Transport Phenomena: an Introduction to Advanced Topics, by Larry A
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Theoretical Studies of Non-Newtonian and Newtonian Fluid Flow Through Porous Media
Lawrence Berkeley National Laboratory Lawrence Berkeley National Laboratory Title Theoretical Studies of Non-Newtonian and Newtonian Fluid Flow through Porous Media Permalink https://escholarship.org/uc/item/6zv599hc Author Wu, Y.S. Publication Date 1990-02-01 eScholarship.org Powered by the California Digital Library University of California Lawrence Berkeley Laboratory e UNIVERSITY OF CALIFORNIA EARTH SCIENCES DlVlSlON Theoretical Studies of Non-Newtonian and Newtonian Fluid Flow through Porous Media Y.-S. Wu (Ph.D. Thesis) February 1990 TWO-WEEK LOAN COPY This is a Library Circulating Copy which may be borrowed for two weeks. r- +. .zn Prepared for the U.S. Department of Energy under Contract Number DE-AC03-76SF00098. :0 DISCLAIMER I I This document was prepared as an account of work sponsored ' : by the United States Government. Neither the United States : ,Government nor any agency thereof, nor The Regents of the , I Univers~tyof California, nor any of their employees, makes any I warranty, express or implied, or assumes any legal liability or ~ : responsibility for the accuracy, completeness, or usefulness of t any ~nformation, apparatus, product, or process disclosed, or I represents that its use would not infringe privately owned rights. : Reference herein to any specific commercial products process, or I service by its trade name, trademark, manufacturer, or other- I wise, does not necessarily constitute or imply its endorsement, ' recommendation, or favoring by the United States Government , or any agency thereof, or The Regents of the University of Cali- , forma. The views and opinions of authors expressed herein do ' not necessarily state or reflect those of the United States : Government or any agency thereof or The Regents of the , Univers~tyof California and shall not be used for advertismg or I product endorsement purposes. -
Fluid Inertia and End Effects in Rheometer Flows
FLUID INERTIA AND END EFFECTS IN RHEOMETER FLOWS by JASON PETER HUGHES B.Sc. (Hons) A thesis submitted to the University of Plymouth in partial fulfilment for the degree of DOCTOR OF PHILOSOPHY School of Mathematics and Statistics Faculty of Technology University of Plymouth April 1998 REFERENCE ONLY ItorriNe. 9oo365d39i Data 2 h SEP 1998 Class No.- Corrtl.No. 90 0365439 1 ACKNOWLEDGEMENTS I would like to thank my supervisors Dr. J.M. Davies, Prof. T.E.R. Jones and Dr. K. Golden for their continued support and guidance throughout the course of my studies. I also gratefully acknowledge the receipt of a H.E.F.C.E research studentship during the period of my research. AUTHORS DECLARATION At no time during the registration for the degree of Doctor of Philosophy has the author been registered for any other University award. This study was financed with the aid of a H.E.F.C.E studentship and carried out in collaboration with T.A. Instruments Ltd. Publications: 1. J.P. Hughes, T.E.R Jones, J.M. Davies, *End effects in concentric cylinder rheometry', Proc. 12"^ Int. Congress on Rheology, (1996) 391. 2. J.P. Hughes, J.M. Davies, T.E.R. Jones, ^Concentric cylinder end effects and fluid inertia effects in controlled stress rheometry, Part I: Numerical simulation', accepted for publication in J.N.N.F.M. Signed ...^.^Ms>3.\^^. Date Ik.lp.^.m FLUH) INERTIA AND END EFFECTS IN RHEOMETER FLOWS Jason Peter Hughes Abstract This thesis is concerned with the characterisation of the flow behaviour of inelastic and viscoelastic fluids in steady shear and oscillatory shear flows on commercially available rheometers. -
CHEMICAL REACTION ENGINEERING* Current Status and Future Directions
[eJij9iviews and opinions CHEMICAL REACTION ENGINEERING* Current Status and Future Directions M. P. DUDUKOVIC and petrochemical industry provided a fertile ground Washington University for further development of reaction engineering con St. Louis, MO 63130 cepts. The final cornerstone of this new discipline was laid in 1957 by the First Symposium on Chemical HEMICAL REACTIONS have been used by man Reaction Engineering [3] which brought together and C kind since time immemorial to produce useful synthesized the European point of view. The Amer products such as wine, metals, etc. Nevertheless, the ican and European schools of thought were not identi unifying principles that today we call chemical reac cal, but in time they converged into the subject matter tion engineering were not developed until relatively a that we know today as chemical reaction engineering, short time ago. During the decade of the 1940's (not or CRE. The above chronology led to the establish even half a century ago!) a transition was made from ment of CRE as an accepted discipline over the span descriptive industrial chemistry to the conceptual un of a decade and a half. This does not imply that all the ification of reaction processes and reactor types. The principles important in CRE were discovered then. pioneering work in this area of industrial practice was The foundation for CRE had already been established done by Denbigh [1] in England. Then in 1947, by the early work of Frank-Kamenteski, Damkohler, Hougen and Watson [2] published the first textbook Zeldovitch, etc., but at that time they represented in the U.S. -
Lecture 1: Introduction
Lecture 1: Introduction E. J. Hinch Non-Newtonian fluids occur commonly in our world. These fluids, such as toothpaste, saliva, oils, mud and lava, exhibit a number of behaviors that are different from Newtonian fluids and have a number of additional material properties. In general, these differences arise because the fluid has a microstructure that influences the flow. In section 2, we will present a collection of some of the interesting phenomena arising from flow nonlinearities, the inhibition of stretching, elastic effects and normal stresses. In section 3 we will discuss a variety of devices for measuring material properties, a process known as rheometry. 1 Fluid Mechanical Preliminaries The equations of motion for an incompressible fluid of unit density are (for details and derivation see any text on fluid mechanics, e.g. [1]) @u + (u · r) u = r · S + F (1) @t r · u = 0 (2) where u is the velocity, S is the total stress tensor and F are the body forces. It is customary to divide the total stress into an isotropic part and a deviatoric part as in S = −pI + σ (3) where tr σ = 0. These equations are closed only if we can relate the deviatoric stress to the velocity field (the pressure field satisfies the incompressibility condition). It is common to look for local models where the stress depends only on the local gradients of the flow: σ = σ (E) where E is the rate of strain tensor 1 E = ru + ruT ; (4) 2 the symmetric part of the the velocity gradient tensor. The trace-free requirement on σ and the physical requirement of symmetry σ = σT means that there are only 5 independent components of the deviatoric stress: 3 shear stresses (the off-diagonal elements) and 2 normal stress differences (the diagonal elements constrained to sum to 0). -
Transport Phenomena: Mass Transfer
Transport Phenomena Mass Transfer (1 Credit Hour) μ α k ν DAB Ui Uo UD h h Pr f Gr Re Le i o Nu Sh Pe Sc kc Kc d Δ ρ Σ Π ∂ ∫ Dr. Muhammad Rashid Usman Associate professor Institute of Chemical Engineering and Technology University of the Punjab, Lahore. Jul-2016 The Text Book Please read through. Bird, R.B. Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena. 2nd ed. John Wiley & Sons, Inc. Singapore. 2 Transfer processes For a transfer or rate process Rate of a quantity driving force Rate of a quantity area for the flow of the quantity 1 Rate of a quantity Area driving force resistance Rate of a quantity conductance Area driving force Flux of a quantity conductance driving force Conductance is a transport property. Compare the above equations with Ohm’s law of electrical 3 conductance Transfer processes change in the quanity Rate of a quantity change in time rate of the quantity Flux of a quantity area for flow of the quantity change in the quanity Gradient of a quantity change in distance 4 Transfer processes In chemical engineering, we study three transfer processes (rate processes), namely •Momentum transfer or Fluid flow •Heat transfer •Mass transfer The study of these three processes is called as transport phenomena. 5 Transfer processes Transfer processes are either: • Molecular (rate of transfer is only a function of molecular activity), or • Convective (rate of transfer is mainly due to fluid motion or convective currents) Unlike momentum and mass transfer processes, heat transfer has an added mode of transfer called as radiation heat transfer. -
The Infinite and Contradiction: a History of Mathematical Physics By
The infinite and contradiction: A history of mathematical physics by dialectical approach Ichiro Ueki January 18, 2021 Abstract The following hypothesis is proposed: \In mathematics, the contradiction involved in the de- velopment of human knowledge is included in the form of the infinite.” To prove this hypothesis, the author tries to find what sorts of the infinite in mathematics were used to represent the con- tradictions involved in some revolutions in mathematical physics, and concludes \the contradiction involved in mathematical description of motion was represented with the infinite within recursive (computable) set level by early Newtonian mechanics; and then the contradiction to describe discon- tinuous phenomena with continuous functions and contradictions about \ether" were represented with the infinite higher than the recursive set level, namely of arithmetical set level in second or- der arithmetic (ordinary mathematics), by mechanics of continuous bodies and field theory; and subsequently the contradiction appeared in macroscopic physics applied to microscopic phenomena were represented with the further higher infinite in third or higher order arithmetic (set-theoretic mathematics), by quantum mechanics". 1 Introduction Contradictions found in set theory from the end of the 19th century to the beginning of the 20th, gave a shock called \a crisis of mathematics" to the world of mathematicians. One of the contradictions was reported by B. Russel: \Let w be the class [set]1 of all classes which are not members of themselves. Then whatever class x may be, 'x is a w' is equivalent to 'x is not an x'. Hence, giving to x the value w, 'w is a w' is equivalent to 'w is not a w'."[52] Russel described the crisis in 1959: I was led to this contradiction by Cantor's proof that there is no greatest cardinal number. -
The Scottish Genealogist
THE SCOTTISH GENEALOGY SOCIETY THE SCOTTISH GENEALOGIST INDEX TO VOLUMES LIX-LXI 2012-2014 Published by The Scottish Genealogy Society The Index covers the years 2012-2014 Volumes LIX-LXI Compiled by D.R. Torrance 2015 The Scottish Genealogy Society – ISSN 0330 337X Contents Please click on the subject to be visited. ADDITIONS TO THE LIBRARY APPRECIATIONS ARTICLE TITLES BOOKMARKS BOOK REVIEWS CONTRIBUTORS FAMILY TREES GENERAL INDEX ILLUSTRATIONS INTRODUCTION QUERIES INTRODUCTION Where a personal or place name is mentioned several times in an article, only the first mention is indexed. LIX, LX, LXI = Volume number i. ii. iii. iv = Part number 1- = page number ; - separates part numbers within the same volume : - separates volume numbers BOOKMARKS The contents of this CD have been bookmarked. Select the second icon down at the left-hand side of the document. Use the + to expand a section and the – to reduce the selection. If this icon is not visible go to View > Show/Hide > Navigation Panes > Bookmarks. Recent Additions to the Library (compiled by Joan Keen & Eileen Elder) LIX.i.43; ii.102; iii.154: LX.i.48; ii.97; iii.144; iv.188: LXI.i.33; ii.77; iii.114; Appreciations 2012-2014 Ainslie, Fred LIX.i.46 Ferguson, Joan Primrose Scott LX.iv.173 Hampton, Nettie LIX.ii.67 Willsher, Betty LIX.iv.205 Article Titles 2012-2014 A Call to Clan Shaw LIX.iii.145; iv.188 A Case of Adultery in Roslin Parish, Midlothian LXI.iv.127 A Knight in Newhaven: Sir Alexander Morrison (1799-1866) LXI.i.3 A New online Medical Database (Royal College of Physicians) -
A Fluid Is Defined As a Substance That Deforms Continuously Under Application of a Shearing Stress, Regardless of How Small the Stress Is
FLUID MECHANICS & BIOTRIBOLOGY CHAPTER ONE FLUID STATICS & PROPERTIES Dr. ALI NASER Fluids Definition of fluid: A fluid is defined as a substance that deforms continuously under application of a shearing stress, regardless of how small the stress is. To study the behavior of materials that act as fluids, it is useful to define a number of important fluid properties, which include density, specific weight, specific gravity, and viscosity. Density is defined as the mass per unit volume of a substance and is denoted by the Greek character ρ (rho). The SI units for ρ are kg/m3. Specific weight is defined as the weight per unit volume of a substance. The SI units for specific weight are N/m3. Specific gravity S is the ratio of the weight of a liquid at a standard reference temperature to the o weight of water. For example, the specific gravity of mercury SHg = 13.6 at 20 C. Specific gravity is a unit-less parameter. Density and specific weight are measures of the “heaviness” of a fluid. Example: What is the specific gravity of human blood, if the density of blood is 1060 kg/m3? Solution: ⁄ ⁄ Viscosity, shearing stress and shearing strain Viscosity is a measure of a fluid's resistance to flow. It describes the internal friction of a moving fluid. A fluid with large viscosity resists motion because its molecular makeup gives it a lot of internal friction. A fluid with low viscosity flows easily because its molecular makeup results in very little friction when it is in motion. Gases also have viscosity, although it is a little harder to notice it in ordinary circumstances. -
Rheology of Petroleum Fluids
ANNUAL TRANSACTIONS OF THE NORDIC RHEOLOGY SOCIETY, VOL. 20, 2012 Rheology of Petroleum Fluids Hans Petter Rønningsen, Statoil, Norway ABSTRACT NEWTONIAN FLUIDS Among the areas where rheology plays In gas reservoirs, the flow properties of an important role in the oil and gas industry, the simplest petroleum fluids, i.e. the focus of this paper is on crude oil hydrocarbons with less than five carbon rheology related to production. The paper atoms, play an essential role in production. gives an overview of the broad variety of It directly impacts the productivity. The rheological behaviour, and corresponding viscosity of single compounds are well techniques for investigation, encountered defined and mixture viscosity can relatively among petroleum fluids. easily be calculated. Most often reservoir gas viscosity is though measured at reservoir INTRODUCTION conditions as part of reservoir fluid studies. Rheology plays a very important role in The behaviour is always Newtonian. The the petroleum industry, in drilling as well as main challenge in terms of measurement and production. The focus of this paper is on modelling, is related to very high pressures crude oil rheology related to production. (>1000 bar) and/or high temperatures (170- Drilling and completion fluids are not 200°C) which is encountered both in the covered. North Sea and Gulf of Mexico. Petroleum fluids are immensely complex Hydrocarbon gases also exist dissolved mixtures of hydrocarbon compounds, in liquid reservoir oils and thereby impact ranging from the simplest gases, like the fluid viscosity and productivity of these methane, to large asphaltenic molecules reservoirs. Reservoir oils are also normally with molecular weights of thousands. -
Or, If the Sine Functions Be Eliminated by Means of (11)
52 BINOMIAL THEOREM AND NEWTONS MONUMENT. [Nov., or, if the sine functions be eliminated by means of (11), e <*i : <** : <xz = X^ptptf : K(P*ptf : A3(Pi#*) . (53) While (52) does not enable us to construct the point of least attraction, it furnishes a solution of the converse problem : to determine the ratios of the masses of three points so as to make the sum of their attractions on a point P within their triangle a minimum. If, in (50), we put n = 2 and ax + a% = 1, and hence pt + p% = 1, this equation can be regarded as that of a curve whose ordinate s represents the sum of the attractions exerted by the points et and e2 on the foot of the ordinate. This curve approaches asymptotically the perpendiculars erected on the vector {ex — e2) at ex and e% ; and the point of minimum attraction corresponds to its lowest point. Similarly, in the case n = 3, the sum of the attractions exerted by the vertices of the triangle on any point within this triangle can be rep resented by the ordinate of a surface, erected at this point at right angles to the plane of the triangle. This suggestion may here suffice. 22. Concluding remark.—Further results concerning gen eralizations of the problem of the minimum sum of distances are reserved for a future communication. WAS THE BINOMIAL THEOEEM ENGKAVEN ON NEWTON'S MONUMENT? BY PKOFESSOR FLORIAN CAJORI. Moritz Cantor, in a recently published part of his admir able work, Vorlesungen über Gescliichte der Mathematik, speaks of the " Binomialreihe, welcher man 1727 bei Newtons Tode . -
Chemical Engineering - CHEN 1
Chemical Engineering - CHEN 1 Chemical Engineering - CHEN Courses CHEN 2100 PRINCIPLES OF CHEMICAL ENGINEERING (4) LEC. 3. LAB. 3. Pr. (CHEM 1110 or CHEM 1117 or CHEM 1030 or CHEM 1033) and (MATH 1610 or MATH 1613 or MATH 1617) and (P/C CHEM 1120 or P/C CHEM 1127 or P/C CHEM 1040 or P/ C CHEM 1043) and (P/C MATH 1620 or MATH 1623 or P/C MATH 1627) and (P/C PHYS 1600 or P/C PHYS 1607). Application of multicomponent material and energy balances to chemical processes involving phase changes and chemical reactions. CHEN 2110 CHEMICAL ENGINEERING THERMODYNAMICS (3) LEC. 3. Pr. (CHEM 1030 or CHEM 1033 or CHEM 1110 or CHEM 1117) and (MATH 1620 or MATH 1623 or MATH 1627) and (CHEN 2100) and (P/C PHYS 1600 or P/C PHYS 1607) and (P/C CHEN 2650). This course is intended to comprehensively introduce the thermodynamics of single- and multi-phase, pure systems, including the first and second laws of thermodynamics, equations of state, simple processes and cycles, and their applications in chemical engineering. CHEN 2610 TRANSPORT I (3) LEC. 3. Pr. (PHYS 1600 or PHYS 1607) and CHEN 2100 and (P/C MATH 2630 or P/C MATH 2637) and (P/C ENGR 2010 or P/C CHEN 2110). CHEN 2100 requires a grade of C or better. Introduction to fluid statics and dynamics; dimensional analysis; compressible and incompressible flows; design of flow systems, introduction to fluid solids transport including fluidization, flow through process media and multiphase flows. CHEN 2650 CHEMICAL ENGINEERING APPLICATIONS OF MATHEMATICAL TECHNIQUES (3) LEC. -
Philosophical Transactions (A)
INDEX TO THE PHILOSOPHICAL TRANSACTIONS (A) FOR THE YEAR 1889. A. A bney (W. de W.). Total Eclipse of the San observed at Caroline Island, on 6th May, 1883, 119. A bney (W. de W.) and T horpe (T. E.). On the Determination of the Photometric Intensity of the Coronal Light during the Solar Eclipse of August 28-29, 1886, 363. Alcohol, a study of the thermal properties of propyl, 137 (see R amsay and Y oung). Archer (R. H.). Observations made by Newcomb’s Method on the Visibility of Extension of the Coronal Streamers at Hog Island, Grenada, Eclipse of August 28-29, 1886, 382. Atomic weight of gold, revision of the, 395 (see Mallet). B. B oys (C. V.). The Radio-Micrometer, 159. B ryan (G. H.). The Waves on a Rotating Liquid Spheroid of Finite Ellipticity, 187. C. Conroy (Sir J.). Some Observations on the Amount of Light Reflected and Transmitted by Certain 'Kinds of Glass, 245. Corona, on the photographs of the, obtained at Prickly Point and Carriacou Island, total solar eclipse, August 29, 1886, 347 (see W esley). Coronal light, on the determination of the, during the solar eclipse of August 28-29, 1886, 363 (see Abney and Thorpe). Coronal streamers, observations made by Newcomb’s Method on the Visibility of, Eclipse of August 28-29, 1886, 382 (see A rcher). Cosmogony, on the mechanical conditions of a swarm of meteorites, and on theories of, 1 (see Darwin). Currents induced in a spherical conductor by variation of an external magnetic potential, 513 (see Lamb). 520 INDEX.