Abstract

Aqueous xanthan gum solutions are non-Newtonian fluids, pseudoplastic fluids possessing yield stress. Their continuous mixing is an extremely complicated phenomenon exhibiting non idealities such as channeling, recirculation and stagnation. To characterize the continuous mixing of xanthan gum solutions, three dynamic models were utilized: (1) a dynamic model with 2 time delays in discrete time domain, (2) a dynamic model with 2 time delays in continuous time domain, and (3) a simplified dynamic model with 1 time delay in discrete time domain. A hybrid genetic algorithm was employed to estimate the model parameters through the experimental input-output dynamic data. The extents of channeling and fully-mixed volume were used to compare the performances of these three models. The dynamic model parameters exerting strong influence on the model response were identified. It was observed that the models with 2 time delays gave a better match with the experimental results.

Highlights

  • Important non-Newtonian fluids such as pulp suspensions, food substances like margarine and ketchup, paints, cement, and certain polymer and biopolymer solutions are pseudoplastic with yield stress

  • Classification of mathematical models Most mathematical models can be classified in the following ways (Kapur, 1998): (1) Linear vs. nonlinear: mathematical models are usually composed by variables, which are abstractions of quantities of interest in the described systems, and operators that act on these variables, which can be algebraic operators, function, differential operators, etc. if all the operators in a mathematical model present linearity, the resulting mathematical model is defined as linear

  • Another key question that must be addressed in establishing a set of candidate models is: can the system under study be represented with linear and time-invariant (LTI) model? The complex mixing system is generally nonlinear and time varying, LTI models may be nearly valid when the data are collected during short time periods of stable, unchanging experimental conditions

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Summary

A THESIS PRESENTED TO RYERSON UNIVERSITY

AUTHOR’S DECLARATION I hereby declare that I am the sole author of this Thesis or major Research Paper. I authorize Ryerson University to lend this thesis or Major Research Paper to other institutions or individuals for the purpose of scholarly research. I further authorize Ryerson University to reproduce this thesis or dissertation by photocopying or by other means, in total or in part, at the request of other institutions or individuals for the purpose of scholarly research

INTRODUCTION
Problem statement
Dynamic models
Hybrid genetic algorithm
Thesis layout This thesis is organized in the following fashion
Introduction
Batch Mixing Operation
Continuous Mixing Operation
Advantages of Continuous Mixing
Disadvantages and Limitations of Continuous Mixing
Rheology of non-Newtonian Fluids
Time-Independent
Time-Dependent Fluids
Viscoelastic Fluids
Literature review on continuous mixing of pseudoplastic with yield stress fluids
Ein-Mozaffari’s dynamic model
Patel’s dynamic model
Soltanzadeh’s dynamic model
Estimation of parameters via hybrid genetic algorithm
Continuous Time Domain Approach
Sensitivity analysis
The method
Strengths
Weaknesses
Steps of algorithm Following is the hybrid genetic algorithm
Experimental overview The experimental data used in this work were gathered by
RESULTS AND DISCUSSION
Model validation In this study the dynamic models were validated in two steps
Model predicted output
Effect of impeller speeds on the extent of channeling and fully mixed volume
Effect of xanthan gum mass concentration on the extent of channeling and fully mixed volume
Effect of fluid flow rates on the extent of channeling and fully mixed volume
Effect of different output locations on the extent of channeling and fully mixed volume
Conclusion
Recommendations for future work
Full Text
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