Molecular Diffusion in Fluids : Molecular Diffusion, Often Simply

Total Page:16

File Type:pdf, Size:1020Kb

Molecular Diffusion in Fluids : Molecular Diffusion, Often Simply Subject: Mass Transfer -I 4th Semester Molecular Diffusion in fluids : Molecular diffusion, often simply called diffusion, is the thermal motion of all (liquid or gas) particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size (mass) of the particles. Diffusion explains the net flux of molecules from a region of higher concentration to one of lower concentration. Once the concentrations are equal the molecules continue to move, but since there is no concentration gradient the process of molecular diffusion has ceased and is instead governed by the process of self diffusion, originating from the random motion of the molecules. According to Fick’s first law for the z direction Where , Steady-State Molecular Diffusion in Fluids at rest and in Laminar flow: When the diffusion is only in z direction with and both constant we can write the equation here 1 indicates the beginning of the diffusion path and 2 indicates end of the diffusion path letting and integrating we get Molecular Diffusion in gases: When the ideal-gas law can be applied equation (2) can be written in a form more convenient for use with gas. Thus, Where Further So equation (2) becomes Or Steady-State diffusion of A through non diffusing B: This might occur for example if Ammonia (A) were being absorbed from air (B) into water. In the gas phase since air does not dissolved appreciably in water, and if we neglect the evaporation of water only the Ammonia diffuses. Thus And equation (3) become Since If we let Then Steady-State equimolal counter diffusion: This is the situation which frequently pertains in distillation operation. Equation (3) becomes indeterminate but we can write according to Ficks law Or for this case Molecular Diffusion in liquids: In case of diffusion in liquids , C and DAB may vary considerably with respect to process conditions. Hence eq. 2 becomes Where ρ is solution density and M is solution molecular weight. Case-I: Diffusion of liquid A through a stagnant liquid B NB=0 NA= Constant. Case -II :Equimolal counter diffusion NA= - NB Note: Reference- R.E. Trebal Assignment (1) : Try to attempt all questions except Q.1,2 and 3, take assumptions if any data is missing .
Recommended publications
  • Air-Sea Gas Exchange
    Air-Sea Gas Exchange OCN 623 – Chemical Oceanography 17 March 2015 Readings: Libes, Chapter 6 – pp. 158 -168 Wanninkhof et al. (2009) Advances in quantifying air-sea gas exchange and environmental forcing, Annual Reviews of Marine Science © 2015 David Ho and Frank Sansone Overview • Introduction • Theory/models of gas exchange • Mechanisms/lab studies of gas exchange • Field measurements • Parameterizations Why do we care about air-water gas exchange? . Globally, to understand cycling of biogeochemically important trace gases (e.g., CO2, DMS, CH4, N2O, CH3Br) . Regionally and locally . To understand indicators of water quality (e.g., dissolved O2) . To predict evasion rates of volatile pollutants (e.g., VOCs, PAHs, PCBs) Factors Influencing Air-water Transfer of Mass, Momentum, Heat From SOLAS Science Plan and Implementation Strategy Basic flux equation Concentration gradient Flux (mol cm-3) (mol cm-2 s-1) “driving force” Gas transfer velocity (cm s-1) “resistance” k: Gas transfer velocity, piston velocity, gas exchange coefficient Cw: Concentration in water near the surface Ca: Concentration in air near the surface α: Ostwald solubility coefficient (temp-compensated Bunsen coeff) Basic conceptual model Turbulent atmosphere C Atmosphere a Laminar Stagnant Cas Boundary Layer zFilm Cws (transport by Ocean molecular diffusion) Cw Turbulent bulk liquid F = k(Cw-αCa) Air/water side resistance Magnitude of typical Ostwald solubility coefficients He ≈ 0.01 Water-side resistance O2 ≈ 0.03 CO2 ≈ 0.7 DMS ≈ 10 Air- and water-side resistance CH3Br
    [Show full text]
  • Part Two Physical Processes in Oceanography
    Part Two Physical Processes in Oceanography 8 8.1 Introduction Small-Scale Forty years ago, the detailed physical mechanisms re- Mixing Processes sponsible for the mixing of heat, salt, and other prop- erties in the ocean had hardly been considered. Using profiles obtained from water-bottle measurements, and J. S. Turner their variations in time and space, it was deduced that mixing must be taking place at rates much greater than could be accounted for by molecular diffusion. It was taken for granted that the ocean (because of its large scale) must be everywhere turbulent, and this was sup- ported by the observation that the major constituents are reasonably well mixed. It seemed a natural step to define eddy viscosities and eddy conductivities, or mix- ing coefficients, to relate the deduced fluxes of mo- mentum or heat (or salt) to the mean smoothed gra- dients of corresponding properties. Extensive tables of these mixing coefficients, KM for momentum, KH for heat, and Ks for salinity, and their variation with po- sition and other parameters, were published about that time [see, e.g., Sverdrup, Johnson, and Fleming (1942, p. 482)]. Much mathematical modeling of oceanic flows on various scales was (and still is) based on simple assumptions about the eddy viscosity, which is often taken to have a constant value, chosen to give the best agreement with the observations. This approach to the theory is well summarized in Proudman (1953), and more recent extensions of the method are described in the conference proceedings edited by Nihoul 1975). Though the preoccupation with finding numerical values of these parameters was not in retrospect always helpful, certain features of those results contained the seeds of many later developments in this subject.
    [Show full text]
  • Modes of Mass Transfer Chapter Objectives
    MODES OF MASS TRANSFER CHAPTER OBJECTIVES - After you have studied this chapter, you should be able to: 1. Explain the process of molecular diffusion and its dependence on molecular mobility. 2. Explain the process of capillary diffusion 3. Explain the process of dispersion in a fluid or in a porous solid. 4. Understand the process of convective mass transfer as due to bulk flow added to diffusion or dispersion. 5. Explain saturated flow and unsaturated capillary flow in a porous solid 6. Have an idea of the relative rates of the different modes of mass transfer. 7. Explain osmotic flow. KEY TERMS diffusion, diffusivity, and. diffusion coefficient dispersion and dispersion coefficient hydraulic conductivity capillarity osmotic flow mass and molar flux Fick's law Darcy's law 1. A Primer on Porous Media Flow Physical Interpretation of Hydraulic Conductivity K and Permeability k Figure 1. Idealization of a porous media as bundle of tubes of varying diameter and tortuosity. Capillarity and Unsaturated Flow in a Porous Media Figure 2.Capillary attraction between the tube walls and the fluid causes the fluid to rise. Osmotic Flow in a Porous Media Figure 3.Osmotic flow from a dilute to a concentrated solution through a semi-permeable membrane. 2. Molecular Diffusion • In a material with two or more mass species whose concentrations vary within the material, there is tendency for mass to move. Diffusive mass transfer is the transport of one mass component from a region of higher concentration to a region of lower concentration. Physical interpretation of diffusivity Figure 4. Concentration profiles at different times from an instantaneous source placed at zero distance.
    [Show full text]
  • Visualizing Molecular Diffusion Through Passive Permeability
    COCHBI-1072; NO. OF PAGES 9 Available online at www.sciencedirect.com Visualizing molecular diffusion through passive permeability barriers in cells: conventional and novel approaches 1 1 1,2 1,3 Yu-Chun Lin , Siew Cheng Phua , Benjamin Lin and Takanari Inoue Diffusion barriers are universal solutions for cells to achieve exist at a variety of cellular structures, including the distinct organizations, compositions, and activities within a nuclear envelope, the annulus of spermatozoa, the lead- limited space. The influence of diffusion barriers on the ing edge of migrating cells, the cleavage furrow of divid- spatiotemporal dynamics of signaling molecules often ing cells, and the budding neck of yeast, as well as in determines cellular physiology and functions. Over the years, cellular extensions such as primary cilia, dendritic spines, the passive permeability barriers in various subcellular locales and the initial segment of the neuronal axon [1 ,6 ,7]. have been characterized using elaborate analytical techniques. While some diffusion barriers exist constitutively in cells, In this review, we will summarize the current state of knowledge others are highly dynamic. The importance of diffusion on the various passive permeability barriers present in barriers is further underscored by the various human mammalian cells. We will conclude with a description of several diseases which result from their dysfunction [3,6 ,8,9]. conventional techniques and one new approach based on chemically inducible diffusion trap (CIDT) for probing Diffusion barriers can be categorized into two major permeable barriers. classes based on the substrates they affect: lateral diffu- Addresses sion barriers and permeability barriers. Lateral diffusion 1 Department of Cell Biology, Center for Cell Dynamics, School of barriers localize in membranes and restrict the movement Medicine, Johns Hopkins University, United States 2 of molecules within the membrane plane such as trans- Department of Biomedical Engineering, Johns Hopkins University, membrane proteins and membrane lipids [1 ].
    [Show full text]
  • Diffusion at Work
    or collective redistirbution of any portion of this article by photocopy machine, reposting, or other means is permitted only with the approval of The Oceanography Society. Send all correspondence to: [email protected] ofor Th e The to: [email protected] Oceanography approval Oceanography correspondence POall Box 1931, portionthe Send Society. Rockville, ofwith any permittedUSA. articleonly photocopy by Society, is MD 20849-1931, of machine, this reposting, means or collective or other redistirbution article has This been published in hands - on O ceanography Oceanography Diffusion at Work , Volume 20, Number 3, a quarterly journal of The Oceanography Society. Copyright 2007 by The Oceanography Society. All rights reserved. Permission is granted to copy this article for use in teaching and research. Republication, systemmatic reproduction, reproduction, Republication, systemmatic research. for this and teaching article copy to use in reserved.by The 2007 is rights ofAll granted journal Copyright Oceanography The Permission 20, NumberOceanography 3, a quarterly Society. Society. , Volume An Interactive Simulation B Y L ee K arp-B oss , E mmanuel B oss , and J ames L oftin PURPOSE OF ACTIVITY or small particles due to their random (Brownian) motion and The goal of this activity is to help students better understand the resultant net migration of material from regions of high the nonintuitive concept of diffusion and introduce them to a concentration to regions of low concentration. Stirring (where variety of diffusion-related processes in the ocean. As part of material gets stretched and folded) expands the area available this activity, students also practice data collection and statisti- for diffusion to occur, resulting in enhanced mixing compared cal analysis (e.g., average, variance, and probability distribution to that due to molecular diffusion alone.
    [Show full text]
  • What Is the Difference Between Osmosis and Diffusion?
    What is the difference between osmosis and diffusion? Students are often asked to explain the similarities and differences between osmosis and diffusion or to compare and contrast the two forms of transport. To answer the question, you need to know the definitions of osmosis and diffusion and really understand what they mean. Osmosis And Diffusion Definitions Osmosis: Osmosis is the movement of solvent particles across a semipermeable membrane from a dilute solution into a concentrated solution. The solvent moves to dilute the concentrated solution and equalize the concentration on both sides of the membrane. Diffusion: Diffusion is the movement of particles from an area of higher concentration to lower concentration. The overall effect is to equalize concentration throughout the medium. Osmosis And Diffusion Examples Examples of Osmosis: Examples of osmosis include red blood cells swelling up when exposed to fresh water and plant root hairs taking up water. To see an easy demonstration of osmosis, soak gummy candies in water. The gel of the candies acts as a semipermeable membrane. Examples of Diffusion: Examples of diffusion include perfume filling a whole room and the movement of small molecules across a cell membrane. One of the simplest demonstrations of diffusion is adding a drop of food coloring to water. Although other transport processes do occur, diffusion is the key player. Osmosis And Diffusion Similarities Osmosis and diffusion are related processes that display similarities. Both osmosis and diffusion equalize the concentration of two solutions. Both diffusion and osmosis are passive transport processes, which means they do not require any input of extra energy to occur.
    [Show full text]
  • Gas Exchange and Respiratory Function
    LWBK330-4183G-c21_p484-516.qxd 23/07/2009 02:09 PM Page 484 Aptara Gas Exchange and 5 Respiratory Function Applying Concepts From NANDA, NIC, • Case Study and NOC A Patient With Impaired Cough Reflex Mrs. Lewis, age 77 years, is admitted to the hospital for left lower lobe pneumonia. Her vital signs are: Temp 100.6°F; HR 90 and regular; B/P: 142/74; Resp. 28. She has a weak cough, diminished breath sounds over the lower left lung field, and coarse rhonchi over the midtracheal area. She can expectorate some sputum, which is thick and grayish green. She has a history of stroke. Secondary to the stroke she has impaired gag and cough reflexes and mild weakness of her left side. She is allowed food and fluids because she can swallow safely if she uses the chin-tuck maneuver. Visit thePoint to view a concept map that illustrates the relationships that exist between the nursing diagnoses, interventions, and outcomes for the patient’s clinical problems. LWBK330-4183G-c21_p484-516.qxd 23/07/2009 02:09 PM Page 485 Aptara Nursing Classifications and Languages NANDA NIC NOC NURSING DIAGNOSES NURSING INTERVENTIONS NURSING OUTCOMES INEFFECTIVE AIRWAY CLEARANCE— RESPIRATORY MONITORING— Return to functional baseline sta- Inability to clear secretions or ob- Collection and analysis of patient tus, stabilization of, or structions from the respiratory data to ensure airway patency improvement in: tract to maintain a clear airway and adequate gas exchange RESPIRATORY STATUS: AIRWAY PATENCY—Extent to which the tracheobronchial passages remain open IMPAIRED GAS
    [Show full text]
  • On the Molecular Diffusion Coefficients of Dissolved , And
    Available online at www.sciencedirect.com Geochimica et Cosmochimica Acta 75 (2011) 2483–2498 www.elsevier.com/locate/gca À On the molecular diffusion coefficients of dissolved CO2; HCO3 , 2À and CO3 and their dependence on isotopic mass Richard E. Zeebe ⇑ School of Ocean and Earth Science and Technology, University of Hawaii at Manoa, 1000 Pope Road, MSB 504, Honolulu, HI 96822, USA Received 21 August 2010; accepted in revised form 7 February 2011; available online 13 February 2011 Abstract À The molecular diffusion coefficients of dissolved carbon dioxide ðCO2Þ, bicarbonate ion ðHCO3 Þ, and carbonate ion 2À ðCO3 Þ are fundamental physico-chemical constants and are of practical significance in various disciplines including geochem- istry, biology, and medicine. Yet, very little experimental data is available, for instance, on the bicarbonate and carbonate ion diffusion coefficient. Furthermore, it appears that no information was hitherto available on the mass-dependence of the dif- fusion coefficients of the ionic carbonate species in water. Here I use molecular dynamics simulations to study the diffusion of the dissolved carbonate species in water, including their dependence on temperature and isotopic mass. Based on the simu- À 2À lations, I provide equations to calculate the diffusion coefficients of dissolved CO2; HCO3 , and CO3 over the temperature range from 0° to 100 °C. The results indicate a mass-dependence of CO2 diffusion that is consistent with the observed 12 13 CO2= CO2 diffusion ratio at 25 °C. No significant isotope fractionation appears to be associated with the diffusion of À 2À the naturally occurring isotopologues of HCO3 and CO3 at 25 °C.
    [Show full text]
  • Diffusion in Porous Media – Measurement and Modeling
    Fakultät Maschinenwesen | Institut für Energietechnik | Professur für Technische Thermodynamik Institutslogo Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 09.12.2011 Diffusion in porous media – measurement and modeling Cornelia Breitkopf for personal use only! Diffusion – what is that? Diffusion – what is that? From G. Gamow „One, Two, Three…Infinity“ The Viking Press, New York, 1955. Dresden, Frauenkirche 2010 Diffusion – application to societies in: Diffusion – application to societies Diffusion – first experiment Robert Brown Robert Brown, (1773-1958) “Scottish botanist best known for his description of the natural continuous motion of minute particles in solution, which came to be called Brownian movement.” http://www.britannica.com/EBchecked/topic/81618/Robert-Brown Diffusion – first experiment Robert Brown “In 1827, while examining grains of pollen of the plant Clarkia pulchella suspended in water under a microscope, Brown observed minute particles, now known to be amyloplasts (starch organelles) and spherosomes (lipid organelles), ejected from the pollen grains, executing a continuous jittery motion. He then observed the same motion in particles of inorganic matter, enabling him to rule out the hypothesis that the effect was life- related…..” http://en.wikipedia.org/wiki/Robert_Brown_(botanist) Diffusion – short history http://www.uni-leipzig.de/diffusion/pdf/volume4/diff_fund_4(2006)6.pdf Diffusion – short history A. E. Fick “Adolf Eugen Fick (1829-1901) was a German physiologist. He started to study mathematics and physics, but then realized he was more interested in medicine. He earned his doctorate in medicine at Marburg in 1851.” “In 1855 he introduced Fick's law of diffusion, which governs the diffusion of a gas across a fluid membrane.” http://en.wikipedia.org/wiki/Adolf_Fick Diffusion – short history Albert Einstein (1879-1955) Marian von Smoluchowski (1872-1917 was a phyiscist.
    [Show full text]
  • Augmenting CO2 Absorption Flux Through a Gas–Liquid Membrane Module by Inserting Carbon-Fiber Spacers
    membranes Article Augmenting CO2 Absorption Flux through a Gas–Liquid Membrane Module by Inserting Carbon-Fiber Spacers Luke Chen 1 , Chii-Dong Ho 2,*, Li-Yang Jen 2, Jun-Wei Lim 3,* and Yu-Han Chen 2 1 Department of Water Resources and Environmental Engineering, Tamkang University, Tamsui, New Taipei 251, Taiwan; [email protected] 2 Department of Chemical and Materials Engineering, Tamkang University, Tamsui, New Taipei 251, Taiwan; [email protected] (L.-Y.J.); [email protected] (Y.-H.C.) 3 Department of Fundamental and Applied Sciences, HICoE-Centre for Biofuel and Biochemical Research, Institute of Self-Sustainable Building, Universiti Teknologi PETRONAS, Seri Iskandar, Perak Darul Ridzuan 32610, Malaysia * Correspondence: [email protected] (C.-D.H.); [email protected] (J.-W.L.); Tel.: +886-2-26215656 (ext. 2724) (C.-D.H.) Received: 18 September 2020; Accepted: 19 October 2020; Published: 22 October 2020 Abstract: We investigated the insertion of eddy promoters into a parallel-plate gas–liquid polytetrafluoroethylene (PTFE) membrane contactor to effectively enhance carbon dioxide absorption through aqueous amine solutions (monoethanolamide—MEA). In this study, a theoretical model was established and experimental work was performed to predict and to compare carbon dioxide absorption efficiency under concurrent- and countercurrent-flow operations for various MEA feed flow rates, inlet CO2 concentrations, and channel design conditions. A Sherwood number’s correlated expression was formulated, incorporating experimental data to estimate the mass transfer coefficient of the CO2 absorption in MEA flowing through a PTFE membrane. Theoretical predictions were calculated and validated through experimental data for the augmented CO2 absorption efficiency by inserting carbon-fiber spacers as an eddy promoter to reduce the concentration polarization effect.
    [Show full text]
  • Near-Drowning
    Central Journal of Trauma and Care Bringing Excellence in Open Access Review Article *Corresponding author Bhagya Sannananja, Department of Radiology, University of Washington, 1959, NE Pacific St, Seattle, WA Near-Drowning: Epidemiology, 98195, USA, Tel: 830-499-1446; Email: Submitted: 23 May 2017 Pathophysiology and Imaging Accepted: 19 June 2017 Published: 22 June 2017 Copyright Findings © 2017 Sannananja et al. Carlos S. Restrepo1, Carolina Ortiz2, Achint K. Singh1, and ISSN: 2573-1246 3 Bhagya Sannananja * OPEN ACCESS 1Department of Radiology, University of Texas Health Science Center at San Antonio, USA Keywords 2Department of Internal Medicine, University of Texas Health Science Center at San • Near-drowning Antonio, USA • Immersion 3Department of Radiology, University of Washington, USA\ • Imaging findings • Lung/radiography • Magnetic resonance imaging Abstract • Tomography Although occasionally preventable, drowning is a major cause of accidental death • X-Ray computed worldwide, with the highest rates among children. A new definition by WHO classifies • Nonfatal drowning drowning as the process of experiencing respiratory impairment from submersion/ immersion in liquid, which can lead to fatal or nonfatal drowning. Hypoxemia seems to be the most severe pathophysiologic consequence of nonfatal drowning. Victims may sustain severe organ damage, mainly to the brain. It is difficult to predict an accurate neurological prognosis from the initial clinical presentation, laboratory and radiological examinations. Imaging plays an important role in the diagnosis and management of near-drowning victims. Chest radiograph is commonly obtained as the first imaging modality, which usually shows perihilar bilateral pulmonary opacities; yet 20% to 30% of near-drowning patients may have normal initial chest radiographs. Brain hypoxia manifest on CT by diffuse loss of gray-white matter differentiation, and on MRI diffusion weighted sequence with high signal in the injured regions.
    [Show full text]
  • Effect of Molecular Structure on Diffusion of Alcohols Through Type-A Zeolite Pores (0.5 Nm)
    Journal of Materials Science and Engineering A 11 (4-6) (2021) 48-55 doi: 10.17265/2161-6213/2021.4-6.003 D DAVID PUBLISHING Effect of Molecular Structure on Diffusion of Alcohols through Type-A Zeolite Pores (0.5 nm) Bryan Fernández-Solano and Julio F. Mata-Segreda Biomass Laboratory, School of Chemistry, University of Costa Rica 11501-2060, Costa Rica Abstract: Drying kinetics for alcohol-soaked type-A zeolite (pore size 0.5 nm) was determined at 50 °C for 12 small-molecule alcohols (from C1 to C10). The second-phase of drying of wet porous materials reports on the mass-transfer characteristics within the solid matrices. This stage follows pseudo first-order kinetics (k1), and the second-order rate constant k2 = k1/(fluxional area) was found to correlate with the surface tension of the liquids imbibing the solid matrix (p < 0.002). k2 values decrease along the homologous linear alcohols, and branched-chain alcohols diffuse faster than their linear analogues due to their lower surface tensions. No independent contribution was found from the molecular size of the alcohols in the experiment reported here. Characteristic velocity and enthalpy of vaporisation of the liquids were not found to be significant independent variables, either. The find agrees with the notion that liquid movement in pores is governed during the drying processes by the liquid chemical potential gradient between the pore space and gas phase above the porous particle surfaces, this gradient being a function of the molecular cohesion of -1 -2 the moving liquid front (surface tension, ). The results can be expressed by the linear Gibbs-energy relation log (k2/s ·m ) = (2.5 ± 0.5) - (1.6 ± 0.2) 102 (/J·m-2).
    [Show full text]