Dynamics in nanoworlds
|
|
- Karen McKenzie
- 8 years ago
- Views:
Transcription
1 Dynamics in nanoworlds Interplay of energy, diffusion and friction in (sub)cellular world 1
2 NB Queste diapositive sono state preparate per il corso di Biofisica tenuto dal Dr. Attilio V. Vargiu presso il Dipartimento di Fisica nell A.A. 2014/2015 Non sostituiscono il materiale didattico consigliato a piè del programma. 2
3 References Books and other sources Biological Physics (updated 1 st ed.), Philip Nelson, Chap. 5 Biochemistry (5 th ed.), Berg et al., Chap. 4 Movies Exercise 3
4 Sorting molecules by mass/charge A way of separating molecules by their mass is to centrifuge them in order to accelerate sedimentation. Recalling Archimedes principle, force driving sedimentation of an object of mass m under the action of a acceleration gravity a s directed along z is: f = du dz = ( m V l ρ l )a s m net a s $% U = ma s Δz ( V l ρ l a s )Δz& ' Flux j of molecules under force f and diffusion D can be calculated as (analogous of Nerst-Planck formula): ( ) = m neta s c( z) j z ς D c z ( ) ς D=k B T ### j z % ( ) = D m net ' k B T a sc z & ( ) c( z) ( * ) 4
5 Sorting molecules by mass/charge Centrifuges are needed because at equilibrium (j=0) thermal agitation often keeps a relevant fraction of particles in suspension: c( z) e m neta s z k T B = e z z* z* = k B T m net a s z* scale height Example a s =g and m typical values of a globular protein (e.g. myoglobin): m 17Kg/mol (m net m/4) gives for z* a value of ~60m. In a tube of 10 cm the concentration at the top is equal to ~ 99.8 % of that at the bottom: c( 10 cm) c( 0 cm)e 0.1m 60m 99.8 c( 0 cm) The suspension never settles out equilibrium colloid or colloidal suspension. Settling occurs when: m net a s h k B T >1 "# h = z top z bottom $ % 5
6 Sorting molecules by mass/charge For a given molecule, one can act on h, T, and on a s, as done in centrifuges, where a s can be as high as 10 6 m/s 2. Equilibrium found again by imposing compensation between drift flux, due to viscosity of the medium where particles are suspended: j drift ( r) = v drift c( r) = f ς c ( r ) = m netω s ς 2 r ( ) = m netω s c r k B T 2 rd c( r) and diffusion flux due to Fick s law: ( ) = D dc ( r ) j D r dr giving the equilibrium concentration as a function of radial position: c( r) e m netω 2 s r 2 2k B T sedimentation distribution in centrifuge 6
7 Sorting molecules by mass/charge A sedimentation coefficient s can be defined which is an intrinsic property of the particle: s = v drift g = m net ς s is the time needed for a particle to reach a terminal velocity, and it is measured in svedbergs (10-13 s). s depends on friction ζ, in turn depending on viscosity η of the fluid where particles are suspended, as well as on their shape. For a spherical particle of radius R in a medium with viscosity η, friction is given by Stokes formula: ς = 6πηR η for water at room temperature is 10-3 Pa s. 7
8 Sorting molecules by mass/charge s = v drift g = m net ς ς = 6πηR 8
9 Sorting molecules by mass/charge In electrophoresis sedimentation is facilitated by means of applied electric field to a ionic solution. Drift velocity will be proportional to charge and electric field strength: v drift = f ς = qe ς As for the centrifuge, an intrinsic coefficient can be defined, the electrophoretic mobility µ e : µ e = q ς!!!!!! µ spherical particles e = q 6πηR Stokes approximation often valid also for non-spherical particles due to solvation shell of charged molecules in polar ionic solutions. With charged biomolecules mobility will depend on viscosity of medium, and on shape and charge of particles. 9
10 Sorting molecules by mass/charge Gel electrophoresis one of preferred techniques to separate and analyze molecular components of biological assemblies. Put macromolecule (DNA, RNA, protein) in a gel and switch on electric field. Add denaturing agent (e.g. SDS for proteins) to reduce effects of different folding. One SDS anion binds about two aa in proteins charge proportional to protein mass. Gel used as molecular sieve enhancing filtration of molecules by their size. Biochemistry, J. Berg et al., 5 th ed.,
11 Sorting molecules by mass/charge Separation is reflected by occurrence of different migration bands (e.g. staining with dye). Small proteins move rapidly through the gel, whereas large ones not. µe of most polypeptide chains under these conditions ~ log M (some carbohydrate-rich proteins and membrane proteins escape this rule). Biochemistry, J. Berg et al., 5th ed.,
12 Mixing and viscosity From Einstein and Stokes relations, inverse proportionality between diffusion coefficient of spherical object and viscosity of medium: D = k B T ς η 1 Greater the viscosity, slower will be diffusion Explains why a small blob of thick fluid can apparently mix and reappear if a slow mixing movement is followed by its reverse. Biological Physics, P. Nelson, 1 st ed. updated,
13 Mixing and viscosity In laminar flow conditions (low Reynolds number) with thick fluids, motion of stirring rod or one cylinder relatively to a second concentric one only cause mixture of peripheral layers of molecules, due to sliding of fluid layers one over another. Diffusion randomize molecules over relatively long times, thus fluid layers can slide back if reverse movement is applied, reassembling blob. The blob has never fully mixed due to the viscosity of the fluid. The opposite occurs with turbulent flows (e.g. milk on coffee). Biological Physics, P. Nelson, 1 st ed. updated,
14 In laminar flow viscous force due to shear motions with (low) v 0 among fluid planes of area A and separated by distance dx given by: f frict = ηadv dx Newtonian fluid, planar geometry Inertia vs. friction Biological Physics, P. Nelson, 1 st ed. updated, 2008 Though no intrinsic definition of large and small viscosity, for isotropic Newtonian fluids viscous regime takes place when ratio f frict /f crit is small, the viscous critical force f crit being: f crit = η 2 ρ m f frict /f crit > 1 inertial forces dominates over friction (turbulent flow: large density mass or low viscosity of fluid). f frict /f crit < 1 friction quickly damps out inertial effects (laminar flow). 14
15 Inertia vs. friction Biological Physics, P. Nelson, 1 st ed. updated, 2008 Newtonian fluid has not intrinsic scale length! Size of forces involved in the process relative to a critical value discriminates between laminar and turbulent flows. f crit of water in range of nn. In molecular world forces have values ~pn friction dominates molecular processes occurring in aqueous solvents! Flows are laminar! 15
16 Reynolds number Reynolds number corresponds to the ratio between inertial and frictional forces in the dynamics of a fluid: R = f inertial f frict = vlρ m η L typical linear dimension of object moving relatively to the fluid. R small (< 1000) friction dominates, laminar flow. R large (> 3000) inertial effects dominate, turbulence. Experiments by Reynolds shown that distinction based on R is generally applicable whenever the object can be characterized by a length scale L. R related to the concept of critical force: R f frict f crit 16
17 Reynolds number Relation demonstrated considering a spherical object immersed in a fluid under laminar flow conditions. Biological Physics, P. Nelson, 1 st ed. updated, 2008 Newton law for small volume of fluid involves pressure and viscous forces: f inertial = mdv dt = f p + f frict Small volume of fluid accelerates nearly sphere: direction changes in Δt R/v. Acceleration comparable to v in size dv/dt v 2 /R. f inertial = mdv dt = ρ m l 3 v 2 R 17
18 Reynolds number Inertial term must be compared to frictional force: f frict = ηl 2 dv dx Net force due to pushing by upper layer and pulling to lower one, approximated by derivative times length of volume fluid: f frict l df dx = ηl 3 d 2 v dx 2 ηl 3 v R 2 Dividing the modulus of this quantity by f frict gives the Reynolds number definition: R = f inertial f frict = vrρ m η A 30m long whale swimming in water at 10 m/s has R~ A 1µm thick bacterium swimming at 30 µm/s has R~3 10-5! 18
19 Reversibility of flow At low Reynolds number, flow is reversible 19
20 Swimming of bacteria Reversibility means that anything swimming by repeated flapping motions can t get anywhere. If it moves forward in one stroke, the other stroke will bring it right back to where it started! At low Reynolds number, body and paddles of bacterium move with friction coefficients ζ 1 and ζ 2 respectively. Δx = u Δt Δx' = u'δt ' Net movement: Δx Δx' =? To estimate u (drift velocity of the body) and Δx due to paddle movement with velocity v, apply reaction law drag forces: f body = f paddle u( ζ 0 +ζ 1 ) = vζ 1 ( ) Δx = vζ 1 ( ζ 0 +ζ 1 ) u = vζ 1 ζ 0 +ζ 1 ( )Δt 20
21 Swimming of bacteria Reversibility means that anything swimming by repeated flapping motions can t get anywhere. If it moves forward in one stroke, the other stroke will bring it right back to where it started! At low Reynolds number, body and paddles of bacterium move with friction coefficients ζ 1 and ζ 2 respectively. Δx = u Δt Δx' = u'δt ' Net movement: Δx Δx' =? u and Δx due to back movement with velocity v are: u' = v'ζ 1 ( ζ 0 +ζ 1 ) Δx' = ( v'ζ 1 ( ζ 0 +ζ 1 ))Δt ' as the paddles return to their initial position, it must be: vδt = v'δt ' Δx' = ( vζ 1 ( ζ 0 +ζ 1 ))Δt = Δx 21
Basic Principles in Microfluidics
Basic Principles in Microfluidics 1 Newton s Second Law for Fluidics Newton s 2 nd Law (F= ma) : Time rate of change of momentum of a system equal to net force acting on system!f = dp dt Sum of forces
More informationXI / PHYSICS FLUIDS IN MOTION 11/PA
Viscosity It is the property of a liquid due to which it flows in the form of layers and each layer opposes the motion of its adjacent layer. Cause of viscosity Consider two neighboring liquid layers A
More informationDiffusion and Fluid Flow
Diffusion and Fluid Flow What determines the diffusion coefficient? What determines fluid flow? 1. Diffusion: Diffusion refers to the transport of substance against a concentration gradient. ΔS>0 Mass
More informationBasic Equations, Boundary Conditions and Dimensionless Parameters
Chapter 2 Basic Equations, Boundary Conditions and Dimensionless Parameters In the foregoing chapter, many basic concepts related to the present investigation and the associated literature survey were
More informationNatural Convection. Buoyancy force
Natural Convection In natural convection, the fluid motion occurs by natural means such as buoyancy. Since the fluid velocity associated with natural convection is relatively low, the heat transfer coefficient
More informationNotes on Polymer Rheology Outline
1 Why is rheology important? Examples of its importance Summary of important variables Description of the flow equations Flow regimes - laminar vs. turbulent - Reynolds number - definition of viscosity
More informationFLUID DYNAMICS. Intrinsic properties of fluids. Fluids behavior under various conditions
FLUID DYNAMICS Intrinsic properties of fluids Fluids behavior under various conditions Methods by which we can manipulate and utilize the fluids to produce desired results TYPES OF FLUID FLOW Laminar or
More informationThe Viscosity of Fluids
Experiment #11 The Viscosity of Fluids References: 1. Your first year physics textbook. 2. D. Tabor, Gases, Liquids and Solids: and Other States of Matter (Cambridge Press, 1991). 3. J.R. Van Wazer et
More informationViscoelasticity of Polymer Fluids.
Viscoelasticity of Polymer Fluids. Main Properties of Polymer Fluids. Entangled polymer fluids are polymer melts and concentrated or semidilute (above the concentration c) solutions. In these systems polymer
More informationSIZE OF A MOLECULE FROM A VISCOSITY MEASUREMENT
Experiment 8, page 1 Version of April 25, 216 Experiment 446.8 SIZE OF A MOLECULE FROM A VISCOSITY MEASUREMENT Theory Viscous Flow. Fluids attempt to minimize flow gradients by exerting a frictional force,
More informationFluids and Solids: Fundamentals
Fluids and Solids: Fundamentals We normally recognize three states of matter: solid; liquid and gas. However, liquid and gas are both fluids: in contrast to solids they lack the ability to resist deformation.
More informationTeil I. Student Laboratory Manuals
Teil I Student Laboratory Manuals 1 IR1 5. Fluid friction in liquids 5.1 Introduction Generally the term fluid is understood to be matter either in the gaseous or liquid state. The physics involved on
More information1 The basic equations of fluid dynamics
1 The basic equations of fluid dynamics The main task in fluid dynamics is to find the velocity field describing the flow in a given domain. To do this, one uses the basic equations of fluid flow, which
More information4 Microscopic dynamics
4 Microscopic dynamics In this section we will look at the first model that people came up with when they started to model polymers from the microscopic level. It s called the Oldroyd B model. We will
More informationFLUID FLOW STREAMLINE LAMINAR FLOW TURBULENT FLOW REYNOLDS NUMBER
VISUAL PHYSICS School of Physics University of Sydney Australia FLUID FLOW STREAMLINE LAMINAR FLOW TURBULENT FLOW REYNOLDS NUMBER? What type of fluid flow is observed? The above pictures show how the effect
More information1. Fluids Mechanics and Fluid Properties. 1.1 Objectives of this section. 1.2 Fluids
1. Fluids Mechanics and Fluid Properties What is fluid mechanics? As its name suggests it is the branch of applied mechanics concerned with the statics and dynamics of fluids - both liquids and gases.
More informationLecture 24 - Surface tension, viscous flow, thermodynamics
Lecture 24 - Surface tension, viscous flow, thermodynamics Surface tension, surface energy The atoms at the surface of a solid or liquid are not happy. Their bonding is less ideal than the bonding of atoms
More informationCBE 6333, R. Levicky 1 Review of Fluid Mechanics Terminology
CBE 6333, R. Levicky 1 Review of Fluid Mechanics Terminology The Continuum Hypothesis: We will regard macroscopic behavior of fluids as if the fluids are perfectly continuous in structure. In reality,
More informationDimensional Analysis
Dimensional Analysis An Important Example from Fluid Mechanics: Viscous Shear Forces V d t / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / Ƭ = F/A = μ V/d More generally, the viscous
More informationLecture 5 Hemodynamics. Description of fluid flow. The equation of continuity
1 Lecture 5 Hemodynamics Description of fluid flow Hydrodynamics is the part of physics, which studies the motion of fluids. It is based on the laws of mechanics. Hemodynamics studies the motion of blood
More informationFor Water to Move a driving force is needed
RECALL FIRST CLASS: Q K Head Difference Area Distance between Heads Q 0.01 cm 0.19 m 6cm 0.75cm 1 liter 86400sec 1.17 liter ~ 1 liter sec 0.63 m 1000cm 3 day day day constant head 0.4 m 0.1 m FINE SAND
More informationThe ratio of inertial to viscous forces is commonly used to scale fluid flow, and is called the Reynolds number, given as:
12.001 LAB 3C: STOKES FLOW DUE: WEDNESDAY, MARCH 9 Lab Overview and Background The viscosity of a fluid describes its resistance to deformation. Water has a very low viscosity; the force of gravity causes
More informationChapter 3 Contd. Western blotting & SDS PAGE
Chapter 3 Contd. Western blotting & SDS PAGE Western Blot Western blots allow investigators to determine the molecular weight of a protein and to measure relative amounts of the protein present in different
More information4.What is the appropriate dimensionless parameter to use in comparing flow types? YOUR ANSWER: The Reynolds Number, Re.
CHAPTER 08 1. What is most likely to be the main driving force in pipe flow? A. Gravity B. A pressure gradient C. Vacuum 2.What is a general description of the flow rate in laminar flow? A. Small B. Large
More informationRheological Properties of Topical Formulations
Rheological Properties of Topical Formulations Hemi Nae, PhD Hydan Technologies, Inc. Key Words Complex Modulus, Creep/Recovery, Dilatant Flow, Dynamic Viscosity, Flow, Flow Curve, Flow Models, Frequency
More informationNUMERICAL ANALYSIS OF THE EFFECTS OF WIND ON BUILDING STRUCTURES
Vol. XX 2012 No. 4 28 34 J. ŠIMIČEK O. HUBOVÁ NUMERICAL ANALYSIS OF THE EFFECTS OF WIND ON BUILDING STRUCTURES Jozef ŠIMIČEK email: jozef.simicek@stuba.sk Research field: Statics and Dynamics Fluids mechanics
More informationFluid Mechanics: Static s Kinematics Dynamics Fluid
Fluid Mechanics: Fluid mechanics may be defined as that branch of engineering science that deals with the behavior of fluid under the condition of rest and motion Fluid mechanics may be divided into three
More informationThe Viscosity of Fluids
Experiment #11 The Viscosity of Fluids References: 1. Your first year physics textbook. 2. D. Tabor, Gases, Liquids and Solids: and Other States of Matter (Cambridge Press, 1991). 3. J.R. Van Wazer et
More informationViscous flow in pipe
Viscous flow in pipe Henryk Kudela Contents 1 Laminar or turbulent flow 1 2 Balance of Momentum - Navier-Stokes Equation 2 3 Laminar flow in pipe 2 3.1 Friction factor for laminar flow...........................
More informationCollision of a small bubble with a large falling particle
EPJ Web of Conferences 67, 212 (214) DOI: 1.11/ epjconf/ 21467212 C Owned by the authors, published by EDP Sciences, 214 Collision of a small bubble with a large falling particle Jiri Vejrazka 1,a, Martin
More informationApproaches that can be used to study expression of specific proteins
Approaches that can be used to study expression of specific proteins Receptors and transporters Homogenate binding studies Receptor autoradiography Radiochemical Western blotting Immunohistochemistry/cytochemistry
More information240EQ014 - Transportation Science
Coordinating unit: 240 - ETSEIB - Barcelona School of Industrial Engineering Teaching unit: 713 - EQ - Department of Chemical Engineering Academic year: Degree: 2015 MASTER'S DEGREE IN CHEMICAL ENGINEERING
More informationMeasurement of the viscosities of He, Ne and Ar for the determination of their gas kinetic diameters.
American Journal of Engineering Research (AJER) e-issn: 2320-0847 p-issn : 2320-0936 Volume-4, Issue-11, pp-57-62 www.ajer.org Research Paper Measurement of the viscosities of He, Ne and Ar for the determination
More informationSteady Heat Conduction
Steady Heat Conduction In thermodynamics, we considered the amount of heat transfer as a system undergoes a process from one equilibrium state to another. hermodynamics gives no indication of how long
More informationLecture L2 - Degrees of Freedom and Constraints, Rectilinear Motion
S. Widnall 6.07 Dynamics Fall 009 Version.0 Lecture L - Degrees of Freedom and Constraints, Rectilinear Motion Degrees of Freedom Degrees of freedom refers to the number of independent spatial coordinates
More informationContents. Microfluidics - Jens Ducrée Physics: Fluid Dynamics 1
Contents 1. Introduction 2. Fluids 3. Physics of Microfluidic Systems 4. Microfabrication Technologies 5. Flow Control 6. Micropumps 7. Sensors 8. Ink-Jet Technology 9. Liquid Handling 10.Microarrays 11.Microreactors
More informationA LAMINAR FLOW ELEMENT WITH A LINEAR PRESSURE DROP VERSUS VOLUMETRIC FLOW. 1998 ASME Fluids Engineering Division Summer Meeting
TELEDYNE HASTINGS TECHNICAL PAPERS INSTRUMENTS A LAMINAR FLOW ELEMENT WITH A LINEAR PRESSURE DROP VERSUS VOLUMETRIC FLOW Proceedings of FEDSM 98: June -5, 998, Washington, DC FEDSM98 49 ABSTRACT The pressure
More informationVISUAL PHYSICS School of Physics University of Sydney Australia. Why do cars need different oils in hot and cold countries?
VISUAL PHYSICS School of Physics University of Sydney Australia FLUID FLOW VISCOSITY POISEUILLE'S LAW? Why do cars need different oils in hot and cold countries? Why does the engine runs more freely as
More informationOUTCOME 3 TUTORIAL 5 DIMENSIONAL ANALYSIS
Unit 41: Fluid Mechanics Unit code: T/601/1445 QCF Level: 4 Credit value: 15 OUTCOME 3 TUTORIAL 5 DIMENSIONAL ANALYSIS 3 Be able to determine the behavioural characteristics and parameters of real fluid
More informationDifferential Relations for Fluid Flow. Acceleration field of a fluid. The differential equation of mass conservation
Differential Relations for Fluid Flow In this approach, we apply our four basic conservation laws to an infinitesimally small control volume. The differential approach provides point by point details of
More informationOcean Tracers. From Particles to sediment Thermohaline Circulation Past present and future ocean and climate. Only 4 hours left.
Ocean Tracers Basic facts and principles (Size, depth, S, T,, f, water masses, surface circulation, deep circulation, observing tools, ) Seawater not just water (Salt composition, Sources, sinks,, mixing
More informationRHEOLOGY RHEOLOGY Science describing the flow and deformation of matter under stress. Rheo = the flow Viscosity (η) is the resistance of a fluid material to flow under stress. The higher the viscosity,
More informationPHYSICS 111 HOMEWORK SOLUTION #10. April 8, 2013
PHYSICS HOMEWORK SOLUTION #0 April 8, 203 0. Find the net torque on the wheel in the figure below about the axle through O, taking a = 6.0 cm and b = 30.0 cm. A torque that s produced by a force can be
More informationLiposomes, micelles, membranes
Liposomes, micelles, membranes Architectures of phospholipids Membrane proteins 1 NB Queste diapositive sono state preparate per il corso di Biofisica tenuto dal Dr. Attilio V. Vargiu presso il Dipartimento
More informationCE 204 FLUID MECHANICS
CE 204 FLUID MECHANICS Onur AKAY Assistant Professor Okan University Department of Civil Engineering Akfırat Campus 34959 Tuzla-Istanbul/TURKEY Phone: +90-216-677-1630 ext.1974 Fax: +90-216-677-1486 E-mail:
More informationIntroduction to Microfluidics. Date: 2013/04/26. Dr. Yi-Chung Tung. Outline
Introduction to Microfluidics Date: 2013/04/26 Dr. Yi-Chung Tung Outline Introduction to Microfluidics Basic Fluid Mechanics Concepts Equivalent Fluidic Circuit Model Conclusion What is Microfluidics Microfluidics
More informationPhysics 9e/Cutnell. correlated to the. College Board AP Physics 1 Course Objectives
Physics 9e/Cutnell correlated to the College Board AP Physics 1 Course Objectives Big Idea 1: Objects and systems have properties such as mass and charge. Systems may have internal structure. Enduring
More informationHeat Transfer Prof. Dr. Ale Kumar Ghosal Department of Chemical Engineering Indian Institute of Technology, Guwahati
Heat Transfer Prof. Dr. Ale Kumar Ghosal Department of Chemical Engineering Indian Institute of Technology, Guwahati Module No. # 04 Convective Heat Transfer Lecture No. # 03 Heat Transfer Correlation
More informationINVESTIGATION OF FALLING BALL VISCOMETRY AND ITS ACCURACY GROUP R1 Evelyn Chou, Julia Glaser, Bella Goyal, Sherri Wykosky
INVESTIGATION OF FALLING BALL VISCOMETRY AND ITS ACCURACY GROUP R1 Evelyn Chou, Julia Glaser, Bella Goyal, Sherri Wykosky ABSTRACT: A falling ball viscometer and its associated equations were studied in
More informationBattery Thermal Management System Design Modeling
Battery Thermal Management System Design Modeling Gi-Heon Kim, Ph.D Ahmad Pesaran, Ph.D (ahmad_pesaran@nrel.gov) National Renewable Energy Laboratory, Golden, Colorado, U.S.A. EVS October -8, 8, 006 Yokohama,
More informationCHEMICAL ENGINEERING AND CHEMICAL PROCESS TECHNOLOGY - Vol. I - Interphase Mass Transfer - A. Burghardt
INTERPHASE MASS TRANSFER A. Burghardt Institute of Chemical Engineering, Polish Academy of Sciences, Poland Keywords: Turbulent flow, turbulent mass flux, eddy viscosity, eddy diffusivity, Prandtl mixing
More informationEXAMPLE: Water Flow in a Pipe
EXAMPLE: Water Flow in a Pipe P 1 > P 2 Velocity profile is parabolic (we will learn why it is parabolic later, but since friction comes from walls the shape is intuitive) The pressure drops linearly along
More informationNewton s Laws. Physics 1425 lecture 6. Michael Fowler, UVa.
Newton s Laws Physics 1425 lecture 6 Michael Fowler, UVa. Newton Extended Galileo s Picture of Galileo said: Motion to Include Forces Natural horizontal motion is at constant velocity unless a force acts:
More informationContents. Microfluidics - Jens Ducrée Physics: Navier-Stokes Equation 1
Contents 1. Introduction 2. Fluids 3. Physics of Microfluidic Systems 4. Microfabrication Technologies 5. Flow Control 6. Micropumps 7. Sensors 8. Ink-Jet Technology 9. Liquid Handling 10.Microarrays 11.Microreactors
More informationSwissmetro travels at high speeds through a tunnel at low pressure. It will therefore undergo friction that can be due to:
I. OBJECTIVE OF THE EXPERIMENT. Swissmetro travels at high speeds through a tunnel at low pressure. It will therefore undergo friction that can be due to: 1) Viscosity of gas (cf. "Viscosity of gas" experiment)
More informationCE 3500 Fluid Mechanics / Fall 2014 / City College of New York
1 Drag Coefficient The force ( F ) of the wind blowing against a building is given by F=C D ρu 2 A/2, where U is the wind speed, ρ is density of the air, A the cross-sectional area of the building, and
More informationwww.mathsbox.org.uk Displacement (x) Velocity (v) Acceleration (a) x = f(t) differentiate v = dx Acceleration Velocity (v) Displacement x
Mechanics 2 : Revision Notes 1. Kinematics and variable acceleration Displacement (x) Velocity (v) Acceleration (a) x = f(t) differentiate v = dx differentiate a = dv = d2 x dt dt dt 2 Acceleration Velocity
More informationFluid Dynamics Viscosity. Dave Foster Department of Chemical Engineering University of Rochester Email: dafoster@che
Fluid Dynamics Viscosity Dave Foster Department of Chemical Engineering University of Rochester Email: dafoster@che che.rochester.eduedu 1 Chemical Engineering What do Chemical Engineers Do? Manufacturing
More informationAN EFFECT OF GRID QUALITY ON THE RESULTS OF NUMERICAL SIMULATIONS OF THE FLUID FLOW FIELD IN AN AGITATED VESSEL
14 th European Conference on Mixing Warszawa, 10-13 September 2012 AN EFFECT OF GRID QUALITY ON THE RESULTS OF NUMERICAL SIMULATIONS OF THE FLUID FLOW FIELD IN AN AGITATED VESSEL Joanna Karcz, Lukasz Kacperski
More informationPharmaceutical Biotechnology. Recombinant DNA technology Western blotting and SDS-PAGE
Pharmaceutical Biotechnology Recombinant DNA technology Western blotting and SDS-PAGE Recombinant DNA Technology Protein Synthesis Western Blot Western blots allow investigators to determine the molecular
More informationWhen the fluid velocity is zero, called the hydrostatic condition, the pressure variation is due only to the weight of the fluid.
Fluid Statics When the fluid velocity is zero, called the hydrostatic condition, the pressure variation is due only to the weight of the fluid. Consider a small wedge of fluid at rest of size Δx, Δz, Δs
More informationVacuum Technology. Kinetic Theory of Gas. Dr. Philip D. Rack
Kinetic Theory of Gas Assistant Professor Department of Materials Science and Engineering University of Tennessee 603 Dougherty Engineering Building Knoxville, TN 3793-00 Phone: (865) 974-5344 Fax (865)
More information1 Wetting your feet. 2 Scaling. 8.298 Lies / Check your understanding: Solutions
1 Wetting your feet 1.1 Estimate how many liters are in a barrel of oil and how many barrels of oil the United States imports every year. A: A barrel may be a few feet high, so h 1m, and have a diameter
More informationAS COMPETITION PAPER 2008
AS COMPETITION PAPER 28 Name School Town & County Total Mark/5 Time Allowed: One hour Attempt as many questions as you can. Write your answers on this question paper. Marks allocated for each question
More informationVISCOSITY OF A LIQUID. To determine the viscosity of a lubricating oil. Time permitting, the temperature variation of viscosity can also be studied.
VISCOSITY OF A LIQUID August 19, 004 OBJECTIVE: EQUIPMENT: To determine the viscosity of a lubricating oil. Time permitting, the temperature variation of viscosity can also be studied. Viscosity apparatus
More informationExperiment 3 Pipe Friction
EML 316L Experiment 3 Pipe Friction Laboratory Manual Mechanical and Materials Engineering Department College of Engineering FLORIDA INTERNATIONAL UNIVERSITY Nomenclature Symbol Description Unit A cross-sectional
More informationSizes, shapes and interactions of molecules in solution
Sizes, shapes and interactions of molecules in solution Light Scattering Analytical Viscometry Ultracentrifugation Steve Harding, NCMH University of Nottingham 1. Molecular weight distribution analysis
More informationUnsteady Pressure Measurements
Quite often the measurements of pressures has to be conducted in unsteady conditions. Typical cases are those of -the measurement of time-varying pressure (with periodic oscillations or step changes) -the
More informationViscosity (VIS) Topic: Mechanics. Laminar and turbulent flow, Reynolds number, Hagen-Poiseuille s law, Stokes law
Seite 1 Viscosity Topic: Mechanics 1 Key words Laminar and turbulent flow, Reynolds number, Hagen-Poiseuille s law, Stokes law 2 Literatur L. Bergmann, C. Schäfer, Lehrbuch der Experimentalphysik, Band
More informationME 305 Fluid Mechanics I. Part 8 Viscous Flow in Pipes and Ducts
ME 305 Fluid Mechanics I Part 8 Viscous Flow in Pipes and Ducts These presentations are prepared by Dr. Cüneyt Sert Mechanical Engineering Department Middle East Technical University Ankara, Turkey csert@metu.edu.tr
More informationChapter 3.8 & 6 Solutions
Chapter 3.8 & 6 Solutions P3.37. Prepare: We are asked to find period, speed and acceleration. Period and frequency are inverses according to Equation 3.26. To find speed we need to know the distance traveled
More informationForces. Definition Friction Falling Objects Projectiles Newton s Laws of Motion Momentum Universal Forces Fluid Pressure Hydraulics Buoyancy
Forces Definition Friction Falling Objects Projectiles Newton s Laws of Motion Momentum Universal Forces Fluid Pressure Hydraulics Buoyancy Definition of Force Force = a push or pull that causes a change
More information5. Forces and Motion-I. Force is an interaction that causes the acceleration of a body. A vector quantity.
5. Forces and Motion-I 1 Force is an interaction that causes the acceleration of a body. A vector quantity. Newton's First Law: Consider a body on which no net force acts. If the body is at rest, it will
More informationDYNAMIC LIGHT SCATTERING COMMON TERMS DEFINED
DYNAMIC LIGHT SCATTERING COMMON TERMS DEFINED Abstract: There are a number of sources of information that give a mathematical description of the terms used in light scattering. However, these will not
More informationEnergy Transport. Focus on heat transfer. Heat Transfer Mechanisms: Conduction Radiation Convection (mass movement of fluids)
Energy Transport Focus on heat transfer Heat Transfer Mechanisms: Conduction Radiation Convection (mass movement of fluids) Conduction Conduction heat transfer occurs only when there is physical contact
More informationSlide 10.1. Basic system Models
Slide 10.1 Basic system Models Objectives: Devise Models from basic building blocks of mechanical, electrical, fluid and thermal systems Recognize analogies between mechanical, electrical, fluid and thermal
More informationPractice Problems on Boundary Layers. Answer(s): D = 107 N D = 152 N. C. Wassgren, Purdue University Page 1 of 17 Last Updated: 2010 Nov 22
BL_01 A thin flat plate 55 by 110 cm is immersed in a 6 m/s stream of SAE 10 oil at 20 C. Compute the total skin friction drag if the stream is parallel to (a) the long side and (b) the short side. D =
More informationTurbulence, Heat and Mass Transfer (THMT 09) Poiseuille flow of liquid methane in nanoscopic graphite channels by molecular dynamics simulation
Turbulence, Heat and Mass Transfer (THMT 09) Poiseuille flow of liquid methane in nanoscopic graphite channels by molecular dynamics simulation Sapienza Università di Roma, September 14, 2009 M. T. HORSCH,
More information02/21/2006 10:13 AM. Viscosity. The Physics Hypertextbook 1998-2005 by Glenn Elert All Rights Reserved -- Fair Use Encouraged.
Viscosity The Physics Hypertextbook 1998-2005 by Glenn Elert All Rights Reserved -- Fair Use Encouraged prev up next Discussion definitions Informally, viscosity is the quantity that describes a fluid's
More informationPhysics 41 HW Set 1 Chapter 15
Physics 4 HW Set Chapter 5 Serway 8 th OC:, 4, 7 CQ: 4, 8 P: 4, 5, 8, 8, 0, 9,, 4, 9, 4, 5, 5 Discussion Problems:, 57, 59, 67, 74 OC CQ P: 4, 5, 8, 8, 0, 9,, 4, 9, 4, 5, 5 Discussion Problems:, 57, 59,
More informationPhysics: Principles and Applications, 6e Giancoli Chapter 4 Dynamics: Newton's Laws of Motion
Physics: Principles and Applications, 6e Giancoli Chapter 4 Dynamics: Newton's Laws of Motion Conceptual Questions 1) Which of Newton's laws best explains why motorists should buckle-up? A) the first law
More informationFree Fall: Observing and Analyzing the Free Fall Motion of a Bouncing Ping-Pong Ball and Calculating the Free Fall Acceleration (Teacher s Guide)
Free Fall: Observing and Analyzing the Free Fall Motion of a Bouncing Ping-Pong Ball and Calculating the Free Fall Acceleration (Teacher s Guide) 2012 WARD S Science v.11/12 OVERVIEW Students will measure
More informationPaul Clements, SpR in Anaesthetics, Hope Hospital, Salford, UK. Carl Gwinnutt, Consultant Anaesthetist, Hope Hospital, Salford, UK.
The Physics of Flow Paul Clements, SpR in Anaesthetics, Hope Hospital, Salford, UK. Carl Gwinnutt, Consultant Anaesthetist, Hope Hospital, Salford, UK. Introduction Flow is defined as the quantity of fluid
More informationCh 7 Kinetic Energy and Work. Question: 7 Problems: 3, 7, 11, 17, 23, 27, 35, 37, 41, 43
Ch 7 Kinetic Energy and Work Question: 7 Problems: 3, 7, 11, 17, 23, 27, 35, 37, 41, 43 Technical definition of energy a scalar quantity that is associated with that state of one or more objects The state
More informationPotential Energy and Equilibrium in 1D
Potential Energy and Equilibrium in 1D Figures 6-27, 6-28 and 6-29 of Tipler-Mosca. du = F x dx A particle is in equilibrium if the net force acting on it is zero: F x = du dx = 0. In stable equilibrium
More informationPhysics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam
Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam INSTRUCTIONS: Use a pencil #2 to fill your scantron. Write your code number and bubble it in under "EXAM NUMBER;" an entry
More informationHEAVY OIL FLOW MEASUREMENT CHALLENGES
HEAVY OIL FLOW MEASUREMENT CHALLENGES 1 INTRODUCTION The vast majority of the world s remaining oil reserves are categorised as heavy / unconventional oils (high viscosity). Due to diminishing conventional
More informationChapter 13 - Solutions
Chapter 13 - Solutions 13-1 Types of Mixtures I. Solutions A. Soluble 1. Capable of being dissolved B. Solution 1. A homogeneous mixture of two or more substances in a single phase C. Solvent 1. The dissolving
More informationPARTICLE SIMULATION ON MULTIPLE DUST LAYERS OF COULOMB CLOUD IN CATHODE SHEATH EDGE
PARTICLE SIMULATION ON MULTIPLE DUST LAYERS OF COULOMB CLOUD IN CATHODE SHEATH EDGE K. ASANO, S. NUNOMURA, T. MISAWA, N. OHNO and S. TAKAMURA Department of Energy Engineering and Science, Graduate School
More informationPUMPS STEAM TURBINES BUILDING & FIRE WASTEWATER SERVICE PUMP CLINIC 22 VISCOSITY
PUMP CLINIC 22 VISCOSITY The viscosity of a fluid is that property which tends to resist a shearing force. It can be thought of as the internal friction resulting when one layer of fluid is made to move
More information1. The Kinetic Theory of Matter states that all matter is composed of atoms and molecules that are in a constant state of constant random motion
Physical Science Period: Name: ANSWER KEY Date: Practice Test for Unit 3: Ch. 3, and some of 15 and 16: Kinetic Theory of Matter, States of matter, and and thermodynamics, and gas laws. 1. The Kinetic
More informationMarmara Üniversitesi Fen-Edebiyat Fakültesi Kimya Bölümü / Biyokimya Anabilim Dalı PURIFICATION AND CHARACTERIZATION OF PROTEINS
EXPERIMENT VI PURIFICATION AND CHARACTERIZATION OF PROTEINS I- Protein isolation and dialysis In order to investigate its structure and properties a protein must be obtained in pure form. Since proteins
More informationLab 7: Rotational Motion
Lab 7: Rotational Motion Equipment: DataStudio, rotary motion sensor mounted on 80 cm rod and heavy duty bench clamp (PASCO ME-9472), string with loop at one end and small white bead at the other end (125
More informationINTRODUCTION TO FLUID MECHANICS
INTRODUCTION TO FLUID MECHANICS SIXTH EDITION ROBERT W. FOX Purdue University ALAN T. MCDONALD Purdue University PHILIP J. PRITCHARD Manhattan College JOHN WILEY & SONS, INC. CONTENTS CHAPTER 1 INTRODUCTION
More informationPhysics 111: Lecture 4: Chapter 4 - Forces and Newton s Laws of Motion. Physics is about forces and how the world around us reacts to these forces.
Physics 111: Lecture 4: Chapter 4 - Forces and Newton s Laws of Motion Physics is about forces and how the world around us reacts to these forces. Whats a force? Contact and non-contact forces. Whats a
More informationJournal bearings/sliding bearings
Journal bearings/sliding bearings Operating conditions: Advantages: - Vibration damping, impact damping, noise damping - not sensitive for vibrations, low operating noise level - dust tight (if lubricated
More informationMolecular Spectroscopy
Molecular Spectroscopy UV-Vis Spectroscopy Absorption Characteristics of Some Common Chromophores UV-Vis Spectroscopy Absorption Characteristics of Aromatic Compounds UV-Vis Spectroscopy Effect of extended
More information3. Diodes and Diode Circuits. 3. Diodes and Diode Circuits TLT-8016 Basic Analog Circuits 2005/2006 1
3. Diodes and Diode Circuits 3. Diodes and Diode Circuits TLT-8016 Basic Analog Circuits 2005/2006 1 3.1 Diode Characteristics Small-Signal Diodes Diode: a semiconductor device, which conduct the current
More information8.2 Elastic Strain Energy
Section 8. 8. Elastic Strain Energy The strain energy stored in an elastic material upon deformation is calculated below for a number of different geometries and loading conditions. These expressions for
More informationSOLID MECHANICS TUTORIAL MECHANISMS KINEMATICS - VELOCITY AND ACCELERATION DIAGRAMS
SOLID MECHANICS TUTORIAL MECHANISMS KINEMATICS - VELOCITY AND ACCELERATION DIAGRAMS This work covers elements of the syllabus for the Engineering Council exams C105 Mechanical and Structural Engineering
More information