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8 - Atomization and Spray Formation

from Part III - Spray Formation and Impact onto Surfaces

Published online by Cambridge University Press:  13 July 2017

Alexander L. Yarin
Affiliation:
University of Illinois, Chicago
Ilia V. Roisman
Affiliation:
Technische Universität, Darmstadt, Germany
Cameron Tropea
Affiliation:
Technische Universität, Darmstadt, Germany
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Summary

The process of atomization involves the generation of drops from bulk fluid, achieved using a wide variety of atomization concepts, depending on the desired local drop number, size and velocity flux densities, as well as on the bulk fluid and its properties, e.g. pure liquids, dispersions, suspensions, emulsions, etc. In the context of collision phenomena, atomization plays a key role in applications such as spray cooling, touchless cleaning and spray coating, whereby the latter can be understood in a very broad sense, encompassing applications such as spray painting, crop spraying, spray based encapsulation, domestic sprays (e.g. hair sprays, polishes) or even inhalators. Indeed, a majority of liquid collision phenomena involve atomization for the generation of individual drops and this fact motivates the present examination of the atomization process in more detail, with the aim of establishing an understanding between the atomization conditions and the resulting properties of the spray.

This chapter divides the atomization process into primary atomization (Section 8.1), i.e. overcoming the consolidating influence of surface tension by the action of internal and external forces (Lefebvre 1989), secondary atomization, and binary drop collisions in a spray, whereby several special modes of secondary atomization are treated in the final four sections. The causes of secondary atomization are manifold and can significantly alter the size distribution in a spray and are therefore important to consider. Typical causes of secondary atomization include aerodynamic forces whenever a drop is exposed to a relative air flow; covered in Section 8.2. Binary drop collisions can also lead to secondary atomization, as they occur in dense sprays, interacting sprays or when spray drops impinging onto a surface interact with drops ejected from the surface. Binary drop collisions are discussed in Section 8.3. Another cause of secondary atomization is when a drop impinges onto or is forced off a filament, for instance in a filter. This atomization scenario is the topic of Section 8.4. Finally, secondary atomization can also be electrically driven. In this case, evaporation in flight of electrified drops issued from electrostatic atomizers diminishes the drop surface area, while the electric charges they carry remain the same. As a result, the shrinking drop size can reach the so-called Rayleigh limit.

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Publisher: Cambridge University Press
Print publication year: 2017

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References

Ashgriz, N. (ed.) (2011). Handbook of Atomization and Sprays: Theory and Applications, Springer, Heidelberg.
Ashgriz, N., Li, X. and Sarchami, A. (2011). Instability of liquid sheets, in N., Ashgriz (ed.), Handbook of Atomization and Sprays: Theory and Applications, Springer, Heidelberg, chapter 3, pp. 75–95.
Ashgriz, N. and Poo, J. Y. (1990). Coalescence and separation in binary collisions of liquid drops, J. Fluid Mech. 221: 183–204.Google Scholar
Balewski, B., Heine, B. and Tropea, C. (2010). Experimental investigation of the correlation between nozzle flow and spray using laser Doppler velocimeter, phase Doppler system, highspeed photography, and X-ray radiography, Atom. Sprays 20: 57–70.Google Scholar
Bird, R. B., Armstrong, R. and Hassager, O. (1987). Dynamics of Polymeric Liquids. Vol. 1: Fluid Mechanics, John Wiley & Sons Inc., New York.
Bisighini, A., Cossali, G. E., Tropea, C. and Roisman, I. V. (2010). Crater evolution after the impact of a drop onto a semi-infinite liquid target, Phys. Rev. E 82: 036319.Google Scholar
Brazier-Smith, P., Jennings, S. and Latham, J. (1972). The interaction of falling water drops: coalescence, Proc. R. Soc. London Ser. A-Math. 326: 393–408.Google Scholar
Brenn, G., Valkovska, D. and Danov, K. D. (2001). The formation of satellite droplets by unstable binary drop collisions, Phys. Fluids 13: 2463–2477.Google Scholar
Castellanos, A. and Pérez, A. (2007). Electrohydrodynamic systems, in C., Tropea, A. L., Yarin and J., Foss (eds.), Springer Handbook of Experimental Fluid Mechanics, Springer, Heidelberg, chapter C21, pp. 1317–1333.
Castleman, R. A. (1931). The Mechanism of the Atomization of Liquids, US Department of Commerce, Bureau of Standards.
Chang, H. C. and Yeo, L. Y. (2010). Electrokinetically Driven Microfluidics and Nanofluidics, Cambridge University Press.
Chen, R. H. (2007). Diesel-diesel and diesel-ethanol drop collisions, Appl. Thermal Eng. 27: 604–610.Google Scholar
Chen, R. H. and Chen, C. T. (2006). Collision between immiscible drops with large surface tension difference: diesel oil and water, Exp. Fluids 41: 453–461.Google Scholar
Chigier, N. and Farago, Z. (1992). Morphological classification of disintegration of round liquid jets in a coaxial air stream, Atom. Sprays 2: 137–153.Google Scholar
Crowe, C. T. (2005). Multiphase Flow Handbook, Vol. 59, CRC Press, Boca Raton.
Czerwonatis, N. and Eggers, R. (2001). Disintegration of liquid jets and drop drag coefficients in pressurized nitrogen and carbon dioxide, Chemical Eng. Technol. 24: 619–624.Google Scholar
Dai, Z. and Faeth, G. M. (2001). Temporal properties of secondary drop breakup in the multimode breakup regime, Int. J. Multiph. Flow 27: 217–236.Google Scholar
Delplanque, J. P. and Sirignano, W. A. (1994). Boundary-layer stripping effects on droplet transcritical convective vaporization, Atom. Sprays 4: 325–367.Google Scholar
Desjardins, O. and Pitsch, H. (2010). Detailed numerical investigation of turbulent atomization of liquid jets, Atom. Sprays 20: 311–336.Google Scholar
Dombrowski, N. and Johns, W. R. (1963). The aerodynamic instability and disintegration of viscous liquid sheets, Chem. Eng. Sci. 18: 203–214.Google Scholar
Duft, D., Achtzehn, T. ,Müller, R., Huber, B. A. and Leisner, T. (2003). Coulomb fission: Rayleigh jets from levitated microdroplets, Nature 421: 128.Google Scholar
Dupré, A. (1867). Theorie mécanique de la Chaleur, Ann. Chim. Phys. 4: 194–220.Google Scholar
Eggers, J., Fontelos, M. A., Josserand, C. and Zaleski, S. (2010). Drop dynamics after impact on a solid wall: theory and simulations, Phys. Fluids 22: 062101.Google Scholar
Faeth, G. M., Hsiang, L. P. and Wu, P. K. (1995). Structure and breakup properties of sprays, Int. J. Multiph. Flow 21: 99–127.Google Scholar
Focke, C. and Bothe, D. (2012). Direct numerical simulation of binary off-center collisions of shear thinning droplets at high Weber numbers, Phys. Fluids 24: 073105.Google Scholar
Fraser, R. P. and Eisenklam, P. (1953). Research into the performance of atomizers for liquids, Imp. Coll. Chem. Eng. Soc. J 7: 52–68.Google Scholar
Fukai, J., Shiiba, Y., Yamamoto, T., Miyatake, O., Poulikakos, D., Megaridis, C. M. and Zhao, Z. (1995). Wetting effects on the spreading of a liquid droplet colliding with a flat surface: experiment and modeling, Phys. Fluids 7: 236–247.Google Scholar
Gao, T. C., Chen, R. H., Pu, J. Y. and Lin, T. H. (2005). Collision between an ethanol drop and a water drop, Exp. Fluids 38: 731–738.Google Scholar
Gelfand, B. E. (1996). Droplet breakup phenomena in flows with velocity lag, Prog. Energy Combust. Sci. 22: 201–265.Google Scholar
Gnirss, M., Heukelbach, K. and Tropea, C. (2004). Influence of nozzle flow on the atomization of liquid sheets and round jets, in P., Walzel and C., Tropea (eds.), Atomization and Spray Processes, Vol. 7 of Schriftenreihe Mechanische Verfahrenstechnik, Shaker Verlag, Aachen.
Gotaas, C., Havelka, P., Jakobsen, H., Svendsen, H. F., Hase, M., Roth, N. andWeigand, B. (2007). Effect of viscosity on droplet-droplet collision outcome: experimental study and numerical comparison, Phys. Fluids 19: 102106.Google Scholar
Grimm, R. L. and Beauchamp, J. L. (2010). Evaporation and discharge dynamics of highly charged multicomponent droplets generated by electrospray ionization, J. Phys. Chem. A 114: 1411–1419.Google Scholar
Guildenbecher, D. R., López-Rivera, C. and Sojka, P. E. (2009). Secondary atomization, Exp. Fluids 46: 371–402.Google Scholar
Ha, J. W. and Leal, L. G. (2001). An experimental study of drop deformation and breakup in extensional flow at high capillary number, Phys. Fluids 13: 1568–1576.Google Scholar
Hasson, D. and Mizrahi, J. (1961). The drop size of fan spray nozzle, measurements by the solidifying wax method compared with those obtained by other sizing techniques, Trans. Inst. Chem. Eng 39: 415–422.Google Scholar
Heukelbach, K. (2002). Untersuchung zum Einfluss der Düseninnenströmung auf die Stabilität von flächigen Flüssigkeitsstrahlen, PhD thesis, Technische Universität Darmstadt.
Hinze, J. O. (1955). Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes, AIChE J. 1: 289–295.Google Scholar
Hiroysau, H. (1996). Effect of internal flow conditions inside injector nozzles on jet breakup processes, in K., Kuo (ed.), Recent Advances in Spray Combustion: Spray Atomization and Drop Burning Phenomena, Vol. 166 of Progress in Astronautics and Aeronauthics, AIAA Inc, New York, pp. 173–184.
Hiroyasu, H. (2000). Spray breakup mechanism from the hole-type nozzle and its applications, Atom. Sprays 10: 511–527.Google Scholar
Hsiang, L. P. and Faeth, G. M. (1993). Drop properties after secondary breakup, Int. J. Multiph. Flow 19: 721–735.Google Scholar
Hsiang, L. P. and Faeth, G. M. (1995). Drop deformation and breakup due to shock wave and steady disturbances, Int. J. Multiph. Flow 21: 545–560.Google Scholar
Hwang, S. S., Liu, Z. and Reitz, R. D. (1996). Breakup mechanisms and drag coefficients of high-speed vaporizing liquid drops, Atom. Sprays 6: 353–376.Google Scholar
Inamuro, T., Ogata, T., Tajima, S. and Konishi, N. (2004). A lattice Boltzmann method for incompressible two-phase flows with large density differences, J. Comp. Phys. 198: 628.Google Scholar
Jiang, Y. J., Umemura, A. and Law, C. K. (1992). An experimental investigation on the collision behaviour of hydrocarbon droplets, J. Fluid Mech. 234: 171–190.Google Scholar
Joseph, D. D., Beavers, G. S. and Funada, T. (2002). Rayleigh–Taylor instability of viscoelastic drops at high Weber numbers, J. Fluid Mech. 453: 109–132.Google Scholar
Joseph, D. D., Belanger, J. and Beavers, G. S. (1999). Breakup of a liquid drop suddenly exposed to a high-speed airstream, Int. J. Multiph. Flow 25: 1263–1303.Google Scholar
Klein, M. (2002). Direkte numerische Simulation des primären Strahlzerfalls in Einstoffzerstäuberdüsen, PhD thesis, Technische Universität Darmstadt.
Klostermann, M., Haensel, R., Venzmer, J., Sieverding, E., Pfoffenberger, C., Roisman, I. V. and Tropea, C. (2015). Mode of action of silicone drift control agents, in C., Poffenberger (ed.), 26th Symposium on Pesticide Formulation and Delivery Systems: Emerging Trends Building on a Solid Foundation, ASTM Committee E35 on Pesticides, Antimicrobials, and Alternative Control Agents, ASTM International.
Krzeczkowski, S. A. (1980). Measurement of liquid droplet disintegration mechanisms, Int. J. Multiph. Flow 6: 227–239.Google Scholar
Landau, L. D. and Lifshitz, E. M. (1987). Fluid Mechanics, Pergamon Press, Oxford.
Leboissetier, A. and Zaleski, S. (2001). Direct numerical simulation of the atomization of a liquid jet, Proc. ILASS-Europe, pp. 2–6.
Lee, C. H. and Reitz, R. D. (2000). An experimental study of the effect of gas density on the distortion and breakup mechanism of drops in high speed gas stream, Int. J. Multiph. Flow 26: 229–244.Google Scholar
Lefebvre, A. H. (1989). Atomization and Sprays, Hemisphere Publishing Corporation, New York.
Lin, S. P. (2003). Breakup of Liquid Sheets and Jets, Cambridge University Press.
Lin, S. P. and Reitz, R. D. (1998). Drop and spray formation from a liquid jet, Annu. Rev. Fluid Mech. 30: 85–105.Google Scholar
Liu, H. (1999). Science and Engineering of Droplets: Fundamentals and Applications, William Andrew, Norwich, New York.
Liu, Z. and Reitz, R. D. (1997). An analysis of the distortion and breakup mechanisms of high speed liquid drops, Int. J. Multiph. Flow 23: 631–650.Google Scholar
Mansour, A. and Chigier, N. (1994). Effect of turbulence on the stability of liquid jets and the resulting droplet size distributions, Atom. Sprays 4: 583–604.Google Scholar
Marengo, M., Antonini, C., Roisman, I. V. and Tropea, C. (2011). Drop collisions with simple and complex surfaces, Curr. Opin. Colloid Interface Sci. 16: 292–302.Google Scholar
Mayer, W. O. H. and Branam, R. (2004). Atomization characteristics on the surface of a round liquid jet, Exp. Fluids 36: 528–539.Google Scholar
Meitner, L. and Frisch, O. R. (1939). Disintegration of uranium by neutrons: a new type of nuclear reaction, Nature 143: 239–240.Google Scholar
Melcher, J. R. and Taylor, G. I. (1969). Electrohydrodynamics: a review of the role of interfacial shear stresses, Annu. Rev. Fluid Mech. 1: 111–146.Google Scholar
Miesse, C. C. (1955). Correlation of experimental data on the disintegration of liquid jets, Ind. & Eng. Chem. 47: 1690–1701.Google Scholar
Miloh, T., Spivak, B. and Yarin, A. L. (2009). Needleless electrospinning: electrically-driven instability and multiple jetting from the free surface of a spherical liquid layer, J. Appl. Phys. 106: 114910.Google Scholar
Nasr, G. G., Yule, A. J. and Bendig, L. (2013). Industrial Sprays and Atomization: Design, Analysis and Applications, Springer, Heidelberg.
Ng, C. L., Sankarakrishnan, R. and Sallam, K. A. (2008). Bag breakup of nonturbulent liquid jets in crossflow, Int. J. Multiph. Flow 34: 241–259.Google Scholar
v. Ohnesorge, W. (1936). Die Bildung von Tropfen an Düsen und die Auflösung flüssiger Strahlen, Z. Angew. Math. Mech. 16: 355–358.Google Scholar
Opfer, L. (2014). Controlling Liquid Atomization using Dilute Emulsions:Mitigation of Pesticide Spray Drift, PhD thesis, Technische Universität Darmstadt.
Opfer, L., Roisman, I. V., Venzmer, J., Klostermann, M. and Tropea, C. (2014). Droplet-air collision dynamics: evolution of the film thickness, Phys. Rev. E 89: 013023.Google Scholar
Orme, M. (1997). Experiments on droplet collisions, bounce, coalescence and disruption, Prog. Energy Combust. Sci. 23: 65–79.Google Scholar
Pan, K. L., Law, C. K. and Zhou, B. (2008). Experimental and mechanistic description of merging and bouncing in head-on binary droplet collision, J. Appl. Phys. 103: 064901.Google Scholar
Pan, K. L. and Roisman, I. V. (2009). Note on “Dynamics of inertia dominated binary drop collisions,” [Phys. of Fluids 16, 3438 (2004)], Phys. Fluids 21: 022101.Google Scholar
Pan, Y. and Suga, K. (2005). Numerical simulation of binary liquid droplet collision, Phys. Fluids 17: 082105.Google Scholar
Panofsky, W. K. H. and Phillips, M. (2005). Classical Electricity and Magnetism, Dover Publications, New York.
Pilch, M. and Erdman, C. A. (1987). Use of breakup time data and velocity history data to predict the maximum size of stable fragments for acceleration-induced breakup of a liquid drop, Int. J. Multiph. Flow 13: 741–757.Google Scholar
Planchette, C., Lorenceau, E. and Brenn, G. (2010). Liquid encapsulation by binary collisions of immiscible liquid drops, Colloid Surf. A-Physicochem. Eng. 365: 89–94.Google Scholar
Pruppacher, H. R. and Klett, J. D. (2012). Microphysics of Clouds and Precipitation: Reprinted 1980, Springer, Heidelberg.
Qian, J. and Law, C. K. (1997). Regimes of coalescence and separation in droplet collision, J. Fluid Mech. 331: 59–80.Google Scholar
Ranger, A. A. and Nicholls, J. A. (1969). Aerodynamic shattering of liquid drops, AIAA J. 7: 285–290.Google Scholar
Lord, Rayleigh (1882). On the equilibrium of liquid conducting masses charged with electricity, Phil. Mag. 14: 184–186.Google Scholar
Reitz, R. D. (1978). Atomization and other Breakup Regimes of a Liquid Jet, PhD thesis, Princeton University.
Rimbert, N. and Castanet, G. (2011). Crossover between Rayleigh-Taylor instability and turbulent cascading atomization mechanism in the bag-breakup regime, Phys. Rev. E 84: 016318.Google Scholar
Rioboo, R., Marengo, M. and Tropea, C. (2002). Time evolution of liquid drop impact onto solid, dry surfaces, Exp. Fluids 33: 112–124.Google Scholar
Rizk, N. K. and Lefebvre, A. H. (1980). The influence of liquid film thickness on airblast atomization, J. Eng. Power 102: 706–710.Google Scholar
Roisman, I. V. (2004). Dynamics of inertia dominated binary drop collisions, Phys. Fluids 16: 3438–3449.Google Scholar
Roisman, I. V. (2009). Inertia dominated drop collisions II: an analytical solution of the Navier- Stokes equations for a spreading viscous film, Phys. Fluids 21: 052104.Google Scholar
Roisman, I. V., Berberović, E. and Tropea, C. (2009). Inertia dominated drop collisions I: on the universal flow in the lamella, Phys. Fluids 21: 052103.Google Scholar
Roisman, I. V., Horvat, K. and Tropea, C. (2006). Spray impact: rim transverse instability initiating fingering and splash, and description of a secondary spray, Phys. Fluids 18: 102104.Google Scholar
Roisman, I. V., Planchette, C., Lorenceau, E. and Brenn, G. (2012). Binary collisions of drops of immiscible liquids, J. Fluid Mech. 690: 512–535.Google Scholar
Russel, W. B., Saville, D. A. and Schowalter, W. R. (1992). Colloidal Dispersions, Cambridge University Press.
Sahu, R. P., Sinha-Ray, S., Yarin, A. L. and Pourdeyhimi, B. (2013). Blowing drops off a filament, Soft Matter 9: 6053–6071.Google Scholar
Sallam, K. A., Dai, Z. and Faeth, G. M. (1999). Drop formation at the surface of plane turbulent liquid jets in still gases, Int. J. Multiph. Flow 25: 1161–1180.Google Scholar
Sallam, K. A. and Faeth, G. M. (2003). Surface properties during primary breakup of turbulent liquid jets in still air, AIAA J. 41: 1514–1524.Google Scholar
Sauerwein, U. K. (1992). Theoretische und experimentelle Untersuchung der Instabilität turbulenter Kapillarstrahlen, PhD thesis, Technische Universität Darmstadt.
Sauter, J. (1926). Die Grössenbestimmung der im Gemischnebel von Verbrennungskraftmaschinen vohrhandenen Brennstoffteilchen:(Mitteilung aus dem Laboratorium für Technische Physik der Technischen Hochschule München), VDI-Verlag.
Saville, D. A. (1997). Electrohydrodynamics: the Taylor-Melcher leaky dielectric model, Annu. Rev. Fluid Mech. 29: 27–64.Google Scholar
Schlichting, H. and Gersten, K. (2003). Boundary-Layer Theory, Springer, Heidelberg.
Schmehl, R. (2003).Modeling droplet breakup in complex two-phase flows (Paper 2–19), ICLASS Conference, Sorento, Italy.
Sevik, M. and Park, S. H. (1973). The splitting of drops and bubbles by turbulent fluid flow, J. Fluids Eng. 95: 53–60.Google Scholar
Shrimpton, J. (2009). Charge Injection Systems – Physical Principles, Experimental and Theoretical Work, Springer, Heidelberg.
Sirignano, W. A. and Mehring, C. (2000). Review of theory of distortion and disintegration of liquid streams, Progr. Energy Comb. Sci. 26: 609–655.Google Scholar
Sun, Z., Xi, G. and Chen, X. (2009). Mechanism study of deformation and mass transfer for binary droplet collisions with particle method, Phys. Fluids 21: 032106.Google Scholar
Tamaki, N., Shimizu, M., Nishida, K. and Hiroyasu, H. (1998). Effects of cavitation and internal flow on atomization of a liquid jet, Atom. Sprays 8: 179–197.Google Scholar
Taylor, G. I. (1959a). The dynamics of thin sheets of fluid II. Waves on fluid sheets, Proc. R. Soc. London Ser. A-Math. 253: 296–312.Google Scholar
Taylor, G. I. (1959b). The dynamics of thin sheets of fluid III. Disintegration of fluid sheets, Proc. R. Soc. London Ser. A-Math. 253: 313–321.Google Scholar
Theofanous, T. G. (2011). Aerobreakup of Newtonian and viscoelastic liquids, Annu. Rev. Fluid Mech. 43: 661–690.Google Scholar
Villermaux, E. and Bossa, B. (2009). Single-drop fragmentation determines size distribution of raindrops, Nat. Phys. 5: 697–702.Google Scholar
Weber, C. (1931). Zum Zerfall eines Flüssigkeitsstrahles, ZAMM-J. of Appl.Math. Mech. 11: 136–154.Google Scholar
Wierzba, A. (1990). Deformation and breakup of liquid drops in a gas stream at nearly critical Weber numbers, Exp. Fluids 9: 59–64.Google Scholar
Willis, K. and Orme, M. (2000). Viscous oil droplet collisions in a vacuum, Exp. Fluids 29: 347–358.Google Scholar
Willis, K. and Orme, M. (2003). Binary droplet collisions in a vacuum environment: an experimental investigation of the role of viscosity, Exp. Fluids 34: 28–41.Google Scholar
Wozniak, G. (2013). Zerstäubungstechnik: Prinzipien, Verfahren, Geräte, Springer, Heidelberg.
Wu, P. K. and Faeth, G. M. (1993). Aerodynamic effects on primary breakup of turbulent liquids, Atom. Sprays 3: 265–289.Google Scholar
Wu, P. K., Miranda, R. F. and Faeth, G. M. (1995). Effects of initial flow conditions on primary breakup of nonturbulent and turbulent round liquid jets, Atom. Sprays 5: 175–196.Google Scholar
Xu, L., Zhang, W. W. and Nagel, S. R. (2005). Drop splashing on a dry smooth surface, Phys. Rev. Lett. 94: 184505.Google Scholar
Yarin, A. L. (1993). Free Liquid Jets and Films: Hydrodynamics and Rheology, Longman and John Wiley & Sons, Harlow and New York.
Yarin, A. L., Kataphinan, W. and Reneker, D. H. (2005). Branching in electrospinning of nanofibers, J. Appl. Phys. 98: 064501.Google Scholar
Yarin, A. L., Pourdeyhimi, B. and Ramakrishna, S. (2014). Fundamentals and Applications of Micro- and Nanofibers, Cambridge University Press.
Yarin, A. L. and Weiss, D. A. (1995). Impact of drops on solid surfaces: self-similar capillary waves, and splashing as a new type of kinematic discontinuity, J. Fluid Mech. 283: 141–173.Google Scholar
Yarin, A. L., Weiss, D. A., Brenn, G. and Rensink, D. (2002). Acoustically levitated drops: drop oscillation and break-up driven by ultrasound modulation, Int. J. Multiph. Flow 28: 887–910.Google Scholar
York, J. L., Stubbs, H. E. and Tek, M. R. (1953). The mechanism of disintegration of liquid sheets, Trans. ASME 75: 1279–1286.Google Scholar

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