New Jersey Institute of Technology Digital Commons @ NJIT Dissertations Electronic Theses and Dissertations Spring 6-30-1968 Viscosity-density correlation of Newtonian liquids Melvin Leonard Druin New Jersey Institute of Technology Follow this and additional works at: https://digitalcommons.njit.edu/dissertations Part of the Chemical Engineering Commons Recommended Citation Druin, Melvin Leonard, "Viscosity-density correlation of Newtonian liquids" (1968). Dissertations. 1333. https://digitalcommons.njit.edu/dissertations/1333 This Dissertation is brought to you for free and open access by the Electronic Theses and Dissertations at Digital Commons @ NJIT. It has been accepted for inclusion in Dissertations by an authorized administrator of Digital Commons @ NJIT. For more information, please contact [email protected]. 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Please Note: The author retains the copyright while the New Jersey Institute of Technology reserves the right to distribute this thesis or dissertation Printing note: If you do not wish to print this page, then select “Pages from: first page # to: last page #” on the print dialog screen The Van Houten library has removed some of the personal information and all signatures from the approval page and biographical sketches of theses and dissertations in order to protect the identity of NJIT graduates and faculty. 68-16,970 DRUIN, Melvin L„ 1941- VISCOSITY-DENSITY CORRELATION OF NEWTONIAN LIQUIDS. Newark College of Engineering, D.Eng.Sc., 1968 Engineering, chemical University Microfilms, Inc., Ann Arbor, Michigan VISCOSITY-DENSITY CORRELATION OF NEWTONIAN LIQUIDS BY MELVIN L. DRUIN A DISSERTATION PRESENTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF ENGINEERING SCIENCE AT NEWARK COLLEGE OF ENGINEERING This dissertation is to be used with due regard to the rights of the author. Bibliographical references may be noted, but passages must not be copied, with­ out permission of the College and without credit being given in subsequent written or published work. Newark, New Jersey 1968 The viscosity of monatomic liquids was modeled by an equation derived from the kinetic theory of gases. Viscosities may be calcu­ lated from data on density and molecular weight of the liquid. In adapting this relationship to polyatomic liquids, a single correction factor was developed for each of five series of homologues; n-paraffins, n-l-alkenes, n-alkylcyclohexanes, n-alkylbenzenes and n-alcohols, to account for the deviations of the calculated viscosities from those reported, extending over a one- to three-hundred degree range. The factor is a function of reduced temperature relative to the normal boiling point, Trg. A single equation for each of the series of homologues, n-paraffins to n-alcohols, was thus used as a predictor for the viscosities with an average error of 6. 8, 4. 9, 7. 9, 4. 9 and 29. 5 per cent, respectively. The correction factors for the hydrocarbon series, excluding the alcohols were sufficiently similar so that they were estimated to be identical. A combined correction factor for two series, n-paraffins and n-l-alkenes, was employed to extrapolate to the alkylbenzenes and alkylcyclohexanes with an accuracy in predicted viscosity of 10. 1 and 18.4 per cent, respectively. The maximum error in both series was only 37. 9 per cent. Thus predictions of liquid viscosity were per­ formed over extended temperature rangeg, with good accuracy with­ out requiring viscosity data. A further refinement of the correction factor for each of the five series of homologues was introduced by correlation with two param­ eters; Trg and with the number of carbon atoms in the alkyl group, C. The use of the carbon parameter decreased the average error in pre­ dicted viscosity to 1. 78, 1. 95, 2. 39, 3. 46 and 14. 5 per cent for the n-paraffins, n-l-alkenes, n-alkylcyclohexanes, n-alkylbenzenes and the n-alcohols, respectively. The idealized liquid state model which is the basis of the present development does not adequately predict the viscous behavior of real liquids. It is significant, however, that the deviations from the model are relatively consistent, and may be taken into account by a relatively simple empirical function, applicable to a wide variety of liquids. This study also describes the experimental determination of density and kinematic viscosity over wide ranges of temperature and of molecu­ lar weight for the n-alcohols. A density apparatus based on the hydro­ static weighing method was constructed and used for the measurement of n-alcohol densities from room temperature to near their normal boiling points. The apparatus permitted a density measurement every 30 minutes on 5 ml of liquid sample with an average accuracy of 1. 4 x 10~4 g/ml, and a reproducibility of 1-4 x 10~4 g/ml. APPROVAL OF DISSERTATION VISCOSITY -DENSITY CORRELATION OF NEWTONIAN LIQUIDS BY MELVIN L. DR UIN FOR DEPARTMENT OF CHEMICAL ENGINEERING NEWARK COLLEGE OF ENGINEERING BY FACULTY COMMIT TEE APPROVED: CHAIRMAN NEWARK, NEW JERSEY JUNE, 1968 iv DEDICATION THE AUTHOR DEDICATES THIS DISSERATION TO THE MEMORY OF HIS FATHER-IN-LAW, LEWIS LEFKOWIT Z v ACKNOWLEDGEMENTS The author acknowledges the encouragement, advice and guidance offered by Dr. S. I. Kreps throughout this investigation. The author thanks Mr. G. Patel for his recommendations in computer programming; and Mr. A. LaSala for his assistance in construction of the experimental apparatus. The author acknowledges the financial support of this work extended by the Newark College of Engineering Research Foundation. In addition, the author offers special thanks to his wife, Marilyn,, for her understanding, patience, encouragement and confidence; and to his parents for their inspiration. vi TABLE OF CONTENTS Page No. TITLE PAGE . i ABSTRACT ii APPROVAL PAGE iv DEDICATION v ACKNOWLEDGEMENTS vi TABLE OF CONTENTS vii LIST OF FIGURES xi LIST OF TABLES xiii INTRODUCTION 1 Gas Viscosity 3 Liquid Viscosity 4 EXTENT OF PRESENT KNOWLEDGE 7 Correlation of Liquid Viscosity 7 Measurement of Liquid Density 12 Measurement of Weight of a Known Volume 12 Pycnometers 12 Dilatometers 13 Buoyancy Methods 14 Hydrostatic Weighing Method of Kohlrausch ... 14 Totally Immersed Hydrostatic Balance 15 Free Floats 15 vii TABLE OF CONTENTS (Continued) Page No. Falling Drop 15 Measurement of Viscosity of Newtonian Liquids .... 16 EXPERIMENTAL STUDIES 19 Compounds 19 Paraffins 19 Alcohols 19 Equipment 21 Density Apparatus 21 Vapor Bath 21 Heater 23 Balance 2 3 Plummet 30 Plummet Level Control • • • 30 Temperature Measurements 32 Pressure Control System 33 Viscosity Apparatus 3 8 Procedures 3 9 Density Measurements 3 9 Loading Density Sample Tube 3 9 Assembling the Density Apparatus 3 9 Weighing Plummet in Air 41 viii TABLE OF CONTENTS (Continued) Page No. Insertion of Plummet Into Density Sample Tube . 41 Weighing Plummet Immersed in Liquid Sample . 42 Calculation of Density 43 Kinematic Viscosity 46 Calculation of Kinematic Viscosity 47 Calibrations 48 Density Apparatus 48 Vapor Bath, Pressure-Temperature 48 Plummets 49 Viscometers 53 Results 56 Density Data of n-Alcohols 56 Interpolation of Density 62 Kinematic Viscosity Data of n-Alcohols 66 VISCOSITY-DENSITY CORRELATION 70 Development of Correlation 70 Viscosity of Monatomic Liquids 70 The Ratio K/fji 75 Viscosity and the Sonic Velocity 76 Application of Correlation 79 Empirical Corrections to the Model 81 ix TABLE OF CONTENTS (Continued) I Page No. Prediction of Viscosities 92 Single Viscosity Equation For Normal Hydrocarbons . 95 Parametric Predictor Equations 98 Significance of Z Function 103 CONCLUSIONS . 107 NOMENCLATURE 112 APPENDIX 116 Tables 116 Computer Programs 230 Sample Calculations 254 BIBLIOGRAPHY 257 VITA 263 x LIST OF FIGURES Figure No. Page No. 1 Vapor Bath 22 2 Density Sample Tube 24 3 Removable Density Adapter 25 4 Thermocouple Holder Tube 26 5 Assembled Density Apparatus (photograph) 27 6 Assembled Density Apparatus With Plummet (photograph) 2 8 7 Density Apparatus With Balance (photograph) 29 8 Plummet 31 9 Pressure Control System (photograph) 34 10 Pressure Control System 35 11 Density Apparatus With Auxiliary Equipment (photograph) 3 6 12 Viscosity Apparatus (photograph) 40 13 Density of n-Alcohols 58 14 Density of n-Alcohols, High Temperature Range 59 15 Kinematic Viscosity of n-Alcohols 67 16 Model for the Transfer of Sound 77 17 Z as a Function of Trg, n-Paraffins 86 18 Z as a Function of Trg, n-l-Alkenes 87 19 Z as a Function of Trg, n-Alkyl Cyclohexanes 88 xi LIST OF FIGURES (Continued) Figure No. Page No. 20 Z as a Function of Trg, n-Alkyl Benzenes 89 21 Z as a Function of Trg, n-Alcohols 90 22 Non-Linear Least Square Fits, Z as a Function of Trg, Five Series of Homologues 91 xii LIST OF TABLES Table No. Page No. 1 History of n-Alcohols