Tesis Viscosidad

Theses and Dissertations

6-2011

Via Sapientiae:

The Institutional Repository at DePaul University

College of Liberal Arts and Social Sciences

The dependence of suspension viscosity on particle

size, shear rate, and solvent viscosity

Marc Pavlik

DePaul University, MARCPAVLIK@COMCAST.NET

Recommended Citation

Pavlik, Marc, "The dependence of suspension viscosity on particle size, shear rate, and solvent viscosity" (2011). Theses and

Dissertations. Paper 71.

http://via.library.depaul.edu/etd/71

This Thesis is brought to you for free and open access by the College of Liberal Arts and Social Sciences at Via Sapientiae. It has been accepted for

inclusion in Theses and Dissertations by an authorized administrator of Via Sapientiae. For more information, please contact mbernal2@depaul.edu.

THE DEPENDENCE OF SUSPENSION VISCOSITY ON

PARTICLE SIZE, SHEAR RATE, AND SOLVENT VISCOSITY

A Thesis

Presented in

Partial Fulfillment of the

Requirements for the Degree of

MASTER OF SCIENCE

August 19, 2009

BY

Marc Pavlik

PHYSICS DEPARTMENT

College of Liberal Arts and Sciences

DePaul University

Chicago, Illinois

TABLE OF CONTENTS

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

4

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

CHAPTER 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 15

CHAPTER 2 Fluid Dynamics . . . . . . . . . . . . . . . . . . . . . . 20

2.1 Newton’s Law of Viscosity . . . . . . . . . . . . . . . . . . . . . . . . 22

2.2 Particle Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.3 Stream Lines and Interacting Spheres . . . . . . . . . . . . . . . . . . 24

2.4 Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.4.1 Einstein . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.4.2 Mooney . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.4.3 Krieger-Dougherty . . . . . . . . . . . . . . . . . . . . . . . . 30

2.4.4 Batchelor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.4.5 Brady . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

CHAPTER 3 Experiment . . . . . . . . . . . . . . . . . . . . . . . . 34

3.1 Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.1.1 Concentric Cylinder . . . . . . . . . . . . . . . . . . . . . . . 34

3.1.2 NESLAB RTE 7 Bath Circulator . . . . . . . . . . . . . . . . 35

3.1.3 Rheometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.2 Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.2.1 Glycerine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.2.2 Glass Particles . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.3 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.3.1 Experiment Procedure . . . . . . . . . . . . . . . . . . . . . . 44

3.3.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

CHAPTER 4 Data/Analysis . . . . . . . . . . . . . . . . . . . . . . . 47

4.1 Universal Trends in the Data . . . . . . . . . . . . . . . . . . . . . . 47

4.1.1 Standard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.1.2 Solvent Viscosity Dependence . . . . . . . . . . . . . . . . . . 49

4.1.3 Angular Velocity Dependence . . . . . . . . . . . . . . . . . . 51

TABLE OF CONTENTS – Continued

3

4.1.4 Particle Size Dependence . . . . . . . . . . . . . . . . . . . . . 53

4.2 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.2.1 Fitting Procedures . . . . . . . . . . . . . . . . . . . . . . . . 53

4.2.2 The Equations . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.3 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

4.3.1 Fitting Parameter . . . . . . . . . . . . . . . . . . . . . . . . 76

4.3.2 Fitting Parameter 'm . . . . . . . . . . . . . . . . . . . . . . . 90

4.3.3 Fitting Parameter ˛ . . . . . . . . . . . . . . . . . . . . . . . 111

4.3.4 Fitting Parameter ˇ . . . . . . . . . . . . . . . . . . . . . . . 116

CHAPTER 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . 121

5.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

APPENDIX A Code used to minimize2. . . . . . . . . . . . . . . 124

LIST OF FIGURES

2.1 A car in a wind tunnel showing laminar flow. Notice the streamlines

4

do not touch or cross while remaining parallel to each other. . . . . . 20

2.2 A cigarette showing both laminar and turbulent flow. The smoke

nearest the cigarette is laminar. The

...