DOCSLIB.ORG

Supersaturation of Water Vapor in Clouds

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Supersaturation of Water Vapor in Clouds 15 DECEMBER 2003 KOROLEV AND MAZIN 2957 Supersaturation of Water Vapor in Clouds ALEXEI V. K OROLEV Sky Tech Research, Inc., Richmond Hill, Ontario, Canada ILIA P. M AZIN Center for Earth and Space Research, George Mason University, Fairfax, Virginia (Manuscript received 18 October 2002, in ®nal form 26 June 2003) ABSTRACT A theoretical framework is developed to estimate the supersaturation in liquid, ice, and mixed-phase clouds. An equation describing supersaturation in mixed-phase clouds in general form is considered here. The solution for this equation is obtained for the case of quasi-steady approximation, that is, when particle sizes stay constant. It is shown that the supersaturation asymptotically approaches the quasi-steady supersaturation over time. This creates a basis for the estimation of the supersaturation in clouds from the quasi-steady supersaturation calcu- lations. The quasi-steady supersaturation is a function of the vertical velocity and size distributions of liquid and ice particles, which can be obtained from in situ measurements. It is shown that, in mixed-phase clouds, the evaporating droplets maintain the water vapor pressure close to saturation over water, which enables the analytical estimation of the time of glaciation of mixed-phase clouds. The limitations of the quasi-steady ap- proximation in clouds with different phase composition are considered here. The role of phase relaxation time, as well as the effect of the characteristic time and spatial scales of turbulent ¯uctuations, are also discussed. 1. Introduction centration and its average size (Squires 1952; Mazin 1966, 1968). Questions relating to the formation of su- The phase transition of water from vapor into liquid persaturation in clouds were discussed in great details or solid phase plays a pivotal role in the formation of by Kabanov et al. (1971). Rogers (1975) studied the clouds and precipitation. The direction and rate of the supersaturation equation for liquid clouds numerically phase transition ``liquid-to-vapor'' or ``ice-to-vapor'' and considered analytical solutions for some special cas- are determined by the vapor supersaturation with respect es. Subsequent re®nements of the supersaturation equa- to liquid or ice, respectively. The early numerical mod- tion and the time of phase relaxation were made by eling by Howell (1949) and Mordy (1959) has shown Korolev (1994). Most studies of the supersaturation are that the supersaturation in a uniformly ascending cloud related to liquid clouds. Only few works consider su- parcel reaches a maximum near the cloud base during persaturation in glaciated clouds (e.g., Juisto 1971; activation of droplets and then monotonically decreases. Heyms®eld 1975). Squires (1952) derived a relationship between supply The present paper is focused on a study of the super- and depletion of water vapor in a vertically moving saturation in clouds of any phase composition: mixed, cloud parcel. The solution of the Squires equation sug- liquid, and ice. In the section 2 we consider the equation gested that, to a ®rst approximation, the supersaturation for supersaturation in a general form for a three-phase is linearly related to a vertical velocity and inversely component system consisting of water vapor, liquid, and proportional to the concentration and the average size ice particles. Section 3 presents a solution of the super- of the cloud droplets. This relationship was later used saturation equation for the case of quasi-steady approx- to determine supersaturation in convective clouds by imation, that is, when the sizes of cloud particles stay Warner (1968), Paluch and Knight (1984), and Politov- constant. Sections 4 and 5 examine supersaturation in ich and Cooper (1988). The characteristic time of phase liquid, ice, and mixed-phase clouds. In section 6 the an- transition due to water vapor depletion by cloud droplets alytical solution for the glaciating time of mixed-phase is inversely proportional to the product of droplet con- clouds for zero vertical velocity is obtained. Section 7 justi®es the possibility of estimating the in-cloud super- saturation from the quasi-steady supersaturation, which Corresponding author address: Alexei V. Korolev, Sky Tech Re- search, Inc., 28 Don Head Village Blvd., Richmond Hill, ON L4C can be calculated from in situ measurements of particle 7M6, Canada. size distributions and vertical velocity. In section 8 the E-mail: [email protected] limiting conditions for the results are discussed. q 2003 American Meteorological Society 2958 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 60 2. General equation dqw 5 BSNrww ww, (4) Consider a vertically moving adiabatic cloud parcel dt consisting of a mixture of liquid droplets and ice par- where Bw 5 4prwAw/ra and r w is the average radius of ticles uniformly distributed in space. Assume that the cloud droplets. cloud particles move with the air and stay inside the Similarly, an equation for changes in the mixing ratio parcel at all times and no activation of new cloud drop- of ice can be written as lets and nucleation of ice particles occur. Thus, the num- ber of droplets and ice particles per unit mass of the air dq 4pNdr1 rimax ` iif (r , , c) rdrd2 idc. stays constant. Another assumption is related to so 5 iir ir i ir i dt ra EE E dt called regular condensation; that is, the water vapor 0 rimin 0 pressure and temperature ®elds at large distance from (5) cloud particles are considered to be uniform, and all Here, Ni is the number concentration of ice particles; ri cloud particles grow or evaporate under the same con- is the characteristic size of ice particles; c is a shape ditions. factor of ice particles characterizing ``capacitance'' in The changes in the supersaturation in the cloud parcel the equation of the growth rate; ri is the density of ice can be described by an equation (appendix A): particles (rimin , ri , rimax); and f i(ri, ri, c)isthe distribution of ice particles by characteristic size, den- 1 dS gL g 1 Ldq2 ww52u 21 wwsity, and shape factor normalized to unity. The size of 22z Swp1 1 dt1212 cRTy RTa qy cRTp y dt an ice particle is an ambiguous parameter, and it can be de®ned in a number of different ways. The ice particle 1 LL dq size r is related to the shape factor c through the rate 21iw i. (1) i 2 of the mass growth. In the following consideration, the 12qcRTdty p y size ri will be de®ned as half the maximum dimension Here, Sw 5 (e 2 Ew)/Ew is the supersaturation with of the ice particle. For this de®nition of ri, the shape respect to water; e is the water vapor pressure; Ew(T) factor varies in the range 0 , c # 1, being equal to 1 is the saturated vapor pressure over liquid water at tem- for ice spheres. perature T; qy , qw, and qi are the mixing ratios of water Using Jeffery's electrostatic analogy, the diffusional vapor, liquid water, and ice, respectively (mass per 1 kg growth rate of the ice particles can be written as (e.g., of dry air); Ry and Ra are the speci®c gas constants of Pruppacher and Klett 1997) water vapor and air, respectively; cp is the speci®c heat capacitance of the air at constant pressure; L and L driii cA S w i 5 . (6) are the latent heat of water evaporation and ice subli- dt ri mation, respectively; g is the acceleration of gravity; uz 2 2 21 is the vertical velocity of the cloud parcel. Here, Ai 5 (riLi /kRy T 1 riRy T/EiD) ; Ei is the sat- The rate of changes in the liquid water mixing ratio urated water vapor pressure over a ¯at ice surface at due to condensation or evaporation of cloud droplets temperature T; Si is the supersaturation over ice. can be described as The supersaturation over ice can be related to the supersaturation over water with dq 4pr Ndr` www5 f (r )rdr2 w. (2) www w e 2 Ei dt ra E dt 0 Siw55jS 1 j 2 1, (7) Ei Here, f w(rw) is the size distribution of cloud droplets normalized to unity, rw is the droplet radius, Nw is the where j(T) 5 Ew(T)/Ei(T). Then, substituting Eqs. (6) number concentration of the cloud droplets, rw and ra and (7) into Eq. (5) and averaging over ri and c gives are the densities of liquid water and dry air, respectively. dq 4pANrc The mass transfer of water from vapor to liquid phase iiii5 (jS 1 j 2 1) , dt w r inside clouds is mainly related to droplets having rw . a 1 mm. For such droplets, the corrections for the droplet which for simplicity yields curvature and salinity can be disregarded, and the equa- tion for a droplet growth can be written as (e.g., Prup- dq i 5 (BS 1 B*)Nr (8) pacher and Klett 1997) dt iw i ii dr A S www5 . (3) if one assumes that c is the same for all ice particles dt rw and that 2 2 21 Here, Aw 5 (rwLw /kRy T 1 rwRy T/EwD) , D is the 4pr cjA 4pr c B 5 ii; B* 5 i(j 2 1)A . coef®cient of water vapor diffusion in the air, and k is iiirr the coef®cient of air heat conductivity. Substituting Eq. aa (3) into Eq. (2) and averaging over r results in Substituting Eqs. (4) and (8) in Eq. (1) yields 15 DECEMBER 2003 KOROLEV AND MAZIN 2959 1 dS Here, we denote a 5 g(LR /c R T 2 1)/R T; a 5 w au aB*Nr 0 a p y a 1 5 0 z 2 2 iii 1/q 1 L2 /c R T 2; a 5 1/q 1 L L /c R T 2.
Load more

Recommended publications
  • Gas Supersaturation Thresholds for Spontaneous Cavitation in Water with Gas Equilibration Pressures up to 570 Atm1 Wayne A
    Gas Supersaturation Thresholds for Spontaneous Cavitation in Water with Gas Equilibration Pressures up to 570 atm1 Wayne A. Gerth and Edvard A. Hemmingsen * Physiological Research Laboratory Scripps Institution of Oceanography University of California, San Diego La Jolla, California 92093 (Z. Naturforsch. 31a, 1711-1716 [1976] ; received October 5, 1976) Supersaturations for the onset of cavitation in water were determined for various gases. At am- bient pressure, the threshold supersaturations (in atm) required for profuse cavitation to initiate both in bulk water and at the glass-water interface were CH4, 120; Ar, 160; N2, 190; He, 360. Exposure of the water and its containing surfaces to hydrostatic pressures up to 1100 atm prior to equilibration with gas had no detectable effect on these threshold values. This indicates that pre- formed gas nuclei are not significantly involved. Cavitation at the glass-water interface was investi- gated for CH4, Ar and N, saturations up to 570 atm. For 320 atm saturations, the threshold super- saturation was about one-half that for decompression directly to ambient pressure, and for 550 atm it was about one-third. These results indicate that the dissolved gas concentration is a critical factor limiting the spontaneous nucleation of bubbles in gas supersaturated liquids. Introduction thereby forcing the resolution of such dissolvable nuclei 4. Water that contains large gas supersaturations The results reported here bear directly upon the can remain stable with the absence of cavitation 2' 3. understanding of the gas supersaturated metastable However, as the gas supersaturation in the water is condition in pure liquids, the factors which limit it, increased, the system eventually fails to tolerate the and the characteristics of its degeneration via the supersaturation and bursts profusely with the for- nucleation and growth of bubbles.
    [Show full text]
  • Chapter 1 the Fundamentals of Bubble Formation in Water Treatment
    Chapter 1 The Fundamentals of Bubble Formation in Water Treatment Paolo Scardina and Marc Edwards1 Keywords: bubble, air binding, filters, nucleation, equilibrium, water treatment, headloss, filtration, gas transfer Abstract: Water utilities can experience problems from bubble formation during conventional treatment, including impaired particle settling, filter air binding, and measurement as false turbidity in filter effluent. Coagulation processes can cause supersaturation and bubble formation by converting bicarbonate alkalinity to carbon dioxide by acidification. A model was developed to predict the extent of bubble formation during coagulation which proved accurate, using an apparatus designed to physically measure the actual volume of bubble formation. Alum acted similar to hydrochloric acid for initializing bubble formation, and higher initial alkalinity, lower final solution pH, and increased mixing rate tended to increase bubble formation. Lastly, the protocol outlined in Standard Methods for predicting the degree of supersaturation was examined, and when compared to this work, the Standard Methods approach produces an error up to 16% for conditions found in water treatment. Introduction: Gas bubble formation is of established importance to divers and fish (i.e., the bends), carbonated beverages, solid liquid separation in mining, cavitation in pumps, gas transfer, stripping, and dissolved air flotation processes. Moreover, it is common knowledge that formation of gas bubbles in conventional sedimentation and filtration facilities is a significant nuisance at many utilities, because bubbles are believed to hinder sedimentation, cause headloss in filters through a phenomenon referred to as “air binding,” and measure as turbidity in effluents without posing a microbial hazard. Utilities have come to accept these problems, and to the knowledge of these authors there is currently no rigorous basis for predicting when such problems will occur or correcting them when they do.
    [Show full text]
  • Cloud Microphysics
    1. Microphysics of Clouds Changes in phase are basic to cloud microphysics. The possible changes are: vapor-liquid evaporation, condensation liquid-solid freezing, melting vapor-solid deposition, sublimation The changes from left to right correspond to increasing molecular order. These transitions don’t occur at thermodynamic equilibrium. There is a strong free en- ergy barrier that must be overcome for droplets to form. To form a droplet by condensation of vapor, surface tension must be overcome by a strong gradient of vapor pressure. This means that phase transitions don’t occur at es(1), or sat- uration over a plane surface of water. Even if a sample of moist air is cooled adiabatically to the equilibrium saturation point for bulk water, droplets should not be expected to form. In fact, water droplets do begin to condense in pure wa- ter vapor only when the relative humidity reaches several hundred percent! This is called Homogeneous Nucleation. The reason why cloud droplets are observed to form in the atmosphere when ascending air just reaches equilibrium saturation is because the atmosphere con- tains significant concentrations of particles of micron and sub-micron size which have an affinity for water. This is called Heterogeneous Nucleation. There are many types of condensation nuclei in the atmosphere. Some become wetted at RH less than 100% and account for haze. Larger condensation nuclei may grow to cloud droplet size. As moist air is cooled adiabatically and RH is close to 100 the hygroscopic CCN begin to serve as centers of condensation. If ascent con- tinues, there is supersaturation by cooling which is depleted by condensation on the nuclei.
    [Show full text]
  • Carbonate Chemistry
    CHAPTER 3 SOLUTION-MINERAL EQUILIBRIA PART 1: CARBONATES Carbonic acid and the carbonate minerals provide another good illustration of the use of equilibrium reasoning in geochemistry. Interactions among these compounds determine the conditions under which limestones and dolomites are fomied or dissolved, and likewise the conditions of formation of carbonate minerals as cements in soils and sandstones and as vein fillings. We start with some qualitative remarks about the most common of these substances, the carbonate of calcium, then go on to a more quantitative treatment and to the reactions of other common carbonate minerals. • 3-1 SOLUBILITY OF CALCITE Calcium carbonate occurs in nature as the two common minerals calcite and aragonite (Sec. 3-3). A third crystal form (vaterite) can be prepared artificially, and is known as a very rare mineral in nature. Under usual conditions near the Earth's surface calcite is the most stable and most abundant of the three forms, and for the discussion in this section and the next it will be the center of attention. Aragonite and vaterite may be assumed to show similar chemical behavior, but in general to react more rapidly and to have greater solubility. 61 62 INTRODUCTION TO GEOCHEMISTRY A strong acid dissolves calcite by the familiar reaction CaC03 + 2H+ ---+ Ca2+ + H20 + C02. (3-1 ) calcite At low acid concentrations a more accurate equation would be CaC03 + H+ - • Ca2+ + HCO) (3-2) calcite showing that W takes co~ - away from Ca2+ to form the very weak (little dissociated) acid HCO:J. (Still greater accuracy would require consideration of the complex ion CaHCOj , but under usual conditions its concentration is small and for the present can be neglected.) These reactions would take place in nature, for example, where acid solutions from the weathering of pyrite encounter limestone.
    [Show full text]
  • The Role of Evolving Surface Tension in the Formation of Cloud Droplets James F
    Technical Note: The Role of Evolving Surface Tension in the Formation of Cloud Droplets James F. Davies1, Andreas Zuend2, Kevin R. Wilson3 1Department of Chemistry, University of California Riverside, CA USA 5 2Department of Atmospheric and Oceanic Sciences, McGill University, Montreal, Quebec, Canada 3Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA USA Correspondence to: James F. Davies ([email protected]) Abstract. The role of surface tension (σ) in cloud droplet activation has long been ambiguous. Recent studies have reported observations attributed to the effects of an evolving surface tension in the activation 10 process. However, adoption of a surface-mediated activation mechanism has been slow and many studies continue to neglect the composition-dependence of aerosol/droplet surface tension, using instead a value equal to the surface tension of pure water (σw). In this technical note, we clearly describe the fundamental role of surface tension in the activation of multicomponent aerosol particles into cloud droplets. It is demonstrated that the effects of surface tension in the activation process depend primarily on the evolution 15 of surface tension with droplet size, typically varying in the range 0.5σw ≲ σ ≤ σw due to the partitioning of organic species with a high surface affinity. We go on to report some recent laboratory observations that exhibit behavior that may be associated with surface tension effects, and propose a measurement coordinate that will allow surface tension effects to be better identified using standard atmospheric measurement techniques. Unfortunately, interpreting observations using theory based on surface film and liquid-liquid 20 phase separation models remains a challenge.
    [Show full text]
  • Solid-Liquid Phase Equilibria and Crystallization of Disubstituted Benzene Derivatives
    Royal Institute of Technology School of Chemical Science and Engineering Department of Chemical Engineering and Technology Division of Transport Phenomena Solid-Liquid Phase Equilibria and Crystallization of Disubstituted Benzene Derivatives Fredrik Nordström Doctoral Thesis Akademisk avhandling som med tillstånd av Kungliga Tekniska Högskolan i Stockholm framlägges till offentlig granskning för avläggande av teknologie doktorsexamen den 30:e Maj 2008, kl. 10:00 i sal D3, Lindstedtsvägen 5, Stockholm. Avhandlingen försvaras på engelska. i Cover picture: Crystals of o-hydroxybenzoic acid (salicylic acid) obtained through evaporation crystallization in solutions of ethyl acetate at around room temperature. Solid-Liquid Phase Equilibria and Crystallization of Disubstituted Benzene Derivatives Doctoral Thesis © Fredrik L. Nordström, 2008 TRITA-CHE Report 2008-32 ISSN 1654-1081 ISBN 978-91-7178-949-5 KTH, Royal Institute of Technology School of Chemical Science and Engineering Department of Chemical Engineering and Technology Division of Transport Phenomena SE-100 44 Stockholm Sweden Paper I: Copyright © 2006 by Wiley InterScience Paper II: Copyright © 2006 by Elsevier Science Paper III: Copyright © 2006 by the American Chemical Society Paper IV: Copyright © 2006 by the American Chemical Society ii In loving memory of my grandparents Aina & Vilmar Nordström iii i v Abstract The Ph.D. project compiled in this thesis has focused on the role of the solvent in solid-liquid phase equilibria and in nucleation kinetics. Six organic substances have been selected as model compounds, viz. ortho-, meta- and para-hydroxybenzoic acid, salicylamide, meta- and para-aminobenzoic acid. The different types of crystal phases of these compounds have been explored, and their respective solid-state properties have been determined experimentally.
    [Show full text]
  • Microbubble Treatment of Gas Supersaturated Water
    MICROBUBBLE TREATMENT OF GAS SUPERSATURATED WATER Contract No. GS-23F-0339K/01PE810319 Desalination and Water Purification R&D Program Report No. 70 December 2001 U.S. Department of Interior Bureau of Reclamation Denver Office Technical Service Center Environmental Resources Team Water Treatment Engineering and Research Group MICROBUBBLE TREATMENT OF GAS SUPERSATURATED WATER Mark A. Lichtwardt ARCADIS G&M, Inc. Highlands Ranch, Colorado Co-Author Andrew Murphy Bureau of Reclamation Denver, Colorado Contract No. GS-23F-0339K/01PE810319 Desalination and Water Purification R&D Program Report No. 70 December 2001 U.S. Department of Interior Bureau of Reclamation Denver Office Technical Service Center Environmental Resources Team Water Treatment Engineering and Research Group Mission Statements U.S. Department of the Interior The mission of the Department of the Interior is to protect and provide access to our Nation’s natural and cultural heritage and honor our trust responsibilities to tribes. Bureau of Reclamation The mission of the Bureau of Reclamation is to manage, develop, and protect water and related resources in an environmentally and economically sound manner in the interest of the American public. Disclaimer The information contained in this report regarding commercial products or firms may not be used for advertising or promotional purposes and is not to be construed as an endorsement of any product or firm by the Bureau of Reclamation. The information contained in this report was developed for the Bureau of Reclamation; no warranty as to the accuracy, usefulness, or completeness is expressed or implied. Acknowledgements This work was financially supported by the U.S. Department of Interior, Bureau of Reclamation under Contract No.
    [Show full text]
  • Crystallisation Behaviour of Sunflower and Longan Honey with Glucose Addition by Absorbance Measurement
    International Food Research Journal 27(4): 727 - 734 (August 2020) Journal homepage: http://www.ifrj.upm.edu.my Crystallisation behaviour of sunflower and longan honey with glucose addition by absorbance measurement Suriwong, V., *Jaturonglumlert, S., Varith, J., Narkprasom, K. and Nitatwichit, C. Graduate Program in Food Engineering, Faculty of Engineering and Agro-Industry, Maejo University, Chiang Mai 50290, Thailand Article history Abstract Received: 11 February 2020 The present work aimed to study the crystallisation behaviour of honey with glucose addition Received in revised form: by using the absorbance measurement at 660 nm. The Avrami model was used to explain the 7 May 2020 crystallisation kinetic. The effect of glucose addition on the colour and microstructure of Accepted: 4 June 2020 crystallised honey was also determined. Sunflower and longan honey were used in the present work. The biochemical compositions of honey samples were analysed before the addition of glucose powder at four concentrations (1.0, 1.5, 2.0, and 2.5%; w/w) and stored at 10 - 15°C. Keywords The absorbance at 660 nm, colour, and microstructure were measured until full crystallisation. crystallisation model, The results showed that different honey compositions exhibited different crystallisation glucose, behaviours, which could be monitored by the absorbance measurement at 660 nm as well. The longan honey, addition of glucose powder could stimulate the crystallisation time, thus affecting the crystal- sunflower honey lisation rate. The Avrami equation was found to be a good model for describing the crystallisa- tion behaviour from the intensity of absorbance values. The highest crystallisation rate was found at 2.0% (w/w) glucose addition at the rate constant (k) of 0.177 ± 0.038 and 0.083 ± 0.039 in sunflower and longan honey, respectively.
    [Show full text]
  • The Influence of Polymers on the Supersaturation Potential of Poor and Good Glass Formers
    pharmaceutics Article The Influence of Polymers on the Supersaturation Potential of Poor and Good Glass Formers Lasse I. Blaabjerg 1 , Holger Grohganz 1,* , Eleanor Lindenberg 2, Korbinian Löbmann 1 , Anette Müllertz 1 and Thomas Rades 1,3 1 Department of Pharmacy, University of Copenhagen, Universitetsparken 2, 2100 Copenhagen, Denmark; [email protected] (L.I.B.); [email protected] (K.L.); [email protected] (A.M.); [email protected] (T.R.) 2 Idorsia Pharmaceuticals Ltd., Hegenheimermwattweg 91, CH-4123 Allschwil, Switzerland; [email protected] 3 Faculty of Science and Engineering, Åbo Akademi University, Tykistökatu 6A, 20521 Turku, Finland * Correspondence: [email protected] Received: 16 August 2018; Accepted: 19 September 2018; Published: 21 September 2018 Abstract: The increasing number of poorly water-soluble drug candidates in pharmaceutical development is a major challenge. Enabling techniques such as amorphization of the crystalline drug can result in supersaturation with respect to the thermodynamically most stable form of the drug, thereby possibly increasing its bioavailability after oral administration. The ease with which such crystalline drugs can be amorphized is known as their glass forming ability (GFA) and is commonly described by the critical cooling rate. In this study, the supersaturation potential, i.e., the maximum apparent degree of supersaturation, of poor and good glass formers is investigated in the absence or presence of either hypromellose acetate succinate L-grade (HPMCAS-L) or vinylpyrrolidine-vinyl acetate copolymer (PVPVA64) in fasted state simulated intestinal fluid (FaSSIF). The GFA of cinnarizine, itraconazole, ketoconazole, naproxen, phenytoin, and probenecid was determined by melt quenching the crystalline drugs to determine their respective critical cooling rate.
    [Show full text]
  • The Mechanism of Phenytoin Crystal Growth
    International Journal of Pharmaceutics, 98 (1993) 189-201 189 0 1993 Elsevier Science Publishers B.V. All rights reserved 0378-5173/93/$06.00 IJP 03264 The mechanism of phenytoin crystal growth Gail L. Zipp ’ and Nair Rodriguez-Horned0 College of Pharmacy, The Universi@ of Michigan, Ann Arbor, MI 48109-1065 (USA) (Received 6 August 1992) (Modified version received 8 March 1993) (Accepted 18 March 1993) Key words: Phenytoin; Crystal growth; Kinetics; Mechanism Summary Phenytoin crystal growth kinetics have been measured as a function of pH, supersaturation and temperature in phosphate buffer. Incorporation of growth units into the crystal lattice was not influenced by diffusion from the bulk to the solid surface. Thus, the rate limiting step for phenytoin growth is surface integration. Phenytoin crystal growth is via a screw-dislocation mechanism; this mechanism explains the observed dependence of growth rate on supersaturation and the increase in growth rate with pH. Introduction bility of these compounds is dependent on pH, in vitro and in vivo crystallization of the free acid or An understanding of crystallization mecha- base can occur as a result of a pH change. In nisms is necessary for the prediction of solids vivo, precipitation follows either dissolution of a properties which influence the dissolution rate solid phase or dilution of a solution of the salt of and bioavailability of oral dosage forms such as a weak acid or base. Precipitation via a pH change particle size, size distribution and morphology. In is also commonly used in industrial crystalliza- addition, formulation of non-precipitating dosage tion. forms requires an understanding of the condi- Previous investigations have highlighted this tions under which crystals will form so that limit- phenomenon.
    [Show full text]
  • MSE3 Ch07 Precipitation
    Chapter 7 Copyright © 2011, 2015 by Roland Stull. Meteorology for Scientists and Engineers, 3rd Ed. preCipitation Contents Hydrometeors are liquid and ice parti- cles that form in the atmosphere. Hydrom- Supersaturation and Water Availability 186 eter sizes range from small cloud droplets Supersaturation 186 7 and ice crystals to large hailstones. Precipitation Water Availability 186 occurs when hydrometeors are large and heavy Number and Size of Hydrometeors 187 enough to fall to the Earth’s surface. Virga occurs Nucleation of Liquid Droplets 188 when hydrometers fall from a cloud, but evaporate Cloud Condensation Nuclei (CCN) 188 before reaching the Earth’s surface. Curvature and Solute Effects 189 Precipitation particles are much larger than cloud Critical Radius 192 particles, as illustrated in Fig. 7.1. One “typical” Haze 192 Activated Nuclei 193 raindrop holds as much water as a million “typical” cloud droplets. How do such large precipitation Nucleation of Ice Crystals 194 Processes 194 particles form? Ice Nuclei 195 The microphysics of cloud- and precipitation- particle formation is affected by super-saturation, Liquid Droplet Growth by Diffusion 196 nucleation, diffusion, and collision. Ice Growth by Diffusion 198 Supersaturation indicates the amount of excess Ice Crystal Habits 198 water vapor available to form rain and snow. Growth Rates 200 The Wegener-Bergeron-Findeisen (WBF) Nucleation is the formation of new liquid or Process 201 solid hydrometeors as water vapor attaches to tiny dust particles carried in the air. These particles are Collision and Collection 202 Terminal Velocity of Hydrometeors 202 called cloud condensation nuclei or ice nuclei. Cloud Droplets 202 Diffusion is the somewhat random migration Rain Drops 203 of water-vapor molecules through the air toward ex- Hailstones 204 isting hydrometeors.
    [Show full text]
  • A Method for the Crystallization of Fructose
    Europaisches Patentamt 0 293 680 J European Patent Office © Publication number: A2 Office europeen des brevets EUROPEAN PATENT APPLICATION © Application number: 88108028.7 © mt.ci.4:C13K 11/00 © Date of filing: 19.05.88 © Priority: 03.06.87 Fl 872487 © Applicant: SUOMEN SOKERI OY Kyllikinportti 2 @ Date of publication of application: SF-00240 Helsinki(FI) 07.12.88 Bulletin 88/49 © Inventor: Heikkila, Heikki © Designated Contracting States: Aallonkohina 4 C AT BE CH DE ES FR GB GR IT LI LU NL SE SF-02320 Espoo(FI) Inventor: Kurula, Vesa American Xyrofin Inc., P.O. Box 488 Thomson Illinois 61285(US) © Representative: Masch, Karl Gerhard et al Patentanwalte Andrejewski, Honke & Partner Theaterplatz 3 Postfach 10 02 54 D-4300 Essen 1(DE) © A method for the crystallization of fructose. © The invention relates to a method for the production of crystalline fructose. The method comprises the steps of adding ethanol to a concentrated fructose solution; evaporating the mixture to a degree of supersaturation of at least 1.02; and adding anhydrous fructose seed crystals; removing ethanol-water azeotrope at^a reduced 75° pressure while maintaining the solution at a substantially constant temperature ranging from 50 to C so as to crystallize fructose; and recovering crystallized fructose, e.g. by centrifugation. 00 CO to LU Xerox Copy Centre EP 0 293 680 A2 A method for the crystallization of fructose This invention relates to a method for the crystallization of fructose from an ethanol-water solution. Fructose, also known as fruit sugar, is a monosaccharide constituting one-half of the sucrose molecule.
    [Show full text]