US3722831A

US3722831A - Mixing machines

Info

Publication number: US3722831A
Application number: US00842949A
Authority: US
Inventors: H Bialas; F Lindenthal
Original assignee: Dierks and Soehne GmbH and Co KG
Current assignee: Dierks and Soehne GmbH and Co KG
Priority date: 1968-07-20
Filing date: 1969-07-18
Publication date: 1973-03-27
Anticipated expiration: 1990-03-27
Also published as: FR2013397A1; CH487721A; NL6911026A; BE736223A; GB1244115A; JPS5122218B1; AT310426B

Abstract

A high speed mixing machine in which power driven tools are arranged to rotate in a mixing vessel to produce a forced vortexlike movement of the material being mixed has a plurality of separate tools rotatable in coacting compartments of the vessel which merge with one another so that the material, particularly synthetic material to be processed and/or mixed e.g. with other material in the form of additives or liquids, is continuously transferred from one compartment to another of the vessel.

Description

ilnited States Fatent n 1 Bialas et al.

[ 1 3,722,831 1 Mar. 27, 1973- [54] MIXING MACHINES [75] Inventors: Horst Bialas, Georgsmarienhutte; Friedrich Lindenthal, Osnabruck, both of Germany [73] Assignee: Dierks & Sohne, Osnabruck, Germany 22 Filed: 'Jiil 8,196'9 [21] Appl.No.:842,949

[30] Foreign Application Priority Data July 20, 1968 Germany ..P 17 82 115.7 Dec. 19, 1968 Germany ..P 18 15 582.3

52 U.S. Cl. ..259/6 [51] Int. Cl. .L.B0lt 7/00, B01f 15/00 [58] Field of Search ..259/5, 6, 15, 21-24, 259/31-33, 37-39, 48, 60-63, 99,101-105, 41

[56] References Cited UNITED STATES PATENTS 3,114,933 12/1963 Ambrette et al ..259/41 X 3,403,894 10/1968 Matsuoka et a1. 259/41 X 2,750,161 6/1956 Simmons 2,893,709 7/1959 Nauta ..259/102 X 2,964,391 12/1960 Benson ..259/6 X 2,987,760 6/1961 Grubenmann et al .259/104 X 3,468,518 9/1969 Koch ..259/6 FOREIGN PATENTS OR APPLICATIONS 1,198,116 12/1964 Germany ..259/6 Primary Examiner-Jordan Franklin Assistant Examiner-G. V. Larkin Attorney-Arthur O. Klein [57] ABSTRACT A high speed mixing machine in which power driven tools are arranged to rotate in a mixing vessel to produce a forced vortex-like movement of the material being mixed has a plurality of separate tools rotatable in coacting compartments of the vessel which merge with one another so that the material, particularly synthetic material to be processed and/0r mixed e.g. with other material in the form of additives or liquids, is continuously transferred from one compartment to another of the vessel.

14 Claims, 14 Drawing Figures Patented March 27, 1973 3,722,831

5 Sheets-Sheet 1 lnvenlar H0 rs! B/ALAS Patented March 27, 1973 3,722,831

5 Sheets-Sheet 2 H1 efr Afforn cy Patented March 27, 1973 3,722,831

5 Sheets-Sheet :5

In men or II'ACIVV' Affor'ney Patented March 27, 1973 3,722,831

5 Sheets$heet 4 9 y- In venfar:

He s! BIA AS Fr 1 ac/r t'c/w L/IVDEIVTHAL H1 Cl A ffarney 5 Sheets-Sheet 5 Fig. 14

lave/liar Horsf BIA LAS fhcir' Affor'n a MIXING MACHINES The present invention relates to mixing machines particularly, although not exclusively, for processing synthetic materials or similar powdered, granular or fine-fragmented substances, with or without the introduction of additive materials or liquids, said machine having a mixer vessel and power-driven tools rotating therein which by centrifugal force produce a funnel-like movement in the material.

Machines of this kind, which are also referred to as high-speed mixers, have a substantially cylindrical basic vessel in which tools co-axially assembled upon a drive shaft, rotate, being driven by an appropriate motor. The drive shaft can project into the mixer vessel either through its base or through its top. Known machines of this kind are limited in terms of size and performance. This limitation is due primarily to the heating which is produced in the material as a consequence of the rotational movement of the tools, and this heating must not exceed a certain level if damaging heat-induced phenomena are to be avoided. This limitation on heating which is imposed by the material being mixed, restricts the dimensions of the tools and these, considered in relation to the r.p.m., determine the rotational speed of same and, therefore, the dimensions of the mixer vessel in a direction radially of the tool rotation axis. The height of the mixer vessel, on the other hand, is restricted by the fact that the level of the material in the vessel may only rise above the'working plane of the tools by a specific amount if a funnel-like flow of material is to be produced in the vessel, the material executing a combination movement composed of a rotational motion about the tool axis and along the external wall, with an axially upward motion and an axially oppositely directed motion toward the vessel center. If the level of the material in the vessel exceeds a certain height, then the kinetic energy of the tools is compensated by the internal resistance presented by the material and the development of the critical funnellike flow pattern which determines the production of the mixing and preparing effect, is impeded.

Any attempt to enlarge the mixing volume of the machine, in order, in one operation and under the same conditions, to be able to process larger charges, meets with problems from the structural point of view too. As the machine size increases it becomes necessary to provide a suitably higher powered motor to drive the tools, and this, at start-up, introduces a very high peak load into the mains, meaning that correspondingly designed mains connections are needed. The power transmitted to the tools is such as to require a disproportionately large outlay in bearing structures for the tool drive shaft which is otherwise a cantilevered design. Also, vibration phenomena cannot be excluded and this kind of problem again means increased structural outlay in order to ensure that the operational life of the machine, its reliability and the quality of material processing, are not adversely affected.

With increasing vessel sizes, furthermore, the efficiency of the machine tails off with the consequence that the attainment of a desired mixing and preparation result takes a longer time and the homogeneity of the finished mix is poorer.

The present invention provides a mixing machine in which power-driven tools are arranged to rotate in a mixer vessel and by centrifugal force produce a funnellike movement in material being mixed in the vessel, the vessel being made up of a plurality of coacting vessels having merging coacting mixing spaces, each with its own mixer tools, the merging coacting mixing spaces combining to form a common mixer space in which a continuous transfer of material from one coacting mixing space thereof to another will occur on operation of the tools.

According to a feature of the invention, said coacting mixing vessels have mutually merging coacting mixing spaces.

Using simple structural means, the present invention may provide a large-capacity mixer the capacity of which can be designed arbitrarily, independently of processing limitations, and which can process in one operation charges of a size which is determined simply by the requirements of the processing industry. Even where large charges are involved, using the machine in accordance with the invention it is possible whilst reducing the mixing time to achieve a qualitative mixing result which is far superior to that obtainable by mixing machines of conventional design. This goes hand-in-hand with a'simplification in the loading outlay, in the weighing of the charge constituents and so on, whilst, furthermore, there is better exploitation of the capacity of further processing machinery, e.g. extruders. The absolute uniformity of the material bulk in a charge moreover ensures that there is no occurrence of quality fluctuations in the end-product, e.g. of the kind which could stem from discrepancies in the quality of preparation in parallel operations carried out in different machines of corresponding coacting capacities. It is furthermore an advantage that even where large vessel capacities are involved, a comparatively low vessel height can still be maintained.

In order to drive the tool or tools in each coacting vessel, preferably a separate drive motor is provided which, having -a correspondingly lower power, imposes lower start-up power peaks on the supply system. By arranging for time-staggered start-up of the motors, it is possible in this context to considerably reduce the loading upon and extent of the connecting network. Also, where. bearing outlay is concerned a reduction is achieved in correspondence with the reduced individual power ratings, whilst at the same time vibrations can be excluded or more easily controlled.

Preferably, the speed of the tool or tools in each coacting vessel is capable of individual control and, in particular where separate drive motors are provided, this presents no difficulty. Alteration of the tool speeds, independently of one another, makes it possible to influence the flow pattern of the material being mixed and to produce zones of differing mixing intensity, differing heating and the like. Preferably, the coacting vessels are identical in size and shape. With this kind of design particularly, economical production is achieved by the use of the same available machine tools and other production equipment. Instead of this, however, it is equally possible for the volumes of the coacting mixing spaces defined by the coacting vessels to differ from one another, and this provides a further possible way of adapting the mixing and preparation operation to special requirements. Because, with this kind of design too, the overall material flow passes through all the coacting vessels, zones are created in which the material is differently affected and which enable special mixing effects to be produced.

The confining walls of coacting mixing'spaces belonging to coacting vessels which exchange a material flow with one another, should intersect one another in a manner which ensures an unimpeded material transfer flow. The transfer opening between the coacting mixing spaces, which is produced by this intersection, should be designed in accordance with the dimension of the funnel-like material flow in the radial direction, in order to prevent any build-up or stagnation of material in the transitional zone.

The tools of the coacting vessels conveniently consist in each case of a set of several coacting tools arranged co-axially above one another at an interval, in a manner which for that matter could equally be used in conventional machines. Advantageously, the operating planes of the individual tools of tool sets in the coacting vessels which co-operate with one another, are angularly offset in relation to one another. This offset creates a material flow in different planes and contributes in a marked measure to the development of a continuous and unimpeded exchange of material between adjacent coacting vessels. At the same time, this measure improves the intensity of the mixing. A further improvement in the intensity of mixing can be achieved if, in accordance with yet another feature of the invention, the fields of operation of the tools in adjacent coacting vessels overlap. By virtue of this overlap and in association with the pattern of flow of the material developed in a transitional zone between mutually merging coacting mixing spaces of coacting vessels, a region of heightened turbulence is developed which makes it possible efficiently to process materials which hitherto were difficult or impossible to mix and prepare in this way. It is well known that in order to improve the funnel-like flow pattern, propeller-like tools should be provided, having a pitch such as to impart to the material a component of movement in the axial direction and in accordance with a feature of this invention the pitch of the tools of the respective coacting vessels is different and this further promotes the attaining of a continuous material flow pattern which extends through all the coacting vessels. In designing the overall vessel in the form of two subsidiary vessels, the tools can be identical with one another and be driven synchronously so that they rotate in the same direction. Instead of this, however, the tools may equally well be given a mirrorsymmetrical design in relation to one another and be driven synchronously but in opposite directions of rotation.

In order to improve the transfer of material between neighboring coacting vessels, in particular at the floor level, and in order to make the flow more uniform in this area, it is provided in accordance with a feature of this invention that the floor levels of adjacent coacting vessels are offset in relation to one another in the direction of the axes of rotation of the tools. The degree of offset advantageously corresponds in this context at least to the effective axial working height of one of the individual tools rotating adjacent the floor, and these tools are themselves offset axially in relation to one another in accordance with the offset between the floors. Preferentially, the direction of offset of the floor levels of the coacting vessels, as well as of the tools adjacent the floor in each case, will correspond with the direction of offset of the other individual tools of the sets. The operating areas of the individual tools located adjacent the floor may, moreover, be arranged to overlap one another.

This kind of design at the same time ensures complete discharge of the overall vessel, leaving no residue, after the completion of an operating cycle.

Other features and advantages of the invention will become apparent from the claims and the ensuing description taken in conjunction with the accompanying drawings, the description and drawings describing several examples of the subject of the invention.

In the drawings:

FIG. 1 is a schematic side elevation of a machine in accordance with the invention, comprising two coacting vessels,

FIG. 2 is a simplified plan view of FIG. 1,

FIGS. 3 and 4 are schematic partial illustrations similar to FIGS. 1 and 2, depicting the flow pattern in the machine of FIGS. 1 and 2,

FIG. 5 is an illustration similar to FIG. 4, of a further machine according to the invention with an overall mixing vessel made up of three coacting vessels,

FIGS. 6 to 12 are schematic illustrations illustrating vessel designs of further machines in accordance with this invention,

FIG. 13 is a schematic partial elevation similar to that of FIG. 1, illustrating a modified design, and

FIG. 14 is a simplified plan view of FIG. 13.

' The machine illustrated in FIGS. 1 to 4, comprises a unitary overall mixing vessel 1 comprising two

coacting vessels

2, 3, having merging coacting mixing spaces, and this is mounted on a machine bed 4 and may for example have an effective volume of between about 1,000 and 1,200 liters. The

inner wall

5 and 6 in each case defining the coacting mixing space of the

coacting vessels

2 and 3, has a substantiallycylindrical form. These walls intersect one another and in so doing define a common transfer opening 7 which extends over the full height of the vessel 1 and, in the example illustrated, has a width corresponding approximately to the radius of a coacting vessel.

The intersection between the

internal walls

5, 6 of the coacting vessels, which determines the width of the transition opening 7, is arranged in such fashion as to achieve an unimpeded flow of material at the transition zone, the dimension of the radial component of the funnel-like flow pattern during operation being a critical quantity in this context upon which to base design.

In the example illustrated, the overall vessel is of double-walled form and it is possible, in the interspace 8 between external wall 9 and the

vessel walls

5, 6, to arrange for the introduction of a coolant or heating medium, e.g. water, oil or the like.

Each

coacting vessel

2, 3 contains its own separate mixing and

processing tools

10 or 11, as the case'may be, and these are fitted to a

drive shaft

13 or 14, extending through the vessel. base into the interior of the vessel, co-axially with the

walls

5, 6. Equally, the

shafts

13, 14 could extend into the vessels from the top, through the top cover.

Each shaft l3, 14, together with its

tools

10, 11, is driven through a

transmission system

15, 16 by a

separate motor

17, 18. The

arrows

19, 20 in each case illustrate the direction of rotation. In the example illustrated, the system is a contrarotating synchronized one, the tools having a mirror-symmetrical design with respect to each other. The drive motion, however, can equally well be a synchronous co-directional one,'in which case the tools are identical to one another.

The

drive motors

17, 18 are variable speed motors and the speeds of rotation of the

tools

10, 11 can thus be regulated simultaneously or independently of one another. This kind of regulation, however, can equally well be introduced through the medium 'of the

transmission systems

15, 16, these for example taking the form of multi-stage gearboxes.

The

tools

10, 11 consist, in the example illustrated, in each case of three sets of individual tools, in the form of

paddles

21, 22, 23 and 24, 25, 26 arranged diametrically in relation to the

drive shafts

13, 14. The base paddles 21, 24 rotate at the same height, whereas the planes of rotation of the center paddles 22, 25 and the top paddles 23, 26, are in each case vertically staggered in relation to one another. The circumferences of the operating areas of the tool paddles intersect one another. In order to produce a movement component parallel to their axis of rotation, the paddles are given a pitch in the manner of a propeller blade, or at any rate have a top surface, facing the top of the vessel 1, which is obliquely located in relation to the direction of rotation, the obliquity or angle of slope increasing with the radius.

In order to supply material to the overall mixing vessel 1 and/or to remove it therefrom, a single outlet and inlet is provided, the coacting vessel 2 having an inlet and outlet connection 27 via which the loading and discharging of the vessel 1 takes place, there being no necessity for several inlets and outlets.

As the arrows of FIGS. 3 and 4 illustrate in more detail, the tools 10, ll produce in the material contained in the overall mixing vessel 1, a motion such that it describes a funnel-like flow pattern. Viewed in a direction parallel to the axes of rotation of the tools, the flow described a figure-of-eight pattern, the material continually transferring from the coacting vessel 2 to the coacting vessel 3 and vice versa. Considered from the side, the material, commencing for example from the bottom paddles 21, follows a rising curving path, enters the range of effectiveness of the paddles 25 and returns in the course of the curving trajectory to the range of effectiveness of the paddles 23 whence it passes back, after moving towards the center in a direction substantially parallel to the axis of rotation, into the range of effectiveness of the paddles 21. Accordingly, commencing from the range of effectiveness of the base paddles 24, the material rises into that of the center paddles 22 thence into that of the upper paddles 26, whence it passes back into that of the base paddles 24. The arrows drawn in in FIGS. 3 and 4 illustrate the actual movement pattern exclusively in a schematic and highly generalized form. In the region to either side of the transition opening 7, because ofthe conflicting flows there, there develops a zone of high turbulence extending above the height of the vessel 1, and this zone is instrumental in the creation of a particularly intensive mixing effect. This zone is indicated schematically by curved arrows.

The design of the machine in FIGS. 1 to 4 can be influenced by regulating the speed of rotation of the

tools

10, 11, by changing the direction of the tool motion, e.g. in the case of symmetrically designed tool paddles, by altering the offset in the planes of operation of the tools, by altering the angle of incidence of the tools and so on, all in accordance with the particular requirements of the quantities of material to be prepared in the operating cycle, so that the most varied circulatory movements can be produced in the material either as a whole or in zones. In this context, the fundamental funnellike shape of the material circulatory motion, and the zone of increased turbulence at the transition between the coacting vessels, is maintained.

FIG. 5 illustrates an overall mixing vessel 28 of cloverleaf form, together with a basic illustration of the flow pattern and material exchange which takes place between the

individual coacting vessels

29, 30, 31 which define mutually merging coacting mixing spaces. The

coacting vessels

29, 30, 31 which together make up the overall vessel 28, are in each case fundamentally designed in accordance with the

coacting vessels

2, 3 of the embodiment of FIGS. 1 to 4, and in particulareach has separate, rotating tools and a separate drive for each of these tools.

The facilities which are available for influencing the mixing operation, correspond to those which have just been described. The volume or capacity of the machine shown in FIG. 5, is 50 percent larger than that of the one shown in FIGS. 1 to 4. In order to further increase the capacity of the machine, coacting vessels can be combined with one another in the most varied ways, as the schematic individual examples of FIGS. 6 to 12 illustrate in more detail. The examples of FIGS. 6 to 12 in no way exhaust the possibilities of combination and variation which are available.

Whereas the illustration of FIG. 6 depicts the conditions governing the design of the machine shown in FIGS. 1 to 4, and the illustration of FIG. 8 depicts those applying to the machine design of FIG. 5, FIG. 7 illustrates a machine made up of two-coacting

vessels

32, 33, constituting an overall mixing vessel 34 which, because of the different diameters of the

coacting vessels

33, 32, is asymmetrical in design. In this embodiment, although the differences in the dimensions mean that the first costs are higher than in the case of machines which are made up of components of uniform dimensions, nevertheless this kind of design enables mixing zones to be created in which mixing takes place under differing conditions, and an essential one of these conditions is the change in density of the material being mixed, i.e. the quantity of mixed material per unit volume. FIG. 9 illustrates' a modification of the machine with the overall vessel 35 made up of three subsidiary vessels, this time the

coacting vessels

36, 37 having identical dimensions but differing from the dimensions of the coacting vessel 38 in relation to which they are diametrically located.

FIG. 10 also illustrates an overall mixing vessel 39 made up of four

coacting vessels

40, 41, 42, 43 arranged in a square pattern. This kind of machine, whilst having a high capacity, is particularly compact in design. FIG. 11 also shows a machine with an overall mixing vessel 50 made up of six coacting vessels 44 to 49, the coacting vessels in the present instance being arranged in two lines intersecting at right angles. With designs of this kind, adjacent pairs of coacting vessels intersect one another and the coacting mixing spaces are not mutually mergent, this in contrast to a design of the kind shown in FIG. 12 where six, or to put it more accurately, seven coacting vessels 51 to 56 and 57 have been combined to form an overall vessel 58. In this design, the coacting vessel 57 is constituted simply by a separate tool without any confining walls.

In the embodiment of the example of FIGS. 13 and 14, the levels of the bases 6' of the neighboring

coacting vessels

2, 3, are offset in relation to one another in the direction of the axes of rotation of the

tools

10, 11. The degree of offset corresponds substantially to the effective axial working height of one of the individual tools 21' or 24' rotating at the base end, and these tools are likewise offset axially in relation to one another corresponding to the base offset. The direction of offset of the bases 5', 6' of the coacting vessels, and of the base-end individual tools 21', 24', corresponds to the direction of offset of the other

individual tools

22, 25 and 23, 26 in relation to one another. The circumferences of the operating areas of all the individual tools or tool blades, intersect one another. Furthermore, all the individual tools are shaped and have an angle of attack like a propeller such that they impart to the material a component of movement directed parallel to their own axes of rotation, this angle at the very least taking the form of an inclined surface on the top side of each blade, facing the top of the vessel 1, the

inclination being in the direction of rotation and the ac-' tual value of the inclination possibly varying as well by means of a twist in the blades.

The offset of the base levels and the'corresponding offset of the tool paddles 21', 24 which are located at the base ends, means that in the base zone 2, a rising trajectory is produced (viewed in side elevation) in the flow of material during operation of the machine. The intersection between the base-end individual tools improves the mixing effect in this zone of the overall vessel too, whilst at the same time it is ensured at the time of discharge that no residues of material can remain behind in the vessel. The uniform offsetting of all the individual tools of the

tool groups

10, 11, in relation to one another, ensures that there is a steady curved trajectory in the mixed material even in the neighborhood of the base-end individual tools, and improves the material transfer during operation.

It goes without saying that numerous other modifications are possible within the scope of the present invention, and these can be achieved with the help of the components and configurations hereinbefore described. Equally, it goes without saying that the machine, besides being especially advantageous for the mixing and preparation of synthetic materials, this being the application for which it is primarily intended, is also applicable to the mixing of other materials.

We claim:

1. A mixing machine having a mixer vessel, powerdriven propeller-like tools extending adjacent to the vertical walls of said vessel and being operatively arranged to rotate about vertical axes in said mixer vessel at relatively high velocities and by centrifugal force produce a funnel-like movement in material being having merging cooperating mixing spaces, each being provided with its own mixer tools, the merging cooperating mixing spaces combining to form a common mixer space in which a continuous transfer of material from one cooperating mixing space thereof to another will occur on operation of the tools wherein said tools have a pitch which imparts to the material a component of axial movement and the tools of the cooperating vessels in each case consist of a set of several individual tools spaced apart and arranged coaxially one above the other, and being angularly offset in relation to one another.

2. A machine as claimed in claim 1, wherein the cooperating vessels are identical in size and shape.

3. A machine as claimed in claim 1, wherein the circumferences described by the outer extremities of the tools in adjacent cooperating vessels, overlap.

4. A machine as claimed in claim 1, the pitch of the tools being different in different ones of said cooperating vessels.

5. A machine as claimed in claim 1 wherein the direction of rotation of the tools in at least one of the cooperating vessels can be reversed.

6. A machine as claimed in claim 1, having asingle inlet, for loading the overall vessel, which inlet opens into one of the cooperating vessels.

7. A machine as claimed in claim 1 having a single outlet, for the discharge of the overall vessel, which outlet opens from one of the cooperating vessels.

8'. A machine as claimed in claim 1 wherein the mixing vessel is made up of two cooperating vessels and the tools are identical with one another, rotating synchronously in the same direction.

9. A machine as claimed in claim 1, wherein the mixing vessel is made up of two cooperating vessels and the tools are of mirror-symmetrical design, rotating synchronously but in opposite directions.

10. A machine as claimed in claim 1 wherein the floor levels of adjacent cooperating vessels are offset in relation to one another in the direction of the axes of rotation of the tools.

11. A machine as claimed in claim 10 wherein the degree of offset corresponds at least to the effective axial operating height of one of the individual tools rotating adjacent the floor, these tools themselves being axially offset in turn in accordance with the offset between the floors.

12. A machine as claimed in claim 10 wherein the direction of offset of the floors and of the individual tools adjacent the floors, corresponds with the direction of offset of the other individual tools.

13. A mixing machine as set forth in vclaim l, in which said cooperating mixing spaces of said coacting vessels are mutually merging and thevolumes of the mixing spaces differ from one another.

14. A mixing machine as set forth in claim 1, wherein a separate motor is operatively connected to each mixer tool and the speed of operation of each mixer tool is independently controllable.

i III I l 7

Claims

1. A mixing machine having a mixer vessel, power-driven propeller-like tools extending adjacent to the vertical walls of said vessel and being operatively arranged to rotate about vertical axes in said mixer vessel at relatively high velocities and by centrifugal force produce a funnel-like movement in material being mixed in the vessel, the improvement comprising that the vessel is made up of a plurality of coacting vessels having merging cooperating mixing spaces, each being provided with its own mixer tools, the merging cooperating mixing spaces combining to form a common mixer space in which a continuous transfer of material from one cooperating mixing space thereof to another will occur on operation of the tools wherein said tools have a pitch which imparts to the material a component of axial movement and the tools of the cooperating vessels in each case consist of a set of several individual tools spaced apart and arranged coaxially one above the other, and being angularly offset in relation to one another.

6. A machine as claimed in claim 1, having a single inlet, for loading the overall vessel, which inlet opens into one of the cooperating vessels.

8. A machine as claimed in claim 1 wherein the mixing vessel is made up of two cooperating vessels and the tools are identical with one another, rotating synchronously in the same direction.

13. A mixing machine as set forth in claim 1, in which said cooperating mixing spaces of said coacting vessels are mutually merging and the volumes of the mixing spaces differ from one another.