16 to the applicator roller 5 at the impingement line A and the tangent 19 of the jet 2.2 at the intersection of the impingement line A. The jet exit angle γ lies between the tangent 16 to the applicator roll 5 at the impingement line A and the center line 17 of the jet 2.2 in the outlet gap B of the nozzle 1.2.

In embodiment shown in FIG. 5, the jet exit angle γ is 35°, for example, and the jet impingement angle β is 58°, for example, so that the ratio β/γ=1.7. Due to the angular orientation of the jet 2.2, caused by the modulation of the angle φ, the resulting impulse force acts in the direction of travel of the roll on impact. In addition to increasing the impulse force, this can prevent the treatment medium, in particular the starch, from splashing back.

The jet outlet angle γ can be adjusted via the angular position φ of nozzle 1.2. The angle of nozzle 1.2 can be adjusted manually or by motor. The jet impingement angle β can be determined using a camera and digital image processing, for example. This data can then be used to automatically adjust the jet exit angle γ.

The ratio of the height adjustment/length adjustment distances (H/D) characterizes the difference between a jet applicator with free jet nozzle and a curtain applicator. While the ratio is very large in the curtain applicator and normally approaches ∞—as the point at which the curtain hits the roll is vertically below the exit point from the nozzle—, it is relatively small in the jet applicator and is preferably below 3.

Typical values for common operating points and commercially available starches are between 1 and 2.

Consequently, the method according to the invention can be designed in such a way that a jet curvature is determined over a path length by a jet exit angle γ between an exiting jet 2.1, 2.2 at the exit gap B of the free jet nozzle 1.1, 1.2 and the tangent 16 on the at least one application roller 4, 5 to the impingement line A and a jet impingement angle β between the tangent 19 of a jet 2.1, 2.2 impinging on the applicator roll 4, 5 and the tangent 16 on the applicator roll 4, 5 at the impingement line A.

The ratio of the jet impingement angle β to the jet exit angle γ from the nozzle 1.1, 1.2 can be selected in the range between β/γ=1 and 6, preferably between β/γ=1 and 3, in order to adapt the intensity of the jet impulse at the impingement line A to specific volume flows of the treatment medium. The jet impingement angle β can be set as a function of the web speed, viscosity/solids content, volume flow of the treatment medium. The jet impingement angle β can be selected in the range between 10° and 90°, preferably between 10° and 60°, and particularly preferably between 20° and 40°. The jet exit angle γ from the nozzle 1.1, 1.2 can be selected in the range between 10° and 90°, preferably between 10° and 45°, and particularly preferably between 15° and 35°. The angle a can be selected in the range between 0° and 90°, preferably between 15° and 45°.

The application medium can be starch, a sizing agent or a coating color.

The distance H from the outlet gap B of the nozzle 1.1, 1.2 to the substrate, in particular to the applicator roll 4, 5, and the jet outlet angle γ can be selected in such a way that the effective height H is between 10 mm and 300 mm, preferably between 10 mm and 150 mm, and particularly preferably between 25 mm and 100 mm.

A device 3.1, 3.2 for boundary layer air removal can be arranged upstream of the impingement line A of the jet 2.1, 2.2 on the substrate, in particular the applicator roll 4, 5, with a distance L of 1 to 100 mm, preferably 10 to 30 mm. The paper or board web speed can be between 250 m/min and 2000 m/min, preferably between 600 m/min and 1800 m/min. The outlet gap B of the nozzle 1.1, 1.2 can be 100-500 μm. The weight of the treatment medium can be in the range between 0.2-15 g/m²per side of the paper or cardboard web. Starch with a solids content of between 6% and 35%, preferably between 15% and 35%, and particularly preferably between 10% and 25%, and a viscosity of between 20 mPa*s and 200 mPa*s can be selected as the treatment medium.

The temperatures of the starch can be between 50° C. and 110° C., preferably between 60° C. and 100° C. The temperature of a treatment medium, in particular a coating color or pigment color, can be 25-45° C. The paper or board web can be coated in an upward or downward direction.

In the case of direct applying, the running substrate can be the surface of a paper, paperboard or other fibrous web and, in the case of indirect applying, the surface of a transfer element that transfers the treatment medium to the surface of the fibrous web in a treatment nip. The above remarks on indirect application by means of an applicator roll 4, 5 thus apply in the same way to direct application of treatment medium to the fibrous web. The applying of treatment medium can be carried out on one or both sides.

The device according to the invention for applying at least one liquid or pasty treatment medium by means of a free-jet applicator to a moving substrate is designed such that the substrate is the surface of a paper, paperboard or other fibrous web in the case of direct application and the surface of a transfer element, in particular an applicator roll 4, 5, in the case of indirect application, which transfers the application medium to the surface of the fibrous web, in particular in a treatment nip N. The free jet applicator has at least one free jet nozzle 1.1, 1.2 with an outlet gap B for emitting a medium jet 2.1, 2.2, which applies the medium jet 2.1, 2.2 to the surface of the substrate like a film and achieves a desired width (in the transverse direction of the machine) of an application layer at an impingement position 12. A device for adjusting the intensity of the jet impulse of the medium jet in the impingement position 12 is arranged, wherein the device is designed as a positioning system for locational and angular shifts 11, 13, 18 of the free jet nozzle 1.1, 1.2 relative to the substrate, wherein a reference direction for describing the instantaneous spatial and angular position of the free jet nozzle 1.1, 1.2 relative to the impingement position 12 is given by the gravitational field.

In order to set a selectable jet curvature on a section length of the medium jet 2.1, 2.2, the positioning system for positional and angular shifts or displacements of the free jet nozzle can be designed for a vertical and/or longitudinal adjustment of the free jet nozzle 1.1, 1.2 in direction 14 of the machine running direction relative to the substrate in a gravity-oriented reference system.

The gravity-oriented reference system can be designed with systems of spatial Cartesian coordinates X, Y, Z, of which one origin for the angular displacement φ can be located in a mouth of the outlet gap B of the free jet nozzle 1.1, 1.2 and another origin for the positional displacement in the impingement position 12 and the impingement line A on the surface of the substrate. The respective X-axis can be directed in such a way that a right-hand system or left-hand system is provided and the perpendicular line is determined by the gravity field-related local perpendicular direction. The free-jet nozzle 1.1, 1.2 can be positioned at an angle φ to the local perpendicular direction in relation to the gravity field, preferably in the range from 30° to 70°. Due to the positioning of the free jet nozzle 1.1. 1.2, the impulse force of the jet 2.1, 2.2 in the impingement position 12 can be selected to be greater, depending on the coating parameters, than an impulse force on the rear side of the jet surface due to a dynamic pressure caused by a boundary layer air on the moving substrate.

FIG. 7 shows operating windows for different paper or board web speeds in conjunction with different volume flows for the positioning of the free jet nozzle 1.1, 1.2 according to FIG. 1 in conjunction with FIG. 5 with regard to the positioning of the outlet gap B in the system x′, y′ in order to adjust the jet curvature of the jet 2.1, 2.2 in relation to the impingement line A.

FIG. 1 shows spray water or water vapor nozzles 8.1, 8.2 and scrapers 7.1, 7.2 with associated collecting tray 6.1, 6.2 preferably provided for cleaning the applicator rolls 4, 5.

FIG. 2 shows a second embodiment of the invention. In contrast to FIG. 1, the air barrier scraper 3.1, 3.2 is attached directly to the nozzle 1.1, 1.2. The embodiment shown here is, for example, with a DST scraper for lifting the scraper blade on and off. A uniform and sensitively adjustable contact pressure is advantageous here. However, other versions of the scraper are also conceivable.

FIG. 3 shows a third embodiment of the invention. In contrast to FIG. 1, a boundary layer air removal device 3.1, 3.2 is provided here instead of the air barrier scraper. This can be, for example, a boundary layer air suction device or a so-called air scraper.

FIG. 4 shows a further embodiment of the invention. In contrast to FIG. 1, the direction of paper travel is opposite here.

The physical processes in the impingement position 12 of the jet 2.1, 2.2 on the roll 4, 5 are explained in more detail with reference to FIG. 6 in combination with FIG. 5 and FIG. 1.

The movement of the substrate, in particular the roll 4, 5, creates a boundary layer air that runs into the jet 2.1, 2.2 from behind and causes a dynamic pressure there. The dynamic pressure can also be seen as the impulse force of the boundary layer air. This impulse force disrupts the coating process. The component S_⊥ of this impulse force presses on the back of the jet surface. This can cause the jet to lift off the roll 4, 5 so that the starch film detaches from the roller 4, 5 again. The air then penetrates between the roll surface and the treatment film and hinders the wetting of the roll 4, 5.

A stabilizing force acts against this, being the impulse force of the jet 2.1, 2.2. The component F_y″ of this force presses the jet 2.1, 2.2 onto the roll 4, 5 at the point of impact of the impingement line A and acts against the lifting of the starch film from the roll surface. The impulse force F_y″ acts perpendicular to the roll surface.

The jet impulse F and the component F_y″ can be calculated using the following equations, which are known from the publication Guyon, E., Hulin, J. P. and Petit, L.: Hydrodynamik, 1997, Braunschweig/Wiesbaden, p. 188:

F
=

ρ
f

⁢

U
f

2

⁢
h

(
1
)

F

y
″

=

F
⁢
sin
⁢
β

(
2
)

F_x″ Component of the impulse force F of jet 2.2 in x″ direction (FIG. 6), N

F_y″ Component of the impulse force F of the jet 2.2 perpendicular to the surface of the applicator roll 5 (FIG. 6), N

ρ_fDensity of the treatment medium, kg/m³

U_fVelocity of the jet 2.2 of the treatment medium in the impingement point of the impingement line A, m/s

h jet thickness at the point of impingement of the impingement line A on the applicator roll 5, μm

The jet thickness h (FIG. 6) at the point of impact of the impingement line A can be calculated from the law of conservation of mass and is the same:

h
=

U
fo

U
f

⁢

h
o

(
3
)

h_oJet thickness at the exit point from nozzle 1.2 (at the outlet gap), μm

U_foVelocity of the jet at the exit point from the nozzle 1.2, m/s

The jet velocity U_fat the point of impact:

U
f

=

U

fx

2

+

U

fy

2

(
4
)

U_fxand U_fyare the components of the jet velocity in the x and y directions at the point of impact.

The component U_fxof the jet velocity in the x-direction:

U

fx

=

U

fo

⁢

cos
⁡
(

90
⁢
°

-
φ

)

=

U

fo

⁢
sin
⁢
φ

(
5
)

φ Angle for the position of nozzle 1.2 according to FIG. 5

The component U_fyof the jet velocity in the y-direction at the point of impact:

U

fy

=

U

fo

2

⁢

sin
2

(

90
⁢
°

-
φ

)

+

2
⁢

gy
a

=

U

fo

2

⁢

cos
2

⁢
φ

+

2
⁢

gy
a

(
6
)

The coordinates x_aand y_aof the point of impact of the jet 2.2 on the applicator roller 5 as shown in FIG. 5 are determined by solving equations (7) and (8):

Equation for the contour of the roll surface:

y
=

r
2

-

(

x
-

x
o

)

2

+

y
o

(
7
)

Equation for the jet contour or for the trajectory parabola:

y
=

x
⁢

tan
⁡
(

90
⁢
°

-
φ

)

-

x
2

⁢
g

2
⁢

U

fo

2

⁢

cos
2

(

90
⁢
°

-
φ

)

=

x
⁢
cot
⁢
φ

-

x
2

⁢
g

2
⁢

U

fo

2

⁢

sin
2

⁢
φ

(
8
)

In equations (7) and (8), the coordinates of the point of impact of the jet 2.2 on the applicator roll x=x_aand y=y_amust be entered.

The absolute values for x_aand y_acorrespond to the effective height H and the horizontal distance D as shown in FIG. 5:

❘
"[LeftBracketingBar]"

x
a

❘
"[RightBracketingBar]"

=
D

❘
"[LeftBracketingBar]"

y
a

❘
"[RightBracketingBar]"

=
H

x_oand y_oCoordinates of the roller center point according to FIG. 1

r Radius of the applicator roller 4, 5.

The jet impingement angle β can be determined using the equations for the tangents 16, 19 for the contour of the roll surface and for the jet contour, which are derived from the differentiation of equations (7) and (8) according to x.

Equation for the tangent 19 of the jet contour:

y
=

(

tan
⁡
(

90
⁢
°

-
φ

)

-

x
a

⁢

g

U

fo

2

⁢

cos
2

(

90
⁢
°

-
φ

)

)

·

(

x
-

x
a

)

+

y
a

=

(

cot
⁢
φ

-

x
a

⁢

g

U

fo

2

⁢

sin
2

⁢
φ

)

·

(

x
-

x
a

)

+

y
a

(
9
)

Equation for the tangent 16 to the roll surface:

y
=

-

x
a

-

x
o

r
2

-

(

x
a

-

x
o

)

2

·

(

x
-

x
a

)

+

y
a

(
10
)

Angle β₁between the jet tangent 19 and the x-axis at the point of impact of the impingement line A:

tan
⁢

β
1

=

tan
⁡
(

90
⁢
°

-
φ

)

-

x
a

⁢

g

U

fo

2

⁢

cos
2

(

90
⁢
°

-
φ

)

=

cot
⁢

φ

-

x
a

⁢

g

U

fo

2

⁢

sin
2

⁢
φ

(
11
)

Angle β₂between the tangent 16 to the roll surface and the x-axis at the point of impact:

tan
⁢

β
2

=

-

x
a

-

x
o

r
2

-

(

x
a

-

x
o

)

2

(
12
)

If the angles β₁and β₂are known, the jet impingement angle β can be calculated:

β
=

β
1

-

β
2

(
13
)

The following formula can be used to calculate the component of the impulse force of the disturbing (troublesome) air flow S_⊥:

S
⊥

=

ρ
a

⁢

q
⁢

U
a

⁢

1
+

cos
⁢

β

sin
⁢

β

(
14
)

S_⊥ Component of the momentum force of the disturbing air flow perpendicular to the jet 2.2, N

ρ_aDensity of air, kg/m³

q specific volume flow of the disturbing air flow, m³/(m*s)

U_aAverage velocity of the disturbing air flow, m/s

This equation is known from the publication Eklund, D. E.: Influence of blade geometry and blade pressure on the appearance of coated surface. Tappi Journal, May (1984), pp. 66-70, equation (1).

The specific volume flow of the air in the boundary layer can be calculated according to Sakiadis, as described below.

Source: Sakiadis, B. .: Part II. The Boundary Layer on a Continuous Flat Surface. AlChE Journal, Vol. 7 (1961), no. 2, p. 221-225

Thickness of the boundary layer air δ (m):

δ
=

4
0.183

⁢

v
⁢

x
′′

U
s

(
15
)

Us Speed of the applicator roll, m/s

v kinematic viscosity of air, m²/s

The specific volume flow of the disturbing air flow q results from the integration of the velocity distribution u (y″) over the thickness of the air boundary layer y″ and can be calculated using equation (16):

q

U
s

=

δ
-

δ
2

+

1
2

⁢

δ
4

-

1
5

⁢

δ
5

(
16
)

x″ and y″ are the coordinates shown in FIG. 6.

At the point of impact of jet 2.2 on roll 5, x″=L.

The mean velocity of the disturbing air flow U_acan be calculated by integrating equation (25) in the publication Sakiadis, B.C. (1961):

U
a

U
s

=

∫

0

1

erfc
⁢

(

η
2

)

⁢

d
⁢
η

(
17
)

The greater the jet velocity, the greater the stabilizing component F_y″ of the impulse force of the jet 2.2. As the velocity of the roll 5 increases, the velocity of the disturbing air flow increases and thus also the disturbing component S_⊥.

To ensure that the interfering air is displaced from the coating zone, the force F_y″ should be greater than S_⊥. On the other hand, the ratio F_y″/S_⊥ must not be too high so that the jet does not bounce off the roll surface. For a good coating, the ratio F_y″/S_⊥ must be within an optimum range. This range must be redetermined for each system configuration, as adhesion forces are also effective in addition to the jet impulse, which can assume different values depending on the roll coating or the type of thickness, for example. For this purpose, reference points must be determined for the lower and upper limits of the current configuration. If these are known, the valid ratio of F_y″/S_⊥ can be derived. The formulas then make it possible to predict the areas in which the system must be operated.

The meaning of the ratio F_y″/S_⊥ is explained in Table 1. The typical coating parameters for the production of CM are given here as an example. In setting no. 1, CM is produced with 160 g/m²at a speed of 800 m/min. Starch of 3.5 g/m²per side with a typical solids content of 12.5% is applied. The distance H is 33.8 mm, for example. The distance D is 30 mm, for example. With these settings, the ratio F_y″/S_⊥ is greater than 1, i.e. the force F_y″ is greater than S_⊥. The starch film remains stable in the point of impact of the impingement on the roll. The jet velocity at the outlet of the nozzle is 1.4 m/s and increases to 1.65 m/s at the point of impact.

When changing to CM with 130 g/m², the weight of the treatment substance is reduced to 3 g/m²and the speed is increased to 1100 m/min (settings no. 2, table 1). The distance H, for example, is 34.9 mm. The increase in speed leads to a deterioration of the ratio F_y″/S_⊥ by approx. 36% to 0.7, i.e. the disturbing component S_⊥ has become greater than F_y″. The impulse force F_y″ is no longer sufficient to counteract the disruptive effect of the boundary air flow. The starch jet lifts off the roll. The wetting of the roll is disturbed. Coating of the paper is no longer possible.

To stabilize the coating process, the nozzle is positioned higher. The distance H to the roll increases accordingly (setting no. 3), for example 99 mm. With these settings, the ratio F_y″/S_⊥ increases to 1.6 and is significantly greater than 1, i.e. the disruptive component S_⊥ is significantly smaller than F_y″. With these settings, the impulse force F_y″ is sufficient to compensate for the disruptive effect of the boundary air flow. The starch jet no longer lifts off the roll. Wetting of the roll is restored. Coating the paper is possible again with this setting.

At low roll speeds, the effect of the boundary layer air becomes weaker and the ratio F_y″/S_⊥ becomes >1 (setting 4) even at low jet speeds at the nozzle outlet.

TABLE 1

Settings
No.
1
2
3
4

Paper grade
—
CM
CM
CM
CM

Basis weight
g/m²
160
130
130
170

Roll speed
m/min
800
1100
1100
600

Treatment substance
g/m²
3.5
3.0
3.0
3

weight per side

Solids content
%
12.5
12.5
12.5
12.5

Specific volume flow
I/(min
21.6
25.4
25.4
13.9

rate, q
m)

Jet velocity coming
m/s
1.4
1.7
1.7
0.9

out of the nozzle

Jet thickness in the
μm
218
225
193
192

impingement point, h

Angle γ
°
15.7
15.5
17.7
16.1

Angle β
°
22.3
20.7
29.2
28

Angle ratio β/γ
—
1.4
1.3
1.65
1.73

Distance L
mm
22
22
22
22

Distance D
mm
30
31.7
78.6
24.1

Distance H
mm
33.8
34.9
99
30.6

Ratio H/D
—
1.13
1.1
1.26
1.27

Angle position of the
°
45.2
45.2
45.2
45.2

nozzle, φ

Jet velocity in the
m/s
1.65
1.9
2.2
1.2

impingement point

Force ratio F