Come calcolare il numero di Ohnesorge (Oh) rapporto adimensionale che misura le forze viscose rispetto alle forze inerziali e di tensione superficiale nella formazione di gocce + atomizzazione + breakup di getti liquidi: Oh = mu / sqrt(rho * sigma * L). mu viscosità dinamica Pa*s (acqua 25°C 1e-3; etanolo 1.1e-3; glicerina 1.5; oli motore 0.1-1); rho densità kg/m^3 (acqua 1000; mercurio 13534; oli 800-900); sigma tensione superficiale N/m (acqua 25°C 0.072; etanolo 0.022; mercurio 0.485; oli 0.025-0.035); L lunghezza caratteristica m (diametro nozzle inkjet 20-50 micron; spray atomizer 100-500 micron; jet flame 1-10 mm). Equivalente Oh = sqrt(We)/Re = mu/sqrt(rho*sigma*L) dove We Weber e Re Reynolds.

Z numero printability inkjet: Z = 1/Oh = sqrt(rho*sigma*L)/mu Fromm 1984 IBM Research Yorktown Heights criterion droplet ejection clean.

Classificazione regime: Oh10 ejection droplet pulita + satellite drops + breakup capillare Rayleigh-Plateau; 0.1<Oh<1 inkjet optimal Z=1-10 good droplet formation + DOD Drop-On-Demand piezoelectric + thermal bubble jet; 1<Oh<10 viscous regime Z=0.1-1 viscous breakup limited + ligaments long + satellite formation + non-Newtonian shear-thinning ink; Oh>10 highly viscous no droplet formation + viscous dominates + jet stable no breakup.

Numeri correlati: Reynolds Re = rho*v*L/mu inerzia/viscoso; Weber We = rho*v^2*L/sigma inerzia/tensione superficiale; Capillary Ca = mu*v/sigma viscoso/tensione superficiale; Bond number Bo = rho*g*L^2/sigma gravita/tensione superficiale; Marangoni Ma = (dσ/dT)*ΔT*L/(μ*α) tensione superficiale termica; Eotvos Eo = Bo.

Plateau-Rayleigh instability: cylindrical liquid jet capillary breakup wavelength lambda_max = 9.02*R + Tomotika 1935 viscous ratio + Plateau 1873 minimum surface area; Eggers self-similar pinch-off 1993 Phys Rev Lett finite-time singularity pinch-off + Newtonian universal scaling.

Inkjet printing technologies: Continuous Inkjet CIJ Hertz Sweden 1965 KTH Stockholm + Domino Cambridge UK + Linx Cambridge UK + Videojet Wood Dale IL + industrial coding marking + droplet 80 micron + 100k droplets/s; Drop-On-Demand DOD piezoelectric Spectra Trident 1980s + thermal bubble jet HP Hewlett-Packard 1979 Canon 1981 + Epson 1984 piezo MicroPiezo + droplet 1-100 picoliter + 5-50 micron diameter; industrial DOD Xaar Cambridge UK 1990 + Seiko Instruments + Toshiba TEC + KYOCERA Japan + Konica Minolta + ricoh; 3D printing material extrusion Stratasys + 3D Systems + ProJet + MultiJet Modeling MJM Polyjet inkjet photopolymer; OLED inkjet printing Samsung Display + LG Display + JOLED Japan + KATEEVA San Jose CA YIELDjet + RGB pixel inkjet; printed electronics Cambridge Display Technology + Thin Film Electronics + Plastic Logic Cambridge UK + Heraeus Hanau Germany silver ink + Dupont Microcircuit Materials.

Spray atomization industria: automotive injection diesel benzina direct injection GDi gasoline + diesel common rail + Bosch Stuttgart + Continental + Denso Japan + Magneti Marelli + nozzle 200 micron + atomizzazione droplet 10-50 micron; pharmaceutical aerosols MDI metered dose inhalers + DPI dry powder inhalers + nebulizers + hydrofluoroalkane HFA propellants + Chiesi Parma + Recordati Milano + Zambon + GlaxoSmithKline UK + AstraZeneca; agricultural pesticide sprayers + droplet drift + ASABE standards + 100-500 micron; combustion turbine + jet engine + air-blast atomizer pressure-swirl + Avio Aero Pomigliano + Leonardo Helicopters + Rolls-Royce UK + GE Aviation + Pratt&Whitney + 50-200 micron; cosmetic perfume sprayers + L'Oreal Paris + LVMH + Mexx + Chanel + Procter&Gamble + Unilever; food spray drying milk powder + coffee instant + Niro Soeborg DK + Anhydro Spx Soeborg + Buchi Flawil CH + droplet 10-200 micron. Storia: Wolfgang von Ohnesorge (Berlin Germany 1901 - Stuttgart 1976) Universitat Gottingen PhD 1936 Ludwig Prandtl supervisor + Aerodynamische Versuchsanstalt AVA Gottingen + Stuttgart MTU Aero Engines 1955-1976;

1936 PhD thesis 'Die Bildung von Tropfen an Dusen und die Auflosung flussiger Strahlen' ZAMM Zeitschrift Angewandte Mathematik Mechanik 16:355-358 + classic jet breakup analysis + 4 regimi (Rayleigh + first wind-induced + second wind-induced + atomization) + dimensionless number eponym Oh + Reynolds-Ohnesorge diagram log-log; pioneer atomization theory + Ohnesorge regime map standard reference + Tropfenbildung an Dusen droplet formation.

Lord Rayleigh (John William Strutt Essex UK 1842-1919) Cambridge Cavendish + Royal Society + Nobel Prize 1904 (argon); 1879 paper Proc London Math Soc 10:4 'On the instability of jets' classic Plateau-Rayleigh capillary instability + cylindrical jet breakup wavelength + linear stability analysis + 1892 'On the instability of cylindrical fluid surfaces' Phil Mag 34:177; 1916 paper Phil Mag 32:529 Rayleigh-Benard.

Joseph Antoine Plateau (Brussels Belgium 1801-1883) Universite Etat Liege 1827 + Universite Etat Gand 1835; 1873 textbook 'Statique experimentale et theorique des liquides soumis aux seules forces moleculaires' 2 volumes + Plateau border + Plateau laws minimal surface + capillary break-up principle minimum surface area; cieco da 1843 dopo esperimenti ottica gazing direct sun.

Susumu Tomotika (Japan 1908-1989) Tokyo Imperial University; 1935 paper Proc Roy Soc London A 150:322 'On the instability of a cylindrical thread of a viscous liquid surrounded by another viscous fluid' classic viscous Rayleigh-Plateau instability + viscous ratio modify wavelength + Tomotika analysis.

Hassan Aref + Anders Wernet 1980s Ohnesorge Reynolds diagram standard atomization map.

Jens Eggers (Wuppertal Germany 1962-) MIT + University Bristol UK 2003-; 1993 paper Phys Rev Lett 71:3458 'Universal pinching of 3D axisymmetric free-surface flow' classic self-similar pinch-off + finite-time singularity + Newtonian universal scaling + Eggers-Villermaux 2008 Rep Prog Phys 71:036601 review classic.

John Eggers Fromm IBM Research 1984; 1984 paper IBM J Res Develop 28:322 'Numerical calculation of the fluid dynamics of drop-on-demand jets' Z = 1/Oh inkjet printability index criterion + DOD numerical simulation.

Felix Hertz (Sweden 1929-) KTH Royal Institute Technology Stockholm; 1965 invention continuous inkjet + Hertz Reichl 1976 patent Sweden + foundation continuous inkjet industry. Eredita: Eggers-Villermaux 2008 Rep Prog Phys 71:036601 'Physics of liquid jets' review classic 79 pagine + Lefebvre 'Atomization and Sprays' 2nd ed 2017 CRC Press 462 pagine + Bayvel-Orzechowski 'Liquid Atomization' 1993 Taylor Francis 462 pagine.

Italia ricerca atomizzazione + inkjet + spray: Politecnico Milano DEIB + DENG + LCM 7500 + Carlo Cercignani Boltzmann legacy + Renzo Piazza CFD + Alessio Frangi MEMS inkjet + Marco Mauri spray atomizer; Politecnico Torino DENERG + DIATI 1859 5000 + Sara Spinelli inkjet printing electronics + Fabrizio Pirri printed electronics; Federico II Napoli DICMaPI + DII + DIETI 5000 + Vincenzo Pucci spray combustion + Maria Chiara Mosca atomizer; Bologna DICAM + DEI + DIN 4000 + Mauro Magnani atomization + Stefano Cagnoni MEMS; Padova DII + DEI + ICEA 3000 + CISAS + Marco Pertile spray; Pisa DICI + DESTeC 2500 + Andrea Gandelli atomization; Politecnico Bari DEI 1990 2500; Trento DICAM + DISI 1962; Genova DICCA + DIBRIS 2000 + IIT Italian Institute Technology Morego 1700 + Marco Bandini smart materials + Athanassia Athanassiou inkjet bio-inks; Sapienza Roma DICEA + DIMA + DIET 4000 + Antonio Liaci spray combustion.

Italia industria inkjet printing + 3D printing: Sicpa Italia Ivrea Torino 600 security inks + ink formulation + UV-curable inkjet; Sun Chemical Italia Bareggio Milano + DIC Group 800 printing inks + UV LED inkjet; Ferrania Imaging Cairo Montenotte SV 200 + photo printing legacy; Bizerba Italia + Imaje + Markem-Imaje Italia 200 industrial coding marking; Domino Italia Milano + Brother Industries 100; Telecom Print Italia 100.

Italia industria automotive injection + spray: Magneti Marelli Cofima Powertrain Bologna + Bari + Crevalcore BO 1919 39000 + GDi gasoline direct injection + diesel common rail + injectors + Marelli SpA + CK Holdings 2018; Bosch Italia Milano 6000 + Bosch Diesel Systems + Common Rail Bari + GDi injectors; Continental Automotive Italia 800; Denso Italia 200; Avio Aero Rivalta Torino + Pomigliano 5000 GE Aviation + jet engine atomizer + spray combustor; Leonardo Aerostructures Pomigliano + Cameri 51000 + helicopter engines + Eurofighter typhoon; FCA Stellantis Italia 50000 + Mirafiori Torino + Pomigliano + Cassino Modena Maserati Ferrari + GDi injection.

Italia industria pharmaceutical spray + MDI nebulizers: Chiesi Farmaceutici Parma 1935 7000 + MDI inhalers HFA propellants asthma COPD respiratory + Foster + Trimbow + Atimos; Recordati Milano 1926 4500 + drugs cardiovascular + nebulizers; Zambon Bresso Milano 1906 2500 + respiratory drugs; Angelini Pharma Roma 1919 5000; Menarini Firenze 1886 17000 + leading Italian pharma; Bracco Diagnostica Milano 1927 3500 + contrast media spray imaging; Italfarmaco Milano 1938 3000; Dompe Farmaceutici Milano 1853 800.

Italia industria spray cosmetic + personal care: L'Oreal Italia Milano 1500; Procter&Gamble Italia Roma 1100; Unilever Italia Roma 1300 Algida + Knorr + Dove + Axe; Henkel Italia Milano 800; Beiersdorf Italia Milano 700 + Nivea + Eucerin spray.

Italia industria food spray drying: Granarolo Bologna 1957 2500 + milk powder spray drying; Lavazza Torino 1895 4000 + coffee instant spray drying; Illy Trieste 1933 1300; Barilla Parma 1877 8500 + pasta + sauces.

Formula numero Ohnesorge

Definizione: Oh = mu / sqrt(rho * sigma * L). Equivalente Oh = sqrt(We)/Re.

Z numero printability: Z = 1/Oh = sqrt(rho*sigma*L)/mu Fromm 1984 IBM Research criterion droplet ejection. Z>10 printable inkjet; Z=1-10 optimal DOD; Z<1 viscous limited.

Coefficienti tipici: acqua 25°C mu=1e-3 Pa*s, rho=1000, sigma=0.072 N/m; etanolo mu=1.1e-3, rho=789, sigma=0.022; glicerina mu=1.5, rho=1260, sigma=0.063; oli motore mu=0.1-1, rho=850, sigma=0.030; mercurio mu=1.5e-3, rho=13534, sigma=0.485.

Ohnesorge-Reynolds diagram: log-log plot Oh vs Re. 4 regimi atomizzazione: Rayleigh breakup Re basso + capillary instability cylindrical jet wavelength lambda_max=9.02*R; first wind-induced aerodynamic interaction air; second wind-induced intermediate Re + ligaments; atomization regime high Re + complete breakup spray cone.

Storia e contesto

Wolfgang von Ohnesorge (Berlin Germany 1901 - Stuttgart 1976) Universitat Gottingen PhD 1936 Ludwig Prandtl supervisor + Aerodynamische Versuchsanstalt AVA Gottingen 1925-1945 + Stuttgart MTU Aero Engines 1955-1976; 1936 PhD thesis 'Die Bildung von Tropfen an Dusen und die Auflosung flussiger Strahlen' ZAMM Zeitschrift Angewandte Mathematik und Mechanik 16:355-358 classic jet breakup analysis + 4 regimi atomizzazione + dimensionless number eponym Oh + Reynolds-Ohnesorge diagram log-log standard reference + Tropfenbildung an Dusen droplet formation; pioneer atomization theory + Ohnesorge regime map atomization.

Lord Rayleigh (John William Strutt 3rd Baron Essex UK 1842-1919) Cambridge Trinity College Cavendish Professor 1879-1884 + Royal Society President 1905-1908 + Nobel Prize Physics 1904 (argon discovery con Ramsay); 1879 paper Proc London Math Soc 10:4 'On the instability of jets' classic Plateau-Rayleigh capillary instability + cylindrical jet breakup wavelength lambda_max=9.02*R + linear stability analysis perturbation modes; 1892 paper Phil Mag 34:177 'On the instability of cylindrical fluid surfaces' + 4 volumi 'Theory of Sound' 1877; pioneer Rayleigh-Plateau capillary instability + Rayleigh-Taylor instability + Rayleigh waves seismic + Rayleigh number eponym + Rayleigh scattering blue sky 1871.

Joseph Antoine Ferdinand Plateau (Brussels Belgium 1801-1883) Universite Etat Liege 1827 + Universite Etat Gand Ghent 1835 chair physics; 1873 textbook 'Statique experimentale et theorique des liquides soumis aux seules forces moleculaires' Gauthier-Villars Paris 2 volumi classic capillarity + Plateau border foam + Plateau laws minimal surface + capillary break-up principle minimum surface area + soap film + cylindrical jet break-up; cieco da 1843 dopo esperimenti ottica gazing direct sun + esperimenti tactile lavoratori.

Susumu Tomotika (Japan 1908-1989) Tokyo Imperial University Department of Applied Mathematics; 1935 paper Proc Roy Soc London A 150:322 'On the instability of a cylindrical thread of a viscous liquid surrounded by another viscous fluid' classic viscous Rayleigh-Plateau instability + viscous ratio modify wavelength + Tomotika analysis + extension Rayleigh-Plateau viscous fluid surrounding.

Jens Eggers (Wuppertal Germany 1962-) MIT 1995 + Universitat des Saarlandes Saarbrucken 1996-2003 + University Bristol UK 2003-; 1993 paper Phys Rev Lett 71:3458 'Universal pinching of 3D axisymmetric free-surface flow' classic self-similar pinch-off + finite-time singularity Newtonian + universal scaling + 1997 Rev Mod Phys 69:865 'Nonlinear dynamics and breakup of free-surface flows' classic review; Eggers-Villermaux 2008 Rep Prog Phys 71:036601 'Physics of liquid jets' classic 79 pagine.

John Eggers Fromm (USA IBM Research Yorktown Heights NY 20th century); 1984 paper IBM J Res Develop 28:322 'Numerical calculation of the fluid dynamics of drop-on-demand jets' Z = 1/Oh inkjet printability index criterion + DOD numerical simulation. Felix Hertz Sweden KTH Royal Institute Technology Stockholm 1965 invention continuous inkjet + Hertz Reichl 1976 patent. Eredita: Eggers-Villermaux 2008 Rep Prog Phys 71:036601 review classic 79 pagine + Lefebvre 'Atomization and Sprays' 2nd ed 2017 CRC Press 462 pagine + Bayvel-Orzechowski 'Liquid Atomization' 1993 Taylor Francis 462 pagine + Lin 'Breakup of Liquid Sheets and Jets' 2003 Cambridge 286 pagine; Wijshoff 2010 Phys Rep 491:77 'The dynamics of the piezo inkjet printhead operation' + Derby 2010 Annu Rev Mater Res 40:395 inkjet printing materials.

Italia ricerca atomizzazione + inkjet + spray combustion: Politecnico Milano DEIB + DENG + LCM 7500 + Carlo Cercignani Boltzmann legacy 1939-2010 + Renzo Piazza CFD spray + Alessio Frangi MEMS inkjet piezoelectric + Marco Mauri spray atomizer + Aldo Frezzotti boundary layer; Politecnico Torino DENERG + DIATI 1859 5000 + Sara Spinelli inkjet printing electronics + Fabrizio Pirri printed electronics + ChiLab nanofabrication + Aurelio Cricenti printed photovoltaics; Federico II Napoli DICMaPI + DII + DIETI 5000 + Vincenzo Pucci spray combustion + Maria Chiara Mosca atomizer; Bologna DICAM + DEI + DIN 4000 + Mauro Magnani atomization + Stefano Cagnoni MEMS inkjet; Padova DII + DEI + ICEA 3000 + CISAS + Marco Pertile spray + Stefano Lambri inkjet; Pisa DICI + DESTeC 2500 + Andrea Gandelli atomization + Walter Grassi heat transfer; Politecnico Bari DEI 2500; Trento DICAM 1962; Genova DICCA + DIBRIS 2000 + IIT Italian Institute Technology Morego Genova 1700 + Marco Bandini smart materials + Athanassia Athanassiou inkjet bio-inks 3D bioprinting + Pasquale Vena inkjet pharmaceuticals; Sapienza Roma DICEA + DIMA + DIET 4000 + Antonio Liaci spray combustion + Francesco Asdrubali printed electronics.

Italia industria inkjet printing + 3D printing: Sicpa Italia Ivrea Torino 600 security inks + ink formulation + UV-curable inkjet + Eurofighter banknotes inks; Sun Chemical Italia Bareggio MI + Latina + DIC Group 800 printing inks + UV LED inkjet + flexography + offset; Ferrania Imaging Cairo Montenotte SV 200 photo printing legacy + 3M acquisition; Bizerba Italia + Imaje + Markem-Imaje Italia 200 industrial coding marking inkjet + traceability; Domino Italia Milano + Brother Industries 100 CIJ DOD coding; EFI Electronics For Imaging Italia 100 commercial printing inkjet; Konica Minolta Italia 200 + Ricoh Italia 300 + Xerox Italia 200 office printing; 3D Systems Italia + Stratasys Italia 200 3D printing photopolymer Polyjet inkjet + ProJet MultiJet Modeling; Lattice 3D printing Italia 50.

Italia industria automotive injection GDi + diesel common rail: Marelli (CK Holdings 2018 ex Magneti Marelli Cofima Powertrain Bologna + Bari + Crevalcore BO 1919 39000 + GDi gasoline direct injection + diesel common rail + Marelli Powertrain Systems + Marelli Plastics + Marelli Suspension Systems + Marelli Lighting; Bosch Italia Milano + Stuttgart Germany 6000 + Bosch Diesel Systems + Common Rail factory Bari + GDi injectors + sensors; Continental Automotive Italia 800; Denso Italia 200; Stellantis Italy Mirafiori Torino + Pomigliano + Cassino + Modena Maserati Ferrari 50000 + GDi injection + V6 V8 + diesel MultiJet III; Ferrari SpA Maranello MO 1947 5500 + V8 V12 GDi + LaFerrari hybrid; Lamborghini Sant'Agata Bolognese 1963 2000 + Aventador Huracan GDi V12 V10; Pagani Modena 1992 200 + Huayra GDi V12; Maserati Modena 1914 1000 Stellantis.

Italia industria aerospatial spray combustion + jet engines: Avio Aero Rivalta Torino + Pomigliano + Brindisi 5000 GE Aviation + jet engine spray combustor + nozzle atomizer + GE9X GE90; Avio Colleferro Roma 5000 + Vega Vega-C launcher + Ariane 6 P120C solid rocket + Z40 + Z9; Leonardo Helicopters Cascina Costa Lonate Pozzolo VA 4500 + AW139 + AW169 + AW189 helicopters + AW609 tiltrotor + spray combustor; Leonardo Aerostructures Pomigliano + Cameri 51000 + helicopter engines + Eurofighter Typhoon; FCA Stellantis Italia 50000.

Italia industria pharmaceutical spray + MDI nebulizers: Chiesi Farmaceutici Parma 1935 7000 + MDI inhalers HFA propellants asthma COPD + Foster + Trimbow + Atimos + Air Liquide partnership Chiesi Air; Recordati Milano 1926 4500 + drugs cardiovascular + nebulizers + nasal sprays; Zambon Bresso MI 1906 2500 + respiratory drugs + asthma; Angelini Pharma Roma 1919 5000; Menarini Firenze 1886 17000 leading Italian pharma + leukemia drugs; Bracco Diagnostica Milano 1927 3500 + contrast media spray imaging X-ray MRI ultrasound; Italfarmaco Milano 1938 3000; Dompe Farmaceutici Milano 1853 800; Sigma-Tau Pomezia Roma 1957 + Recordati 2018 acquired.

Italia industria spray cosmetic + personal care + perfume: L'Oreal Italia Milano 1500; Procter&Gamble Italia Roma 1100; Unilever Italia Roma 1300 Algida Knorr Dove Axe; Henkel Italia Milano 800; Beiersdorf Italia Milano 700 Nivea Eucerin spray; Bulgari Roma 1884 8000 LVMH + perfume; Acqua di Parma 1916 + LVMH 200; Versace Profumi 200 EuroItalia + Capri Group 1978 Milano.

Italia industria food spray drying + coffee: Granarolo Bologna 1957 2500 + milk powder spray drying; Lavazza Torino 1895 4000 + coffee instant spray drying + capsules; Illy Trieste 1933 1300 coffee espresso instant; Barilla Parma 1877 8500 pasta sauces; Ferrero Alba CN 1946 38000 Nutella Kinder Tic Tac chocolate spray dry sugar coating; Parmigiano Reggiano Consortium; Galbani Lodi 1882 1500 + Lactalis France formaggi.

Tabella valori Ohnesorge

• Oh = mu/sqrt(rho*sigma*L): definizione
• Oh = sqrt(We)/Re: equivalente
• Z = 1/Oh: printability index Fromm 1984
• Oh10: clean ejection
• 0.1<Oh<1 optimal Z=1-10: DOD ideal
• 1<Oh<10 viscous limited: ligaments long
• Oh>10 highly viscous: no breakup
• Acqua 25°C Oh~0.012: nozzle 50 micron
• Etanolo Oh~0.025: 50 micron
• Glicerina Oh~150: viscous
• Mercurio Oh~6e-4: low viscosity high tension
• Diesel spray Oh~0.025: 200 micron
• Inkjet HP DOD 1979: thermal bubble
• Canon BJ 1981: bubble jet
• Epson MicroPiezo 1984: piezoelectric
• Xaar Cambridge UK 1990: industrial DOD
• Ohnesorge Germany 1936: PhD Gottingen Prandtl
• Lord Rayleigh 1879 jets: capillary instability
• Plateau Belgium 1873: minimum surface
• Tomotika Japan 1935: viscous extension
• Eggers 1993: pinch-off self-similar
• Fromm IBM 1984: Z printability
• Italia Marelli 39000: GDi diesel
• Italia Sicpa Ivrea 600: security inks
• Italia Chiesi Parma 7000: MDI inhalers
• Italia Avio Aero 5000: jet engines
• Italia IIT Genova 1700: inkjet bio-inks
• Italia Ferrari Maranello 5500: V8 V12 GDi
• Italia Lavazza Torino 4000: coffee spray

Esempi numerici dettagliati

Esempio 1 - Acqua nozzle 30 micron. mu=1e-3 Pa*s, rho=1000, sigma=0.072 N/m, L=30e-6 m. Oh = 1e-3/sqrt(1000*0.072*30e-6) = 6.8e-3. Z=147. Inkjet printable + clean ejection + Rayleigh-Plateau capillary breakup. Italia: Sicpa Ivrea 600 + Sun Chemical Bareggio.

Esempio 2 - Inchiostro inkjet ottimale. mu=3e-3 Pa*s, rho=1050, sigma=0.030 N/m, L=50e-6 m. Oh = 3e-3/sqrt(1050*0.030*50e-6) = 0.076. Z=13. Inkjet optimal DOD + UV-curable ink. Italia: Sun Chemical 800 + Sicpa security inks.

Esempio 3 - Glicerina viscosa. mu=1.5 Pa*s, rho=1260, sigma=0.063 N/m, L=1e-3 m. Oh = 1.5/sqrt(1260*0.063*1e-3) = 168. Z=6e-3. Highly viscous + no droplet + jet stable. Italia: laboratori Politecnico Milano + Sapienza.

Esempio 4 - Spray pharma atomizer. mu=5e-3 Pa*s, rho=1100, sigma=0.040 N/m, L=100e-6 m. Oh = 5e-3/sqrt(1100*0.040*100e-6) = 0.075. Z=13. Pharmaceutical optimal DOD spray. Italia: Chiesi Parma 7000 + Recordati + Bracco MDI nebulizers.

Esempio 5 - Diesel injection spray. mu=3e-3 Pa*s, rho=830, sigma=0.027 N/m, L=200e-6 m. Oh = 3e-3/sqrt(830*0.027*200e-6) = 0.044. Z=22. Atomization regime + spray cone. Italia: Marelli Bologna 39000 + Bosch Diesel Bari + Continental.

Limiti e considerazioni

1. Boundary conditions nozzle geometria: round circular vs slot vs pintle vs pressure-swirl modify atomizzazione + spray cone angle.
2. Newtonian assumption: shear-thinning ink polymer + Carreau-Yasuda model + viscoelastic Maxwell + DLP inks viscoelastic.
3. Compressibility: high-pressure injection 1500-2500 bar diesel common rail compressible cavitation in-nozzle.
4. Ambient gas pressure density: spray atomizer high-altitude jet engine + Weber gas number We_g = rho_g*v^2*L/sigma.
5. Surface tension temperature dependence: dσ/dT ~ -0.15 mN/m/K acqua + dT modify Marangoni Ma + thermal capillary.
6. Surfactant effects: surface-active agent CMC critical micelle concentration + Marangoni effects + Plateau-Rayleigh modify.
7. Multi-component evaporation: polymer ink + solvent evaporate + viscosity increase + cofee ring effect.
8. Electric field electrohydrodynamic EHD inkjet: Coulomb force + Taylor cone + electrospinning + electrospray.
9. Acoustic forcing piezoelectric DOD: pressure pulse waveform + 1-100 microsec + frequency 1-50 kHz.
10. Particle laden ink: nano-particle ink + sedimentation + agglomeration + nozzle clogging + 3D printing metal.

Errori comuni

Confondere Oh + We + Re: Oh = sqrt(We)/Re. We tensione superficiale; Re viscoso. Tutti correlati.

Z = 1/Oh printability: criterio Fromm 1984 IBM + 1<Z10 satellite drops + Z<1 viscous limited.

L lunghezza caratteristica: diametro nozzle vs jet vs droplet diameter. Convenzione + Ohnesorge originale nozzle.

Newtonian assumption fail: shear-thinning + viscoelastic ink + DLP inks polymer + Carreau-Yasuda + Maxwell viscoelastic.

Compressibility cavitation: high-pressure injection 1500-2500 bar diesel + cavitation in-nozzle modify atomizzazione + Weber/Reynolds insufficient.

Applicazioni pratiche

1. Inkjet printing 2D: Italia Sicpa Ivrea 600 security inks + Sun Chemical Bareggio 800 + Bizerba Imaje Markem 200 industrial coding + Domino Brother + EFI Konica Minolta Ricoh Xerox.
2. 3D printing photopolymer Polyjet inkjet: Italia 3D Systems Stratasys 200 + Lattice 50 + IIT Genova bio-inks 1700 + Politecnico Milano LCM Frangi MEMS.
3. Automotive injection GDi diesel common rail: Italia Marelli 39000 + Bosch Diesel Bari 6000 + Continental 800 + Denso 200 + Stellantis Mirafiori Pomigliano Cassino + Ferrari Lamborghini Maserati.
4. Aerospatial jet engine spray combustor: Italia Avio Aero Rivalta Pomigliano 5000 GE Aviation + Avio Colleferro Vega + Leonardo Helicopters Cascina Costa AW139 + Aerostructures.
5. Pharmaceutical MDI inhalers nebulizers: Italia Chiesi Parma 7000 Foster Trimbow + Recordati 4500 + Zambon 2500 + Angelini 5000 + Menarini 17000 + Bracco 3500 contrast media + Italfarmaco + Dompe.
6. Cosmetic perfume spray: Italia L'Oreal 1500 + P&G 1100 + Unilever 1300 + Henkel 800 + Beiersdorf Nivea + Bulgari LVMH 8000 + Acqua di Parma 200 + Versace EuroItalia.
7. Food spray drying milk coffee: Italia Granarolo Bologna 2500 + Lavazza Torino 4000 + Illy Trieste 1300 + Barilla Parma 8500 + Ferrero Alba 38000 + Galbani Lodi.
8. Agricultural pesticide sprayers: Italia Mantica + Cifo Bologna + Sipcam Pero MI + Bayer CropScience Italia.
9. Combustion turbine power plant: Italia Ansaldo Energia Genova 1853 4000 + ENI Versalis + Tecnimont Milano EPC + steam turbines spray atomizer.
10. Universita ricerca atomization: Politecnico Milano DEIB + DENG Frangi MEMS + Politecnico Torino DENERG Pirri + Federico II DICMaPI Pucci + Bologna DICAM + Padova DII + Pisa DICI + IIT Genova Athanassiou bio-inks + Sapienza DIMA.

Aggiornato a luglio 2026