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The conversion of bulk liquid into a dispersion of small droplets ranging in size from submicron to several hundred microns (micrometers) in diameter is of importance in many industrial processes such as spray combustion, spray drying, evaporative cooling, spray coating, and drop spraying; and has many other applications in medicine, meteorology, and printing. Numerous spray devices have been developed which are generally designated as atomizers, applicators, sprayers, or nozzles.

A spray is generally considered as a system of droplets immersed in a gaseous continuous phase. Sprays may be produced in various ways. Most practical devices achieve atomization by creating a high velocity between the liquid and the surrounding gas (usually air). All forms of pressure nozzles accomplish this by discharging the liquid at high velocity into quiescent or relatively slow-moving air. Rotary atomizers employ a similar principle, the liquid being ejected at high velocity from the rim of a rotating cup or disc. An alternative method of achieving a high relative velocity between liquid and air is to expose slow-moving liquid into a high-velocity stream of air. Devices based on this approach are usually termed air-assist, airblast or, more generally, twin-fluid atomizers.

Most practical atomizers are of the pressure, rotary, or twin-fluid type. However, many other forms of atomizers have been developed that are useful in special applications. These include “electrostatic” devices in which the driving force for atomization is intense electrical pressure, and ‘ultrasonic’ types in which the liquid to be atomized is fed through or over a transducer which vibrates at ultrasonic frequencies to produce the short wavelengths required for the production of small droplets. Both electrical and ultrasonic atomizers are capable of achieving fine atomization, but the low liquid flow rates normally associated with these devices have tended to curtail their range of practical application.

Basic Processes

There are several basic processes associated with all methods of atomization, such as the conversion of bulk liquid into a jet or sheet and the growth of disturbances which ultimately lead to disintegration of the jet or sheet into ligaments and then drops. These processes determine the shape, structure, and penetration of the resulting spray as well as its detailed characteristics of droplet velocity and drop size distribution. All these characteristics are strongly affected by atomizer size and geometry, the physical properties of the liquid, and the properties of the gaseous medium into which the liquid stream is discharged. The liquid properties of importance in atomization are surface tension, viscosity, and density. Basically, atomization occurs as a result of the competition between the stabilizing influences of surface tension and viscosity and the disruptive actions of various internal and external forces. In most cases, turbulence in the liquid, cavitation in the nozzle, and aerodynamic interaction with the surrounding gas (referred to henceforth as air), all contribute to atomization. In all cases, atomization occurs when the magnitude of the disruptive force just exceeds the consolidating surface tension force. Many of the larger drops produced in the initial breakup of the liquid jet or sheet are unstable and undergo further disintegration into smaller droplets. Thus, the drop size characteristics of a spray are governed not only by the drop sizes produced in primary atomization but also by the extent to which the largest of these drops are further disintegrated during secondary atomization.

Breakup of liquid jets

Rayleigh (1878) was among the first to study theoretically the breakup of liquid jets. He considered the simple situation of a laminar jet issuing from a circular orifice and postulated the growth of small disturbances that produce breakup when the fastest growing disturbance attains a wavelength λopt of 4.51 d, where d is the initial jet diameter. After breakup, the cylinder of length 4.51 d becomes a spherical drop, so that


and hence D, the drop diameter, is obtained as


Figure 1a shows an idealization of Rayleigh breakup for a liquid jet. Observations of actual jets show good agreement with this theory, but also reveal the presence of “satellite” drops which are created as the individual cylinders neck down and separate. Thus, the end result is a pattern of large drops with much smaller single drops between them.

Rayleigh’s analysis takes into account surface tension and inertial forces but neglected viscosity and the effect of the surrounding air. Weber (1931) later extended Rayleigh’s work to include the effect of air resistance on the disintegration of jets into drops. He found that air friction shortens the optimum wavelength for drop formation. For zero relative velocity he showed that the value of λopt is 4.44d, which is close to the value of 4.51d predicted by Rayleigh for this case. For a relative velcocity of 15 m/s, Weber showed that λopt becomes 2.8d and the drop diameter becomes 1.6d. Thus the effect of relative velocity between the liquid jet and the surrounding air is to reduce the optimum wavelength for jet breakup which results in a smaller drop size.

Weber also examined the effect of liquid viscosity on jet disintegration. He showed that the effect of an increase in viscosity is to increase the optimum wavelength for jet breakup. We have




This group is sometimes referred to as the Z number, the stability number, or the Ohnesorge number (Oh).

At higher jet velocities, breakup is caused by waviness of the jet (Figure 1b). This mode of drop formation is associated with a reduction in the influence of surface tension and increased effectiveness of aerodynamic forces. The term “sinuous” is often used to describe the jet in this regime. At even higher velocities, the atomization process is enhanced by the effect of relative motion between the surface of the jet and the surrounding air. This aerodynamic interaction causes irregularities in the previously smooth liquid surface. These irregularities or ruffles in the jet surface become amplified and eventually detach themselves from the liquid surface, as illustrated in Figure 1c. Ligaments are formed which subsequently disintegrate into drops. As the jet velocity increases, the diameter of the ligaments decrease. When they collapse, smaller droplets are formed, in accordance with Rayleigh’s theory.

Figure 1. 

Thus the various modes of atomization may be classified into four groups according to the relative velocity between the jet and the surrounding air, as follows:

  1. At low velocities, the growth of axisymmetric oscillations on the jet surface cause the jet to disintegrate into drops of fairly uniform size. This is Rayleigh mechanism of breakup. Drop diameters are roughly twice the initial jet diameter. Drop sizes are increased by increases in liquid viscosity and are reduced by increases in jet velocity.

  2. At higher velocities, breakup is caused by oscillations of the jet as a whole with respect to the jet axis. The jet has a twisted or sinuous appearance. This mode occurs over only a fairly narrow range of velocities.

  3. Droplets are produced by the unstable growth of small waves on the jet surface caused by interaction between the jet and the surrounding air. These waves become detached from the jet surface to form ligaments which disintegrate into drops. Mean drop diameters are much smaller than the initial jet diameter.

  4. Atomization. At very high relative velocities atomization is complete within a short distance from the discharge orifice. A wide range of drop sizes is produced, the mean drop diameter being considerably less than the initial jet diameter.

Another factor influencing jet breakup is the turbulence of the jet as it emerges from the nozzle. When the liquid particles flow in streams parallel to the main flow direction, the flow is described as laminar. Laminar flow is promoted by low flow velocity, high liquid viscosity and the absence of any flow disturbances. With laminar flow, the velocity profile varies across the jet radius in a parabolic manner, rising from zero at the outer surface to a maximum at the jet axis. If a laminar jet is injected into quiescent or slow-moving air, there is no appreciable velocity difference between the outer surface of the jet and the surrounding air. Consequently the necessary conditions for atomization by air friction do not exist. Eventually, surface irregularities develop that cause the jet to disintegrate into relatively large drops.

If the liquid particles do not follow the flow streamlines but cross each other at various velocities in a random manner, the flow is described as turbulent. Turbulence is promoted by high flow velocities, low liquid viscosity, surface roughness, and cavitation. If the flow emerging from the atomizer is fully turbulent, the strong radial velocity components quickly disrupt the jet surface, thereby promoting air friction and rapid disintegration of the jet. It is of interest to note that when the issuing jet is fully turbulent, air friction is not essential for breakup. Even when injected into a vacuum, the jet will disintegrate solely under the influence of its own turbulence.

Breakup of liquid sheets

Many atomizers do not form jets of liquid, but rather form flat or conical sheets. Flat sheets can be produced by the impingement of two liquid streams or by feeding the liquid to the center of a rotating disc or cup. Conical sheets can be generated by imparting a tangential velocity component to the flow as it issues from the discharge orifice.

The mechanisms of sheet integration are broadly the same as those responsible for jet breakup, as discussed above. If the liquid sheet is flowing at high velocity, the turbulence forces generated within the liquid may be strong enough to cause the sheet to disintegrate into groups without any aid or intervention from the surrounding air. However, the principal cause of sheet breakup stems from interaction of the sheet with the surrounding air, whereby rapidly growing waves are superimposed on the sheet. Disintegration occurs when the wave amplitude reaches a critical value and fragments of sheet are torn off. Surface tension forces cause these fragments to contract into irregular ligaments which then collapse into droplets according to the Rayleigh mechanism. The dependence of the drop sizes produced in this mode of atomization on air and liquid properties can be expressed as


where δ is the sheet thickness and We, the Weber number, is U2AρAδ/σ.

Drop Size Distribution

Owing to the random and chaotic nature of the atomization process, the threads and ligaments formed by the various mechanisms of jet and sheet disintegration vary widely in diameter, and their subsequent breakup yields a correspondingly wide range of drop sizes. Most practical atomizers produce droplets in the size range from a few microns up to several hundred microns. A simple method of illustrating the distribution of drop sizes in a spray is to plot a histogram in which each ordinate represents the number of droplets whose dimensions fall between the limits D − ΔD/2 and D + ΔD/2. As ΔD is made smaller, the histogram assumes the form of a frequency distribution curve, provided it is based on sufficiently large samples.

Because the graphical representation of drop size distribution is laborious, many attempts have been made to replace it with mathematical expressions that provide a satisfactory fit to the drop size data. All of these distribution parameters, which include normal, lognormal, and upper limit distributions, have drawbacks of one kind or another, and no single parameter has yet been found which has clear advantages over the others. At present the most widely used expression for drop size distribution is one proposed by Rosin and Rammler (1933). It may be expressed in the form


where Q is the fraction of the total spray volume contained in drops of diameter less than D, and X and q are constants. This expression allows the drop size distribution to be described in terms of the two parameters X and q. For most sprays the value of q lies between 1.5 and 4. The higher the value of q, the more narrow is the distribution of drop sizes in the spray.

For most engineering purposes the distribution of drop sizes in a spray may be described satisfactorily in terms of two parameters (as in the Rosin-Rammler expression, for example), one of which is a representative diameter and the other a measure of the range of drop sizes. There are many possible choices of representative diameter, of which the most widely used is the mass median diameter (MMD) or volume mean diameter (VMD). These terms denote the drop diameter such that 50 percent of the total mass (or volume) of the spray is in drops of smaller diameter.

In many calculations of mass transfer it is convenient to work in terms of mean diameters instead of the complete drop size distribution. The most common of these is the Sauter Mean Diameter (SMD) which is the diameter of the droplet whose surface to volume ratio is the same as that of the entire spray.

In summary, it is important to recognize that no single parameter can completely define a drop size distribution, two sprays are not similar just because they have the same VMD or SMD. However, if a Rosin-Rammler distribution is assumed, the distribution of drop sizes in a spray may be expressed by two parameters, a representative or mean diameter and a measure of drop size distribution.


The following discussion is confined to atomizers of the pressure, rotary, and twin-fluid types, as shown schematically in Figure 2. Information on other spray devices, such as electrostatic and ultrasonic atomizers is contained in Lefebvre (1989).


When a liquid is discharged under pressure through a small orifice, pressure energy is converted into kinetic energy. If the pressure drop across the discharge orifice is sufficiently high, the issuing liquid jet or sheet will disintegrate into droplets. Combustion applications for plain-orifice atomizers, as shown in Figure 2a, include diesel, rocket and turbojet engines.

The narrow spray cone angles of about 10° produced by discharging the liquid through a simple circular orifice are disadvantageous for many spraying applications. Much wider cone angles of between 30° to 150° can be achieved with pressure-swirl nozzles in which a swirling motion is imparted to the liquid so that as it emerges from the discharge orifice it spreads radially outward to form a hollow conical spray. The simplest form of hollow-cone atomizer is the so-called simplex atomizer, as illustrated in Figure 2b.

A drawback to all types of pressure nozzles is that doubling the liquid flow rate requires a fourfold increase in injection pressure. Due to practical limits on injection pressures, this seriously restricts the range of liquid flow rates that any given atomizer can handle. This basic drawback has led to the development of various “wide-range” atomizers which are capable of providing good atomization over ratios of maximum to minimum flow rate in excess of 20 without having to resort to impractical levels of injection pressure. The most common form of wide-range atomizer is the dual-orifice nozzle, shown schematically in Figure 2c, which has been widely used on many types of aircraft and industrial gas turbines. Essentially, a dual-orifice comprises two simplex nozzles that are fitted concentrically one inside the other. When the liquid flow rate is low it all flows through the inner, primary nozzle, and atomization quality is high because the small flow passages dictate a high injection pressure. As the liquid flow rate is increased, an injection pressure is eventually reached at which the pressurizing valve opens and admits liquid to the outer, secondary nozzle. This nozzle has large flow passages which allow high flow rates to be achieved without resorting to excessively high injection pressures.


Rotary atomizers utilize centrifugal energy to achieve the high relative velocity between air and liquid that is needed for good atomization. A rotating surface is employed which may take the form of a flat disc, vaned disc, cup, bell, or slotted wheel. A simple form of rotary atomizer, comprising a spinning disc with means for introducing liquid at its center, is shown in Figure 2d. The liquid flows radially outward across the disc and is discharged at high velocity from its periphery. Several mechanisms of atomization are observed with a rotating flat disc, depending on the liquid flow rate and the rotational speed of the disc. At low flow rates the liquid is discharged from the edge of the disc in the form of droplets of fairly uniform size. At higher flow rates, ligaments are formed along the entire periphery which subsequently disintegrate into droplets according to the Rayleigh mechanism. With further increase in flow rate the condition is eventually reached where the ligaments can no longer accommodate the flow of liquid, and a thin continuous sheet is formed that extends beyond the rim of the disc. This sheet eventually breaks down into ligaments and drops, but because the ligaments are formed from a ragged edge, the resulting spray is characterized by a wide range of drop sizes. Serrating the edge of the disc delays the transition from ligament formation to sheet formation.


Most twin-fluid atomizers employ the kinetic energy of a flowing airstream to shatter a liquid jet or sheet into ligaments and then drops. Atomizers of this type are usually called “airblast” or “air-assist”, the main difference between them being the amount of air employed and its flow velocity. Air-assist atomizers are characterized by the use of a relatively small quantity of high-velocity air. This air does not flow continuously but is used only as and when needed to supplement some other mode of atomization. Airblast atomizers on the other hand employ large quantities of atomizing air flowing continuously at relatively low velocities (20-120 m/s).

Airblast atomizers have many advantages over pressure atomizers in combustion applications. They require lower injection pressures and produce a finer spray. Moreover, because the atomization process ensures thorough mixing of fuel drops and air, the ensuring combustion process is characterized by low soot formation, low flame radiation, and clean combustion products.

In most airblast atomizers the liquid is first spread out on a “prefilming” surface to form a thin continuous sheet and then subjected to the atomizing action of high-velocity air, as shown in Figure 2e. Two separate airflows are provided to allow the atomizing air to impact on both sides of the liquid sheet. Swirling airflows are often used, not to improve atomization, but to deflect the droplets formed in atomization radially outward to create a conical spray.

With air-assist and airblast atomizers, high velocity air is used either to augment atomization or as the sole driving force for atomization. An alternative approach is to introduce low-velocity air directly into the bulk liquid at some point upstream of the nozzle discharge orifice, as illustrated in Figure 2f. The injected air forms bubbles which produce a two-phase bubbly flow at the nozzle exit. As the air bubbles flow through the discharge orifice they assist atomization by squeezing the liquid into thin shreds and ligaments. When the air bubbles emerge from the nozzle they “explode”, thereby shattering the liquid shreds and ligaments into small droplets.

Figure 2. 

Influence of Liquid and Air Properties on Atomization

The three liquid properties of relevance to atomization are density, surface tension, and viscosity. In practice, the significance of density for atomization performance is diminished by the fact that most liquids exhibit only minor differences in this property. Surface tension is important to atomization because it resists the formation of new surface area which is fundamental to the atomization process. Whenever atomization occurs under conditions where surface tension is important, the Weber Number is a dimensionless parameter for correlating drop size data. From a practical standpoint viscosity is an important liquid property. The main role of viscosity is to inhibit the development of instabilities in the liquid jet or sheet emerging from the nozzle, and generally to delay the onset of atomization. This delay causes atomization to occur further downstream from the nozzle where conditions are less conducive to the production of small drops. Another important practical consideration is that whereas the variations normally encountered in surface tension are only about three to one, the corresponding variations in viscosity could be as high as three orders of magnitude.

The most important air property influencing atomization is density. With air-assist airblast atomizers, an increase in air density improves atomization by increasing the Weber number. With pressure-swirl atomizers it is found that drop sizes increase with ambient air density up to a maximum value and then decline with any further increase in density.

Mean Drop Size

The physical processes involved in atomization are not yet sufficiently well understood for mean diameters to be expressed in terms of equations derived from first principles. In consequence, the majority of investigations into the drop size distributions produced in atomization have been empirical in nature and have resulted in empirical equations for mean drop size. The most authentic of these equations are those in which mean drop size (usually SMD, MMD, or VMD) is expressed in terms of dimensionless groups such as Reynolds number, Weber number, or Ohnesorge Number (Oh = We0.5/Re). Most of the mean drop size equations published before the 1970’s should be regarded as suspect due to deficiencies in the methods available for drop size measurements. Even equations based on accurate experimental data should only be used within the ranges of air properties, liquid properties, and atomizer operating conditions employed in their derivation.

The equations for mean drop size (SMD) presented below are considered as being among the best available in the literature. More detailed information on drop size equations for all types of atomizers may be found in Lefebvre (1989).

Pressure atomizers

Due to the formidable problems involved in making drop size measurements in the dense sprays produced by plain-orifice nozzles, few equations for mean drop size have been published. According to Elkotb (1982)


For pressure-swirl nozzles, mean drop sizes are usually correlated using empirical equations of the form


A typical example, which has an advantage over most other equations in that it is dimensionally correct, is the following:


Rotary atomizers

For this type of atomizer, any equation for mean drop size should take into account the effects of variations in disc or cup diameter and rotational speed, in addition to liquid properties and lquid flow rate.

For atomization by direct drop formation, Tanasawa et al. (1978) obtained a good correlation between their experimental data and the following expression for mean drop size


For atomization by ligament formation, these same workers propose the following equation


An interesting feature of this equation is that it predicts the mean droplet size to increase slightly with increase in liquid viscosity.

Twin-fluid atomizers

The mean drop sizes produced by twin-fluid atomizers are usually correlated in terms of the Weber and Ohnesorge numbers and the air/liquid mass ratio (ALR), as illustrated below


where A, B, and c are constants whose values depend on atomizer design and must be determined experimentally. Lc is a characteristic dimension of the atomizer. For prefilming types of airblast atomizer we have [El-Shanawany and Lefebvre (1980)]


where Dh is the hydraulic mean diameter of the atomizer air duct at its exit plane, and Dp is the prefilmer diameter.


Elkotb, M. M. (1982) Fuel Atomization for Spray Modelling, Progress in Energy and Combustion Science, 8, 61-91. DOI: 10.1016/0360-1285(82)90009-0

El-Shanawany, M. S. M. R. and Lefebvre, A. H. (1980) Airblast Atomization: The Effect of Linear Scale on Mean Drop Size, J. Energy, 4, 184-189.

Lefebvre, A. H. (1989) Atomization and Sprays, Hemisphere Publishing Corporation, New York.

Rayleigh, Lord. (1878) On the Instability of Jets, Proc. London Math. Soc., 10, 4-13.

Rosin, P. and Rammler, E. (1933) The Laws Governing the Fineness of Powdered Coal, J. Inst. Fuel, 7, 29-36.

Tanasawa, Y., Miyasaka, Y. and Umehara, M. (1978) Effect of Shape of Rotating Discs and Cups on Liquid Atomization, Proceedings of First International Conference on Liquid Atomization and Spray Systems, Tokyo, 165-172.

Weber, C. (1931) Disintegration of Liquid Jets, Z. Angew, Math. Mech. , 11, (2): 136-159.


ALR air/liquid ratio by mass

D drop diameter, m

d initial jet diameter, m

MMD mass median diameter or disc diameter, m

m flow rate, kg/s

N rotational speed, rps

ΔPL pressure differential across nozzle, Pa

Oh Ohnesorge number

Re Reynolds number

SMD Sauter mean diameter, m

u velocity, m/s

VMD volume median diameter, m

We Weber number

δ sheet thickness, m

λ wavelength, m

η dynamic viscosity, kg/ms

ν kinematic viscosity, m2/s

ρ density, kg/m3

σ surface tension, kg/s2


A air

L liquid


  1. Elkotb, M. M. (1982) Fuel Atomization for Spray Modelling, Progress in Energy and Combustion Science, 8, 61-91. DOI: 10.1016/0360-1285(82)90009-0
  2. El-Shanawany, M. S. M. R. and Lefebvre, A. H. (1980) Airblast Atomization: The Effect of Linear Scale on Mean Drop Size, J. Energy, 4, 184-189.
  3. Lefebvre, A. H. (1989) Atomization and Sprays, Hemisphere Publishing Corporation, New York.
  4. Rayleigh, Lord. (1878) On the Instability of Jets, Proc. London Math. Soc., 10, 4-13. DOI: 10.1112/plms/s1-10.1.4
  5. Rosin, P. and Rammler, E. (1933) The Laws Governing the Fineness of Powdered Coal, J. Inst. Fuel, 7, 29-36.
  6. Tanasawa, Y., Miyasaka, Y. and Umehara, M. (1978) Effect of Shape of Rotating Discs and Cups on Liquid Atomization, Proceedings of First International Conference on Liquid Atomization and Spray Systems, Tokyo, 165-172.
  7. Weber, C. (1931) Disintegration of Liquid Jets, Z. Angew, Math. Mech. , 11, (2): 136-159. DOI: 10.1002/zamm.19310110207
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