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 smoke furthest from the

cigarette is turbulent as shown by the swirling smoke patterns. . . . . 21

2.3 Couette Flow. Simple experiment showing the effects of viscosity[1]. 23

2.4 Free-body Diagram for a sphere traveling in a fluid at terminal velocity. 24

2.5 Stream lines flowing around a sphere traveling in a fluid at terminal

velocity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.6 Three equal spheres flowing at a constant velocity in the direction

of the arrows at various times showing how particle interaction can

increase and decrease the velocities of the spheres. . . . . . . . . . . . 27

2.7 Streamlines of Fluid relative to moving cloud. . . . . . . . . . . . . . 28

2.8 A singlet is where the two particles rotate independently and a dou-

blet is where the two particles rotate together like a dumbbell. . . . . 31

3.1 Images of concentric cylinder (a) is the inside geometry, (b) is the

outside geometry, and (c) is the inside geometry inserted into the

outside geometry with the sample filling the gap. . . . . . . . . . . . 34

3.2 The NESLAB RTE 7 Bath Circulator. . . . . . . . . . . . . . . . . . 36

3.3 Cut away of the head of the AR 1500ex Rheometer showing the vari-

ous components used to rotated the geometry used to take measure-

ments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.4 The AR 1500ex Rheometer from TA Instruments. . . . . . . . . . . . 38

3.5 A plot of viscosity as a function of temperature for the calibration

curve of the custom concentric cylinder (black triangles with error

bars) and DOW Standard values for 98% (red squares) pure glycerin,

99% (green stars) pure glycerin, and 100% (blue diamonds) pure glyc-

erin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.6 The digital microscope model number DC4-410. . . . . . . . . . . . . 41

3.7 Image of the particles (a D 51 m) under the microscope using Motic

Images Plus 2.0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.8 Histogram of particles showing the mean and standard deviation values. 43

LIST OF FIGURES – Continued

4.1 The Standard System. The standard system using the following

parameters of Á0 D 3017 cP ˙ 4 cP, ! D 1:000 rad=s ˙ 0:001 rad=s,

and a D 36 m ˙ 3 m with Mooney’s Equation 2.11 the green

line with values of D 2:8 ˙ 0:3 and 'm D 0:79 ˙ 0:11, Krieger-

Doughtery’s Equation 2.12 the blue line with values of D 3:2 ˙ 0:4

and 'mD 0:57˙0:10, Batchelor’s Equation 2.13 (Standard) the black

line with

...