RESEARCH ARTICLE

Characteristics of liquid sheets formed by splash plate nozzles

M. Ahmed Æ A. Amighi Æ N. Ashgriz ÆH. N. Tran

Received: 19 February 2007 / Revised: 8 August 2007 / Accepted: 8 August 2007 / Published online: 12 September 2007

� Springer-Verlag 2007

Abstract An experimental study was conducted to

identify the effect of viscosity on the characteristics of

liquid sheets formed by a splash plate nozzle. Various

mixtures of corn syrup and water are used to obtain vis-

cosities in the range 1–170 mPa.s. Four different splash

plates with nozzle diameters of 0.5, 0.75, 1, and 2 mm,

with a constant plate angle of 55� were tested. Liquid

sheets formed under various operating conditions were

directly visualized. The sheet atomization process for the

range of parameters studied here is governed by two dif-

ferent mechanisms: Rayleigh–Plateau (R–P) and Rayleigh–

Taylor (R–T) instabilities. R–P occurs at the rim and R–T

occurs on the thin sheet. The rim instability can be laminar

or turbulent, depending on the jet Reynolds number. The

R–T instability of the sheet is observed at the outer edges

of the radially spreading sheet, where the sheet is the

thinnest. It can also occur inside the sheet, due to formation

of holes and ruptures.

1 Introduction

Splash plate nozzles are very effective in producing a spray

from highly viscous liquids even when they contain solid

particles. These nozzles are used in kraft pulp recovery

boilers to spray black liquor, a by-product of wood pulp

production, which contains up to 90% solids. A splash

plate nozzle typically consists of an oval shaped flat plate

attached at an angle to the end of a pipe. Black liquor flows

through the pipe and impinges on the splash plate. The

forces developed in the region of impact drive the liquid

out radially forming a liquid sheet, which eventually breaks

and forms droplets. Therefore, droplet size and velocity

distribution are intimately dependent on the characteristics

of the liquid sheet formed by the nozzle.

In addition to splash plate nozzles, there are several

other methods of generating spreading liquid sheets, the

main ones being impinging jets, flat fan nozzles and swirl

nozzles. Dombrowski and Fraser (1954) provided an

overview of various methods for generating liquid sheets.

Among these, sheets formed by two impinging jets are the

most studied, mainly because of their application in rocket

engines. Dombrowski and Hooper (1963) considered the

factors that influence the breakup of a sheet formed by two

impinging jets. They used the flow Weber number and the

Reynolds number to characterize their results. They

reported the formation of hydrodynamic waves (or impact

waves) on the surface of the sheet when the Weber number

of each jet exceeds a critical value (We = qVd2sin2a/r,

where q is the fluid density, V the mean jet velocity, d the

jet diameter, a the half-angle of impingement, and r is the

surface tension). The formation of hydrodynamic waves is

independent of the Reynolds number. They also noted that

the droplet sizes formed are dependent on the mechanism

of disintegration of the liquid sheet.

M. Ahmed � A. Amighi � N. Ashgriz (&)

Department of Mechanical and Industrial Engineering,

University of Toronto, 5 King’s College Road,

Toronto, ON, Canada M5S 3G8

e-mail: ashgriz@mie.utoronto.ca

Present Address:M. Ahmed

Mechanical Engineering Department,

Assiut University, Assiut 71516, Egypt

H. N. Tran

Department of Chemical Engineering & Applied Chemistry,

University of Toronto, 200 College Street,

Toronto, ON, Canada M5S 3E5

123

Exp Fluids (2008) 44:125–136

DOI 10.1007/s00348-007-0381-4

More recently, Lai et al. (2005) studied the effect of

fluid properties on the liquid sheet formed by two

impinging-jets. They classified the sheets into three types:

closed rim, open rim, and fully developed sheets. The

closed rim is subdivided into closed rim with ligament

disintegration, closed rim cascade, closed rim with periodic

drop, closed rim without drop shedding, and closed rim

with drop shedding. The open rim is subdivided into open

rim with thread shedding, open rim with film perforation,

open rim with open shedding, open rim with both drop

shedding and perforation pattern, and fully developed or

perforation type.

Li and Ashgriz (2006) identified two breakup modes for

sheets formed by two impinging jets: capillary and Kelvin-

Helmholtz instability dominated modes. In the former

mode, capillary instability dominates the droplet formation

from the rim of the sheet, while in the latter one the

interaction between the sheet and the ambient air causes

the sheet to break up. These two modes are further subdi-

vided into five more regimes based on the characteristics of

the sheet. The boundaries between each regime are found

to be related to the jet Reynolds number.

There are numerous other reported studies on the causes

of sheet instability and sheet break down. These studies

have shown that the principal cause of sheet breakup is the

interaction of the sheet with the surrounding atmosphere,

whereby rapidly growing waves are induced on the sheet

surface. Sheet breakup occurs when the amplitude of these

waves reach a critical value. Characteristics of these waves

have been investigated for invicid liquid sheets of uniform

thickness using linear instability analysis (Squire 1953;

Hagerty and Shea 1955). The results obtained for invicid

planar sheets have been extended by Dombrowski and

Johns (1963) to include the effect of liquid viscosity, and

the variation of sheet thickness. They found that viscous

forces retard the growth of perturbations. The breakup of a

sheet is governed by the fastest growing disturbance.

Finally, Shen and Poulikakos (1998) and Choo and Kang

(2001) studied sheet thickness distribution and Choo and

Kang (2003) and Li and Ashgriz (2006) studied velocity

distribution within the sheet. They concluded that the sheet

thickness is independent of the jet velocity but dependent

on the jet angle, jet diameter and liquid viscosity.

Compared to two impinging jets, studies on the splash

plate nozzles are scarce. Choo and Kang (2003, 2001) and

Lai et al. (2005) compared spreading liquid sheets formed

by the impact of a jet on an inclined solid surface with a

spreading liquid sheet due to two impinging jets. It was

found that the velocity required to form a sheet is much less

in the case of two impinging jets than in the case of a jet

impacting on an inclined solid surface. This difference is

attributed to the frictional effects due to the solid surface,

which increases with increasing liquid viscosity.

Spielbauer and Aidun (1992a, b, 1994a, b) studied the

atomization of glycerin-water mixtures using a large splash

plate nozzle. They identified two different sheet breakup

mechanisms for a high viscosity liquid sheet formed by a

splash plate nozzle: a wave and a sheet perforation

breakup. They indicated that the dominant mechanism is

the formation and growth of perforations. There are also

several theoretical studies on the splash plate nozzles,

however, none of them provide any general understanding

of the sheet formation and its breakup (Mckibben and

Aidun 1994; Fard et al. 2003; Foust et al. 2002).

The objective of the present experimental study is to

provide a detailed account of various types of liquid sheets

formed by splash plate nozzles. The effect of various

parameters, including fluid viscosity (l), nozzle diameter

(d) and liquid jet velocity (v) on the break up of the liquid

sheet formed by a splash plate nozzle is studied and

presented here.

2 Experimental setup and procedures

A simple splash plate nozzle design is used in our exper-

iments. A cross-sectional view of this nozzle is shown in

Fig. 1. This nozzle is constructed by machining an alumi-

num rod of length A, such that a pipe with an inner

diameter of d is formed (this is the nozzle diameter). The

rod is then machined through its cross section at 55� angle

to clear the pipe opening. For the nozzle with a pipe

diameter of d = 1 mm, the dimensions shown in Fig. 1 are

A = 40.3 mm, B = 21 mm, C = 8.23 mm, H = 5.04 mm,

and L = 15.25 mm. All other nozzles are geometrically

scaled by the pipe diameter. Four different nozzle diame-

ters of d = 0.5, 0.75, 1, and 2 mm were used. The splash

plate angle was kept constant at 55�.

Solutions of corn syrup with water were used, instead of

Glycerin, to obtain a wide range of viscosities, ranging

from 1.0 mPa.s to 170 mPa.s. Viscosities were measured

using a RheometricsARES-RFS3 mechanical spectrometer

using 50 mm cone and plate geometry. By knowing the

density of the corn syrup at room temperature

(q = 1450 kg/m3), densities of the solutions of corn syrup

and water were calculated. In addition, the surface tension

of the solution was measured using Kruss K100MK2

Tensiometer. A high-speed video camera was used for

imaging the liquid sheets produced by splash plate nozzles.

The flow velocities in the splash plate nozzle ranged from

5 m/s to about 44 m/s. A rotameter was used to measure

the flow rate of the liquid from the pressurized tank to the

splash plate nozzle. Two rotameters were used to measure

flows in the range of 0.1–1.8 l/min, and 2.0–7.0 l/min,

respectively. For solutions of water and corn syrup, a

graded cylinder and stop watch were used to measure the

126 Exp Fluids (2008) 44:125–136

123

flow rate by collecting certain volume of solution over a

known time.

The physical properties of corn syrup solutions used are

shown in Table 1. Variation of measured shear viscosity

with shear rate for solutions of different mixing ratios of

1:1, 1:2, and 1:3 of water/corn syrup is shown in Fig. 2.

Based on this figure, a Newtonian behavior is observed for

these solutions at shear rates greater than one. However,

increasing the mixing ratio results in an increase in the

value of shear rate required for the solution to behave as a

Newtonian fluid.

The overall experimental set up is shown in Fig. 3. The

splash plate nozzle is connected to a pressure tank through

a flow meter. A constant pressure supply of compressed

nitrogen is used via a pressure regulator, to pressurize a

solution of corn syrup and water inside the tank. The sheet

formation is visually studied using a high speed video

camera.

3 Results and discussions

The sheet development process at a viscosity of 14 mPa.s

is shown in Fig. 4. At a low flow velocity of 2.3 m/s, a

liquid jet is formed at the tip of the splash plate nozzle,

which later breaks up due to capillary instability (see

Fig. 4a). Increasing the flow velocity to 12.2 m/s, results in

the formation of a closed rim sheet. The sheet appears

smooth with no surface perturbations. The Reynolds

number based on the jet diameter for this case is Re =

1230. Here, the Reynolds number is defined as Re = Vd/m,

where V is the jet velocity, d the orifice or jet diameter, and

m the liquid kinematic viscosity. The liquid jet exiting the

nozzle is laminar; resulting in the formation of a smooth

laminar liquid sheet. A close-up image of this sheet is

shown in Fig. 5. The rim of the sheet is characterized by a

relatively thicker fluid layer. The shape of the liquid sheet

is determined based on the competition between the

momentum and the surface tension forces at the sheet

boundaries. Several features of this type of liquid sheet can

be identified by inspecting Fig. 5. The rim of the sheet goes

through an asymmetric capillary instability, as shown in

Fig. 5b. Bremonde and Villermaux (2006) showed that this

instability is governed by Rayleigh–Plateau (Rayleigh

1879; Plateau 1873) type instability. A theoretical analysis

of this type of instability is provided by Savtchenko and

Ashgriz (2005) and its experimental study is provided by

Li and Ashgriz (2006).

As soon as a drop is pinched off from the rim, the

thickness of the rim suddenly drops to that of the sheet

thickness. Therefore, the surface tension forces, which are

inversely proportional to the sheet curvature at its rim, or

Fig. 1 (a) Cross section of the splash plate nozzles used in the

experiments. (b) A close up image of the splash plate nozzle

Table 1 Properties of various mixtures of corn syrup and water

Mixing ratio by volume

water: corn syrup

1:1 1:2 1:3

Viscosity, mPa.s 14 80 170

Density, kg/m3 1225 1300 1335

Surface tension, N/m 0.06695 0.06603 0.06775

Shear Rate (1/s)

Sh

ear

Vis

cosi

ty, m

Pa.

s

10-1 100 101 102 103100

101

102

103

Cornsyrup solution (1:2)

Test Temperature 25°C

Cornsyrup solution (1:1)

Cornsyrup solution (1:3)

Fig. 2 Shear viscosity versus shear rate for different solution mixing

ratio

Exp Fluids (2008) 44:125–136 127

123

the sheet thickness, suddenly increase. This pushed the

sheet inward, reducing the width of the sheet. Regions I

and II in Fig. 5a show the regions before and after pinch-

off of the rim drops. The change in the curvature of the rim

of the sheet is clear at the boundary between regions I and

II and as amplified in Fig. 5c. If the rim does not become

unstable for longer distances, the sheet may stretch and

breakup before the rim goes unstable. This results in open

rim sheets. (This is shown later on Fig. 6d).

Once a droplet is pinched off of the rim, it may still be

attached to the sheet. As the sheet retreats at a rapid rate, it

cannot pull the relatively large droplet with itself. There-

fore a thin liquid ligament forms which keeps the sheet and

the droplet attached. Later, this ligament becomes unstable

and breaks off into several small drops and releases the

main droplet. This type of structure was referred to as fluid

‘‘fishbones’’ by Bush and Hasha (2004). Figure 5d shows

the formation and instability of ligaments attached to the

pinched droplet. We will refer to this type of sheet insta-

bility as the ‘‘laminar rim instability.’’

As the flow velocity is further increased, the sheet

becomes larger and wider. Eventually, the sheet opens,

forming an open rim sheet as shown in Fig. 4c for

V = 16.5 m/s. In this case, Re = 1670 and consequently,

the sheet is still laminar and smooth. At relatively low flow

velocities, the outer rims of the open rim sheet are thick.

This results in the formation of large droplets at the edges

of the sheet. The central part of the sheet, which is very

thin, results in relatively small droplets. Therefore, a

bimodal drop size distribution results from this type of

sheet breakup. Laminar rim instability is still observed at

the outer edges of this case. However, the central part goes

through a film rupture and perforation instability that will

be discussed later.

Fig. 3 Schematic of the

experimental setup

(a) jet breakup instability

V= 2.3 m/s Re= 240

(d) fully perforation

V = 37 m/s Re= 3790

(c) open rim with edge ligaments

Re=1670 V = 16.5 m/s

(b) laminar rim

V =12.2 m/s Re=1230

Fig. 4 Sheet development

process formed by splash plate

nozzle with 1.0 mm diameter

and liquid viscosity of

14.0 mPa.s

128 Exp Fluids (2008) 44:125–136

123

When the flow velocity is further increased to 37 m/s,

the radial spreading momentum governs the flow until the

sheet is broken into ligaments and droplets. Figure 4d

shows surface perforations that are formed on the sheet due

to both sheet thinning and turbulent fluctuations.

Figure 6 shows the sheet development process for a

higher viscosity of 170 mPa.s. At the low flow velocity of

1.1 m/s, a liquid jet is first formed at the tip of the splash

plate, which later breaks due to Rayleigh jet instability (see

Fig. 6a). An increase in flow velocity to 11.7 m/s, results in

a closed rim cascade sheet. A closed rim cascade sheet is

due to repetitive impingement of the two attached jets

forming the edges of the closed rim sheet. Each impinge-

ment forms another sheet in the plane perpendicular to the

impingement plane as shown in Fig. 7. Bush and Hasha

(2004) referred to this as a liquid chain. The mean sheet

velocity reduces along the cascade until the sheet finally

breaks into ligaments and drops. The sheets and ligaments

in Fig. 7 are not symmetrical due to imperfections in the

nozzle. This asymmetry results in the rotation of the sheet

chain. These ligaments will later breakup into droplets as

shown in Fig. 7a.

Figure 8 shows the growth of small perturbation on the

rim of the sheet. The rim of the sheet acts as a curved liquid

jet. According to Rayleigh (1879), any perturbation with a

wavelength greater than the perimeter of the jet will grow

and make the jet unstable (i.e., R–P instability). Figure 8

shows that even for a closed rim cascade sheet, the rim can

become unstable and generate droplets if R–P instability

conditions are satisfied.

Liquid sheets are formed only above a critical flow

velocity for ‘‘sheeting.’’ Even then, the sheet will close

forming a jet at its tip, if the velocity is not high enough.

Sheet breakup (as opposed to jet breakup) occurs after

certain critical velocity. The transition from jet breakup to

sheet breakup for all the cases tested here is plotted in

Fig. 9 in terms of flow velocity versus liquid viscosity. The

transition flow velocity increases with increasing viscosity.

(a)

I

II

(b)

(c)

(d)

Fig. 5 Rayleigh–Plateau edge instability process for a closed-rim

liquid sheet. l = 14 mPa.s, d = 1.0 mm, V = 12.2 m/s and Re = 1140

(a) jet breakup without drop shedding V=1.1m/s

V = 16.6 m/s Re= 10

(d) open rim with thread

V = 29 m/s Re= 230

(c) closed rim

Re=130

(b) closed rim cascade

V = 11.7 m/s Re= 90

Fig. 6 Sheet development

process formed by splash plate

nozzle with 1.0 mm diameter

and liquid viscosity of

l = 170 mPa.s

Exp Fluids (2008) 44:125–136 129

123

For 1 mm nozzle, the transition velocity is about 10 m/s

for l = 1 mPa.s, while it is about 20 m/s for l = 170

mPa.s. In addition, the transition Reynolds number

decreases with increasing viscosity (not shown here). At

l = 1 mPa.s, the transition Reynolds number is about 104,

whereas at l = 170 mPa.s, it is about 150. Further increase

of the flow velocity to 16.6 m/s results in the formation of a

closed rim smooth sheet, as shown in Fig. 6c. This figure

should be compared with Fig. 4c, which has almost the

same velocity. It is clear that the liquid viscosity dampens

the radial spreading of the sheet. The sheet in Fig. 6c has

spread much less than that in Fig. 4c.

When the flow velocity is further increased to 29 m/s

(Fig. 6d), an open rim sheet is formed. The rim of the

sheet is relatively thick, which delays its breakup. For the

case shown in Fig. 6d, the rim of the sheet does not show a

significant instability growth by the time the sheet is sep-

arated from it. The sheet itself becomes thin and finally

breaks up into small droplets. The observed process of

sheet breakup is quite different than the traditional sheet

instability. In the traditional sheet instability theory, based

on Dombrowski and Fraser (1954), the sheet goes through

sinuous or varicose instability, forming liquid ligaments.

The ligaments later go through Rayliegh–Plateau instabil-

ity to form droplets. The sheet instability observed in

Figs. 4c and 6d are quite different than that described by

Dombrowski and Fraser. There are no ligaments, and the

sheet breaks by perforation process. A close-up picture of

Fig. 6d is shown in Fig. 10. This figure shows large surface

waves on the sheet. These waves, however, do not form

liquid ligaments. The sheet is very thin, and it is easily

disturbed by the surrounding air. As these waves grow,

they stretch the sheet and make it thinner, until it ruptures.

As soon as the sheet ruptures, it retreats backwards at a

Fig. 7 Cascade Sheet formation and breakup

Fig. 8 Time evolution of

growth of perturbations on the

rim of a slowly rotating sheet

130 Exp Fluids (2008) 44:125–136

123

rapid rate. This results in a Rayleigh–Taylor (Rayleigh

1883; Taylor 1950) type of instabilities. Figure 10b shows

a close-up image of the surface waves or ruffles.

Figure 10c and d show the rupture points of the sheet and

the formation of droplets. Rapid retreat of the sheet forms

small cusps on the sheet periphery which eventually

breakup forming small droplets. This type of sheet

breakup, which is characteristics of a high viscosity liquid,

is referred to as R–T breakup of the sheet.

Figure 11 shows the effect of liquid viscosity on the

sheet breakup for three different flow velocities of 15, 21,

and 30 m/s and for a splash-plate with 1 mm diameter

nozzle. Fluid viscosity is changed by changing the water to

corn syrup ratio. At a low jet velocity of 15 m/s and a low

viscosity of 1 mPa.s (water only), the liquid sheet formed

is non-smooth but coherent. The sheet has an open rim and

a bay leaf like shape and it breaks into small droplets at its

edges. At a higher viscosity of 14 mPa.s, the sheet becomes

smooth and it is still open rim. Increasing the viscosity to

80 mPa.s, results in the contraction of the sheet angle and

extension of the breakup point. The sheet becomes thicker

and, consequently, it takes a longer time for it to breakup.

Increasing viscosity to 170 mPa.s, results in a closed rim

bay leaf without any atomization. Generally, increasing the

viscosity dampens the surface waves and reduces the

lateral spreading of the fluid.

The second and the third columns in Fig. 11 show liquid

sheets formed from the same nozzle but at higher jet

velocities of 21 m/s and 30 m/s, respectively. The high

velocity increases the lateral spreading of the sheet. For

low viscosity liquids, sheets become unstable more rapidly

than for high viscosity cases. However, for high viscosity

liquids, i.e., l = 170 mPa.s, sheets become smoother,

longer and narrower.

Effects of velocity and viscosity on the sheet are some-

what different. An increase in jet velocity, forces the fluid to

exit the splash plate through a wider angle, whereas an

increase in viscosity limits spreading of the fluid. Therefore,

fluid velocity sets the initial spreading angle, whereas the

fluid viscosity limits the extension of fluid spreading. This

may become evident by considering the first row in Fig. 11,

which represents water sheets at three different velocities of

15, 21, and 30 m/s, from right to left, respectively. It is

noted that the spreading angle substantially increases as the

Viscosity, mPa.s

Flo

w v

elo

city

, m/s

0 50 100 150 2000

5

10

15

20

25

Splash plate nozzle diameter = 1.0 mm

Jet breakup

Sheet breakup

Transition from jet to sheet

Fig. 9 Transition from jet to sheet formation

Fig. 10 Rayleigh–Taylor

instability of the liquid sheet.

l = 170 mPa.s, d = 1.0 mm,

V = 29 m/s and Re = 230

Exp Fluids (2008) 44:125–136 131

123

velocity increases. This is also evident for all other vis-

cosities in Fig. 11. Considering the columns of Fig. 11

(constant velocity) shows that the initial spreading angle

decreases and the width of the sheet reduces as the viscosity

increases. After a certain viscosity, there is no rim breakup

and droplets are formed only after the sheet is broken.

Effect of flow velocity on the sheet break-up is shown in

Fig. 12 for two different nozzle diameters of 1 and 2 mm.

For pure water (1 mPa.s) issuing from the 1 mm nozzle

(Fig. 12b), sheet break-up changes from turbulent edge

instability to perforated sheet type as the flow velocity is

increased from 21 m/s to 30 m/s. By increasing the flow

velocity, the flow Reynolds number increases from 21000

to more than 30000. Therefore, the jet issuing from the

nozzle becomes more turbulent and consequently the liquid

sheet becomes more unstable, resulting in a higher perfo-

ration density. A similar trend is found for the 2 mm

nozzle, where the transition from turbulent edge instability

to sheet perforation occurs at approximately the same

Reynolds number as in the 1 mm diameter case. However,

at a higher viscosity of 80 mPa.s, increasing the flow

velocity from 17 m/s to 40 m/s does not change the

V=15 m/s V=21 m/s V=30 m/s

(f) µ = 14.0 mPa.s (e) µ = 14.0 mPa.s (d) µ = 14.0 mPa.s

(i) µ = 80.0 mPa.s (h) µ = 80.0 mPa.s (g) µ = 80.0 mPa.s

(j) µ = 170.0 mPa.s (k) µ = 170.0 mPa.s (l) µ = 80.0 mPa.s

(a) µ = 1.0 mPa.s (b) µ = 1.0 mPa.s (c) µ = 1.0 mPa.s

Fig. 11 Effect of the viscosity

on break-up regime at different

values of flow velocityusing a

splash-plate nozzle with 1.0 mm

diameter

132 Exp Fluids (2008) 44:125–136

123

breakup mechanism. In this case, the flow Reynolds

number is very small, i.e., Reynolds number varying

between 270 and 660, respectively.

The effect of splash plate nozzle diameter on the break-

up regime at the flow velocity of 18 m/s is shown in

Fig. 13. In this case, the Reynolds number is changed by

changing the jet diameter. As the Reynolds number is

increased from 9000 (d = 0.5 mm) to 37000 (d = 2 mm),

the breakup regime changes from ‘‘turbulent edge insta-

bility’’ to ‘‘sheet perforation regime’’. Furthermore, it was

found that the sheet angle increases due to increasing the

nozzle diameter.

The sheet breakup regimes can be classified according to

the fluid viscosity and the initial flow Reynolds number:

(1) Rayleigh–Taylor (R–T) sheet instability. This sheet

breakup process is exemplified in Fig. 10 for l = 170

mPa.s and Re = 230. It is a reminiscence of high viscosity

liquid sheets flowing at low Reynolds numbers. The

breakup process includes: sheet (film) thinning; sheet

rupture; and R–T instability of retreating ruptured sheet.

V = 6 m/s V=10.6 m/s V = 21 m/s V= 32 m/s (a) Nozzle diameter of 2mm (µ = 1 mPa.s)

V= 12.5 m/s V= 21 m/s V=30 m/s V= 40 m/s (b) Nozzle diameter of 1 mm (µ = 1 mPa.s)

V= 17 m/s V=25 m/s V= 33 m/s V= 40.5 m/s (c) Nozzle diameter of 1 mm (µ = 80 mPa.s)

Fig. 12 Effect of the splash-

plate nozzle velocity on break-

up regime at different values

splash-plate nozzle diameters

(1 and 2 mm)

Re = 9000 Re = 13000 Re = 18000 Re = 37000 d = 0.5 mm d = 0.75 mm d = 1.0 mm d = 2.0 mm

Fig. 13 Effect of the splash-

plate nozzle diameter on break-

up regime at flow velocity of

18 m/s and viscosity of

1.0 mPa.s

Exp Fluids (2008) 44:125–136 133

123

Figure 14 clearly shows the spray waves which are pro-

duced by R–T instability. Because of the continuous

extension of the sheet followed by ruptures and retraction,

the spray formed comes as waves of small droplets.

Figure 14a shows three waves of drops forming by this

type of atomization. Figure 14b shows the formation of

droplets due to R–T instability. Clearly, there are no liga-

ments due to Kelvin-Helmholtz instability. When the sheet

becomes turbulent, then the R–T instability becomes

turbulent as well. It is very difficult to identify the type of

instability in turbulent cases.

(2) Rayleigh–Plateau (R–P) edge (rim) instability. The

rim of the sheet behaves as an attached curved liquid jet,

and it goes through a R–P capillary instability. This was

shown in Fig. 5 for l = 14 mPa.s and Re = 1230. For

lower viscosity fluids, the side edges of the sheet become

unstable. At this viscosity, the sheet has a closed rim for

Reynolds numbers in the range of 700–1400. At the

Reynolds number of 1400, an open rim sheet is observed.

However, in both closed and open rim cases and for

l = 14 mPa.s, the break up occurs due to a laminar rim

R–P instability.

As the flow Reynolds number is increased by increasing

flow velocity or the orifice diameter, but keeping liquid

viscosity at l = 14 mPa.s, local disturbances in the sheet

become more dominant until ruptures are formed near the

nozzle exit and breakup occurs due to sheet perforation.

Figure 14 shows a high viscosity perforated sheet at

Reynolds number of 2300. Perforations may occur by

surface wave disturbances, non-wetting particles or air

bubbles (Spielbauer and Aidun 1994a). Once a small per-

foration appears in the sheet, it may rapidly grow forming

thicker rims. Rims of adjacent holes may coalesce to pro-

duce ligaments of irregular shapes which finally break-up

into droplets of varying sizes.

When the liquid viscosity is further reduced to l = 1

mPa.s—resulting in even higher flow Reynolds numbers,

perturbed sheets with unstable edges are observed.

Figure 15 shows a typical image for Re = 14800. This

breakup is referred to as ‘‘turbulent edge instability’’ since

(a)

(b)

Fig. 14 Rayleigh–Taylor

instability of a sheet.

(a) R–T instability at the edges

of the sheet, showing the spray

wave formation (l = 80 mPa.s,

d = 1 mm, V = 25 m/s).

(b) R–T instability inside the

sheet forming a rupture and at

the edges (l = 14 mPa.s,

d = 2 mm, V = 8.6 m/s)

134 Exp Fluids (2008) 44:125–136

123

droplets are formed mainly from the turbulent edges of the

sheet. Perturbations in the sheet are attributed to the

turbulent flow inside the splash plate nozzle.

Similar to Fig. 14a low viscosity sheet perforation is

formed at a higher Reynolds number of 30000. In this case

the breakup regime is similar to the high viscosity sheet

perforation regime. However, in this regime, the spreading

angle is close to 180� due to low viscosities effect, and the

Reynolds number is much higher compared to the previous

regime. This leads to highly local disturbances in the sheet

that become more dominant until holes are formed near the

nozzle exit.

Various sheet breakup regimes are plotted in Fig. 16

in Ohnesorge-Reynolds plane, where Ohnesorge number

is defined as Oh ¼ l=ffiffiffiffiffiffiffiffi

qdrp

: It is found that the transi-

tion of breakup mechanism from one state to another is

independent of the flow Weber number and mainly

dependent on the Reynolds number. The Oh-Re plane is

divided into three main regions. Below line I, sheet does

not form and the breakup process is by R–P jet insta-

bility. Above line I, a clear liquid sheet is formed and the

breakup process is mainly by the breakup of the sheet.

The empirical relation for the transition from jet to sheet

breakup is found to be:

Oh ¼ 75

Re1:1

Line II represents the boundary between sheet breakup

without (below the line) and with perforations. The transition

from laminar to turbulent sheets are observed at Re & 3000.

Fig. 15 Turbulent edge

instability, l = 1.0 mPa.s,

d = 2.0 mm, V = 7.4 m/s, and

Re = 14800

Re

hO

101 102 103 104 10510-3

10-2

10-1

100

101

Jet breakup

Oh = 75 Re -1.1

Turbulent SheetLaminar Sheet

Sheet Perforation

Stable rim with R-Tsheet instability

Unstable rim with turbulentR-T sheet instability

Unstable rim with laminarR-Tsheet instability

A

B

C

I

II

Fig. 16 Jet and sheet breakup regimes behavior with Reynolds

number and Ohnesorge number

Exp Fluids (2008) 44:125–136 135

123

The region between lines I and II can be divided into three

zones. Sheets produced in zone ‘‘A’’ (Re \ 800) have rela-

tively stable rim. The Reynolds numbers are low, therefore,

viscous effects dominate. Open rim sheets are typically

broken at their open edges by R–T instability.

As the Reynolds number is increased, the rims become

unstable rapidly. Therefore, in zone ‘‘B’’ (800 £ Re £3000), the sheet breakup process includes both a laminar

R–P instability at the rims and R–T instability on open

edges of the sheet. Similar breakup process is observed in

zone ‘‘C’’, except that the whole flow is turbulent. There-

fore, the breakup process in this zone is identified as

turbulent R–P rim instability combined with turbulent R–T

sheet instability. The data points in this zone are within

7000 £ Re £ 18000. For Re ‡ 18000 the rim cannot be

distinguished, and the breakup process is mainly turbulent

sheet breakup.

4 Conclusions

An experimental investigation is carried out to identify the

breakup mechanisms of liquid sheets formed by a simple

splash plate nozzle. Effects of fluid viscosity, flow velocity

and nozzle diameters on the breakup process are consid-

ered. At low flow Reynolds numbers a liquid sheet cannot

sustain itself, and it closes to form a liquid jet at its tip. The

onset of the sheet breakup, versus jet breakup, is correlated

by Oh = 75/Re1.1.

The breakup of the sheet formed by a splash plate nozzle

is composed of breakup of the rim and the breakup of the

thin sheet. Rim being the side edges of the sheet, which is

usually thicker than the rest of the sheet and its flow,

resembles that of a curved liquid jet.

The sheet atomization process for the range of parame-

ters studies here is governed by two different mechanisms:

(1) Rayleigh–Plateau and Rayleigh–Taylor instabilities.

R–P occurs at the rim and R–T occurs on the thin sheet. The

rim instability can be laminar or turbulent, depending on the

jet Reynolds number. The R–T instability of the sheet is

always observed at the outer edges of the radially spreading

sheet, where the sheet is the thinnest. It can also occur inside

the sheet, due to formation of holes and ruptures.

Acknowledgments This work is jointly supported by the NSERC

and the research consortium on ‘‘ Increasing Energy and Chemical

Recovery Efficiency in the Kraft Process’’ at the university of

Toronto.

References

Bremonde N, Villermaux E (2006) Atomization by jet impact. J Fluid

Mech 549:273–306

Bush J, Hasha A (2004) On the collision of laminar jets: fluid chains

and fishbones. J Fluid Mech 511:285–310

Choo Y, Kang B (2003) A study on the velocity characteristics of the

liquid elements produced by two impinging jets. Exp Fluids

34:655–661

Choo Y, Kang B (2001) Parametric study on impinging-jet liquid

sheet thickness distribution using an interferometric method. Exp

Fluids 31:56–62

Dombrowski N, Fraser R (1954) A photographic investigation into the

disintegration of liquid sheets. Philos Trans R Soc Lond A

247:101–130

Dombrowski N, Hooper PC (1963) A study of spray formed by

impinging jets in laminar and turbulent flow. J Fluid Mech

18:392–440

Dombrowski N, Johns W (1963) The aerodynamic instability and

disintegration of viscous liquid sheets. Chem Eng Sci 18:203–

213

Fard M, Ashgriz N, Mostaghimi J, Leveseque D, Morrison S (2003)

Film thickness and velocity distribution in a splash plate

atomizer: comparison between simulations and experiments’’.

In: Proceeding of the 9th international conference on liquid

atomization and sprays systems, Sorrento, Italy

Foust D, Hamman K, Detering B (2002) Numerical simulation of

black liquor spray characteristics’’.In: Proceedings of

IMECE’02-ASME international mechanical engineering con-

gress & exposition, New Orleans, Louisiana, USA

Hagerty W, Shea J (1955) A study of the stability of plane fluid

sheets. J Appl Mech 22:289–289

Lai WH, Huang TH, Jiang TL, Huang W (2005) Effect of fluid

properties on the characteristics of impinging-jet sprays. Atom-

ization Sprays 15:457–468

Li R, Ashgriz N (2006) Characteristics of liquid sheets formed by two

impinging jets. Phys Fluids 18:087104

Mckibben J, Aidun C (1994) Computational analysis of flows. TAPPI

J 77(5):143–148

Plateau J (1873) Stattique experimentale et theoretique des liquids

soumie aux seules forces moleicularies. Chanthier Vallars, Paris

Rayleigh L (1879) On the instability of jets. Proc Lond Math Soc 4:10

Rayleigh L (1883) Investigation of the character of equilibrium of an

incompressible heavy fluid of variable density. Proc R Soc Lond

14:170–177

Savtchenko S, Ashgriz N (2005) Temporal instability of a capillary jet

with a source of mass. Phys Fluids 17:112102

Shen Y, Poulikakos D (1998) Thickness variation of liquid sheet

formed by two impinging jets using holographic interferometry.

ASME J Fluid Eng 120:482–487

Spielbauer T, Aidun C (1992a) Mechanisms of liquid sheet breakup

and the resulting drop size distributions, Part 1: types of spray

nozzles and mechanisms of sheet disintegration. TAPPI J

73(2):36–142

Spielbauer T, Aidun C (1992b) Mechanisms of liquid sheet breakup

and the resulting drop size distributions, Part 2: strand breakup

and experimental observations. TAPPI J 73(3):195–200

Spielbauer T, Aidun C (1994a) The cause and effects of perforations

in a liquid sheet from a splash-plate nozzle. Atomization Sprays

4:405–436

Spielbauer T, Aidun C (1994b) The wave-thinning and breakup of

liquid sheets. J Fluid Eng 116:728–734

Squire H (1953) Investigation of the instability of a moving liquid

film. Br J Appl Phys 4:167–169

Taylor GI (1950) The instability of liquid surfaces when accelerated

in the direction perpendicular to their plane. Proc R Soc Lond A

201:192–196

136 Exp Fluids (2008) 44:125–136

123