assurer une diffusion radiale et axiale dans le reacteur et a rendre les pellicules et pores resistantes aux ecoulements de chaleur et de masse. On a differencie a l'etat fini et integre dans le temps les equations differentielles non-lineaires et partielles, lesquelles sont associees a une expression generale de vitesse de reaction. On a compare le rendement du modele detaille avec les rendements predits pour deux modeles plus simples, a savoir un modele de reacteur homogene et un modele de reacteur a resistance superficielle. On a aussi indique l'echelle des variables dans les limites desquelles les dites considerations sont importantes.

Mathematical models for the transient behavior of a packed bed Reactor

The problem of a steady state plug flow transport or moving bed reactor has been solved by computer techniques for the case where the solid phase acts as a heat carrier and chemical reaction occurs only in the gas phase. The mathematical model reduces to a set of simultaneous ordinary first order differential equations, which are solved by both the Runge-Kutta-Gill method on a digital computer and by simulation on an analog computer.

A computer model for moving beds — chemical reaction in fluid phase only

The transient behavior of a packed bed of uniform spheres is considered, where heat (or mass) transfer inside the sphere is described by a linear parabolic second order partial differential equation — the standard diffusivity equation. One dimenisonal plug flow is assumed; hence, the fluid behavior is given by a set of first order partial differential equations, with bed axial position and time as the independent variables. The existence of chemical reaction in the fluid makes these equations non-linear. The two systems of equations describing the solid and the gas are coupled by the equations for heat (or mass) transfer at the surface. Numerical methods for solving both the linear (no reaction) and non-linear (with reaction) cases are presented. In the former, the implicit Crank-Nicholson method is used; in the latter the two systems of equations are first decoupled and then solved separately.



On considere le comportement transitoire d'un lit fixe forme de spheres uniformes dans lequel le transfert de chaleur (ou de masse) a l'interieur de la sphere est represente par l'equation de diffusivite soit une equation differentielle partielle lineaire parabolique du deuxieme ordre. Le comportement du fluide est donne par des equations differentielles partielles du premier ordre dont les variables independantes sont le temps et la position axiale du lit. La presence de reaction chimique dans le fluide rend ces equations non-lineaires. Les deux systemes d'equations decrivant les phases gaz et solide sont completes par les equations de transfert de chaleur (et de masse) a la surface. On presente des methodes numeriques pour resoudre les equations lineaires et non-lineaires. Dans le premier cas la methode implicite de Crank-Nicholson est utilisee; dans le deuxieme cas les deux systemes d'equations sont separes et resolus separement.

A computer model for the regenerative bed

The partial differential equation describing transient conduction (or diffusion) in non-homogeneous media may be approximated by a set of first order linear ordinary differential equations if the derivatives involving the space variables are replaced by finite difference expressions. A general method of obtaining a closed form solution of these equations is presented, using some operational methods of linear algebra. The solution is given in terms of a matrix, which describes the spatial distribution of physical properties in the media, and vectors describing the initial and boundary conditions.



On peut evaluer l'equation partielle et differentielle qui decrit la conduction (ou diffusion) dans des milieux nonhomogenes au moyen d'une serie d'equations differentielles ordinaires et lineaires de premier ordre, en remplacant les derives qui se rapportent aux variables de l'espace par des expressions finies de difference. On presente une methode generale pour obtenir une solution, sous forme fermee, de ces equations en utilisant certaines methodes d'operation de I'algebre lineaire. La solution est exprimee en matrice, ou l'on decrit la repartition spaciale des proprietes physiques dans les milieux en question, et en vecteurs ou l'on expose les conditions initiales et limites.

Analytical solutions to the semi‐discrete form of the conduction equation for non‐homogeneous media

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

D. Quon

Author Tools

Chat about Author