CN101556233B - Device and method for measuring unique real viscosity of generalized Newtonian fluid - Google Patents

Device and method for measuring unique real viscosity of generalized Newtonian fluid Download PDF

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CN101556233B
CN101556233B CN 200910076987 CN200910076987A CN101556233B CN 101556233 B CN101556233 B CN 101556233B CN 200910076987 CN200910076987 CN 200910076987 CN 200910076987 A CN200910076987 A CN 200910076987A CN 101556233 B CN101556233 B CN 101556233B
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viscosity
rate
newtonian fluid
section
shear
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CN101556233A (en
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任冬云
宋维宁
刘继红
林祥
马艳娥
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Beijing University of Chemical Technology
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Abstract

The invention relates to a device and a method for measuring the unique real viscosity of generalized Newtonian fluid. The method includes the following steps of: calculating the real viscosity of polymer melt; calculating the tensile rate on the spindle axis of a pressure sensor in a contracted flow channel; calculating shearing rate; and calculating shearing stress. The device for measuring the unique real viscosity of generalized Newtonian fluid consists of a nose, a visualized charging barrel, a piston screw, a servo motor and a position sensed system. An internal flow channel of the nose takes contracted shape of continuous gradual change. The piston screw is provided with an axial guide slot structure. The polymer solution or melt passes through a charging device to enter the visualized charging barrel. Under the drive of the servo motor, the piston screw presses down materials to be squeezed out from the nose at a constant velocity. Pressure signals in flow process are collectedand enter a computer data system to calculate the real viscosity. The device and method can not only reflect the shearing viscosity of materials, but also reflect the elongational viscosity of materi als, and effectively solve the uniformity problem of the elongational viscosity and the shearing viscosity.

Description

Measure the apparatus and method of unique real viscosity of generalized Newtonian fluid
Technical field
The present invention relates to the test-type polymer performance theory of testing and performance testing device and method, particularly a kind of forming polymer manufacture field.
Background technology
According to Maxwell's Theory of Viscoelasticity model, great majority belong to the macromolecular material of pseudoplastic fluid, have both had viscosity, have again elasticity.But in the Viscosity Measurement Methods of present superpolymer, such as adopting capillary rheometer, cone-and-plate-rheometer, all be directly to survey the shear viscosity of polymkeric substance under flow state, so tensile viscosity is the very important property of superpolymer.In commercial production, tensile property also can be one of main determining factor of Polymer Processing sometimes, such as the processing at spinning, Precise Extrusion, film rolling and tubule product, the tensile viscosity of polymkeric substance all will directly affect pulling strengrth and the measure of precision of product.So, have great importance and the wide market space for the tensile property of Study Polymer Melts melt.Yet, in the flowing of reality, shear often and the state of the coexistence that stretches, produce a pure stretching field of force and be difficulty relatively.Research about tensile property is continued until now, but, in A1, the M1 and S1 engineering research of the nineties, the conclusion of last gained is all different, be rambling trend (with reference to N.E.Hudson and T.E.R.Jones, The A1 project-an overview[J], J.Non-Newtonian Fluid Mecha.46 (1993) 69-88), at this moment just produced a kind of what is called and namely contained the transition viscosity that shearing contains again stretching.
Since can't obtain a kind of pure elongational flow, doctor W.N.Song once proposed a kind of method of measuring true viscosity under compound flow state, weigh viscosity number (with reference to W.N.Song and Z.M.Xia by the second invariant, A phenomenogical viscosity model for polymeric fluid[J], J.Non-Newtonian Fluid Mecha., 53 (1994) 151-163).Be the true viscosity of polymer melt:
η G = 1 2 ( II τ II d ) 1 2 = 1 / 3 σ 2 + τ 2 3 ϵ · 2 + γ · 2 - - - ( 1 )
Song thinks, no matter be pure shear, or pure extension flows, and is not that the polymer fluid of reality flows, and therefore two kinds of extreme situations just, measure wherein all comprehensive flow characteristicss of characterize polymers of any one viscosity.Should both measure its tensile viscosity from the angle of true viscosity, measure again its shear viscosity, the viscosity number that is namely characterized by formula (1).
According to viscosity and the second constant the relationship between quantities, in compound the flowing that stretches and shear, if σ, τ,
Figure GSB00000736651500021
Can record, then its true viscosity can be calculated.
Professor D.F.James and G.M.Chandler once designed the runner of a permanent rate of extension and studied elongational viscosity (with reference to D.F.James and G.M.Chandler, J.Non-Newtonian Fluid Mecha., 35 (1990) 421-433), the curvilinear equation of its contracted channel is:
R 2(z-C 1)=C 2 (2)
Wherein, C 1, C 2Be undetermined constant, R, Z are respectively runner radius coordinate and ordinate of orthogonal axes.Rate of extension on its runner central axis is:
ϵ · = 4 π · Q D 2 l c p - - - ( 3 )
After flow rate Q and model were determined, rate of extension was just invariable.
Summary of the invention
The object of the invention is to, by a kind of theoretical method and corresponding experimental provision that calculates the polymkeric substance real viscosity is provided, to realize the true reflection to the polymkeric substance viscoelasticity.
The present invention adopts following technological means to realize:
A kind of method of measuring unique real viscosity of generalized Newtonian fluid, the method contain the viscosity and the elongational viscosity that reflects material of the stickiness of reflection polymer melt or solution;
The true viscosity of step 1, calculating polymer melt:
Rate of extension on step 2, the calculating contracted channel pressure sensor axle line:
Step 3, calculating shear rate;
Step 4, calculating shear stress.
Aforesaid rate of extension is the rate of extension on the pressure transducer axle line: comprising: the melt velocity on the central axis of pressure transducer right cylinder upper end; The average velocity of the melt on the pressure transducer cross section; Volume flow rate (mm through pressure transducer right cylinder upper end cross section 3/ s); Pressure transducer right cylinder upper end diameter of section; The distance of upper end from true origin to the pressure transducer right cylinder;
The viscosity of aforesaid fluid is unique, and described viscosity comprises shear viscosity and elongational viscosity, and shear viscosity and elongational viscosity respectively characterize an aspect of fluid viscosity performance.
The aforesaid viscosity model of setting up unique real viscosity of generalized Newtonian fluid, viscosity model and denseness m and underworld rule index n are irrelevant.
The strain rate scope that aforesaid viscosity is measured can be regulated; Change the diameter of machine head port mould, measure the real viscosity under the high strain rate.
A kind of device of measuring unique real viscosity of generalized Newtonian fluid, this device is comprised of head, charging barrel with visual, piston screw, servomotor and position sensing system, the head inner flow passage is the continuous gradation collapsed shape, and piston screw has axially directed groove structure.
Aforesaid polymer solution body or melt enter charging barrel with visual through feeding device, under described driven by servomotor, described piston screw at the uniform velocity presses down material and extrudes from head, gathers the pressure signal in the flow process, enter computer data system, calculate real viscosity.
Aforesaid when fluid is flowed through the head inner flow passage with large Reynold number, rate of extension is invariable on its central axis, can calculate the pure extension viscosity; Only have shear action at the barrel wall, can calculate the pure shear viscosity.
Aforesaid device is Based Intelligent Control, and the displacement of described position sensing system control piston screw rod, and real-time data collection import PC and carry out real viscosity calculating.
The present invention measures the apparatus and method of unique real viscosity of generalized Newtonian fluid, compared with prior art, obvious advantage and beneficial effect is arranged:
Can truly reflect the viscosity performance of fluid comprehensively, and be not only the one side that stresses cutting performance or tensile property.Shear viscosity and elongational viscosity are the signs of two special circumstances in this viscosity model.For Newtonian fluid, satisfy the Trouton rule.Can characterize the rheological behaviour of high strain rate.This viscosity model and flow index m, n are irrelevant, have relatively wide versatility.Adopt the runner of permanent rate of extension, the rate of extension of Fluid Flow in A mainly by geometric parameter and the flow rate control of runner, has the rate of extension of accurate stable.Adopt ball-screw-transmission, and by driven by servomotor, can realize the stable control of rate of extrusion.Has the reinforced characteristic of accurate measurement.Pressure by two almost in one plane the pressure transducer of upper/lower positions measure, two sensors differs 1~3 millimeter in the installation site of Z-axis direction.Deficiency to existing flow graph provides a kind of Viscosity Model that can comprehensively reflect the stickiness of polymer melt or solution, its characteristics are that this model can reflect the shear viscosity of material, the elongational viscosity that can reflect again material has effectively solved the unitarity problem of elongational viscosity and shear viscosity.
Description of drawings
Fig. 1 is the runner schematic diagram of polymer melt;
Fig. 2 is that melt is at the rate curve schematic diagram in a certain cross section;
Fig. 3 is the schematic diagram of unit dz;
Fig. 4 is the stressed schematic diagram that melt flows in the dz infinitesimal;
Fig. 5 is the experiment flow graph schematic diagram that the polymkeric substance real viscosity is measured.
Wherein, 1 servomotor, belt drive part, 2 lead screw transmission structures, 3 charging apertures, heating jacket, 4 material storage tubes, heating jacket, 5 pistons, 6 contracted channels, heating jacket.
Embodiment
Specifically describe this experiment is novel below by embodiment;
Theoretical calculation method of the present invention can be applicable to flow graph and measures calculating, deficiency to existing flow graph provides a kind of Viscosity Model that can comprehensively reflect the stickiness of polymer melt or solution, this model can reflect the shear viscosity of material, the elongational viscosity that can reflect again material has effectively solved the unitarity problem of elongational viscosity and shear viscosity.
(1) theoretical method of the present invention is as follows:
According to aforesaid formula (1), only need to obtain σ, τ,
Figure GSB00000736651500041
Just can obtain the real viscosity of material.
(1) rate of extension determines
According to formula (2) formula, a contracted channel is arranged as shown in Figure 1, at tap1, tap2, tap3 three place's setting pressure sensors, and obtain rate of extension on the axle line:
ϵ · = 4 π · Q D 2 l c p - - - ( 4 )
Wherein:
c p = U 2 V 2 - - - ( 5 )
U---the melt velocity on the tap3 place central axis;
V---the average velocity of the melt on the cross section, tap3 place;
Q---through the volume flow rate (mm in cross section, tap3 place 3/ s);
D---tap3 place diameter of section;
L---the distance from true origin to tap3.
Suppose: the even stable-state flow of melt, and incompressible; Wall is without slippage; Behind constant pressure differential, flow rate remains unchanged; Pressure only is the function of z.
After coordinate is fixing, can determine constant C 1, C 2And the equation of curved surface, and l=z 3-C 1, D=2R 3, and flow rate is determined by the speed that piston moves, like this, by (4) formula, we just can obtain shrinking the rate of extension on the curved sections central axis.
(2) calculating of shear rate
As for the calculating of shear rate, said as the front, we can only measure the shear rate at wall place
Figure GSB00000736651500051
γ · = 1 2 ( ∂ v z ∂ r + ∂ v r ∂ z ) - - - ( 6 )
Therefore only need to obtain the equation of speed gets final product.
Under the superincumbent assumed condition, the constant strain rate section is at any point z=z 0On, there is continuity equation
Q = 2 π ∫ 0 r z 0 v ( r , z 0 ) · r ( z 0 ) dr - - - ( 7 )
Geometrical boundary condition: R 2(z-c 1)=c 2
At z=z 0The cross section on, its rate curve can be assumed to be the para-curve such as Fig. 2:
Therefore, at the central axis place, its velocity amplitude is maximum; And at the wall place, speed is 0.
v ( R , z 0 ) = 0 v ( 0 , z 0 ) = v max - - - ( 8 )
Because the continuity that flows is at any one z 0The place, its flow rate should be consistent with the former, therefore:
Q ′ = ∫ 0 R v ( r , z ) · dA = 2 π ∫ 0 R v ( r , z ) · rdr ~ f ( r , z ) = Q - - - ( 9 )
Here, owing to can't obtain the expression of speed, suppose that the rate curve equation is:
v=(Ar 2+B)·z (10)
Wherein, v-----speed
The coordinate of r-----radial direction
The z-----axial coordinate
A, the B----undetermined constant
With (10) formula substitution (9), integration:
Q c = 2 π z 0 ( 1 4 AR 4 + 1 2 BR 2 ) - - - ( 11 )
Like this, easily obtain A, one group of experimental data of B, thus obtain rate curve, shear rate
Figure GSB00000736651500062
Also just can obtain.
(3) calculating of shear stress
(be separated by 1~2mm), measure the pressure of two sections, then at a, b two places
Δp ab=p a-p b (12)
Suppose: 1, in dz infinitesimal section, fluid flows through with identical speed
2, with Δ p=p a-p bExpression dz infinitesimal section central plane pressure differential up and down
Then got by the shearing force on the dz infinitesimal section and external force balance:
τ = πr 2 ( z ) · Δp 2 πr ( z ) · Δz = r ( z ) · Δp 2 Δz - - - ( 13 )
Work as r=R WThe time, have:
τ w = R · Δp 2 Δz - - - ( 14 )
Wherein: R is characteristic radius, arithmetic mean or the logarithmic mean value of desirable tap1 and tap2 place radius.
(4) calculating of drawing stress
Figure 4 shows that the force analysis of constant strain rate section, establishing measured pressure differential is Δ p, and shear stress is shown in (14).Because rate of extension is constant, its tensile viscosity is constant, therefore drawing stress is constant,, ignores little variable Δ τ of shear stress here wThen:
p(A s+ΔA s)+σA s=τ wA s+(p+Δp)A s+σ(A s+ΔA s) (15)
Wherein: the pressure of a position among p-------Fig. 3;
A s------sectional area of a position among Fig. 3;
Δ A s-----cross section product moment of a and b position among Fig. 3;
The drawing stress of σ------a position among-Fig. 3;
The pressure differential of a and b position among Δ p------Fig. 3;
τ w------shearing force at wall place among-Fig. 4;
A w------lateral area of internal face among-Fig. 4.
Its boundary condition:
σ r=R=0 (16)
σ r=0=σ max (17)
Abbreviation (15):
(p-σ)ΔA s-ΔpA s=τ wA w(18)
Then:
σ = Δp A s - τ w A w ΔA s + p - - - ( 19 )
The invention still further relates to the experiment rheology instrument apparatus of test polymer real viscosity, this device comprises: servomotor, belt drive part 1, lead screw transmission structure 2, charging aperture, heating member 3, material storage tube, heating member 4, piston 5, contracted channel, heating member 6 form.Servomotor, belt drive part 1 are installed in the prime of lead screw transmission structure 2, charging aperture 3 is installed on the same rank with material storage tube, heating member 4, piston 5 is installed in material storage tube, heating jacket 4 higher levels, contracted channel, heating member 6 are installed in the subordinate of material storage tube, heating jacket 4,10 is drive unit, and 20 for monitoring mouth.
In sum, according to theoretical method of the present invention, just can test out the real viscosity of polymkeric substance.
During experiment, fluid melt or solution enter material storage tube, heating member 4 by charging aperture, heating member 3, start servomotor, belt drive part 1, fluid piston 5 with certain velocity variations form under, extrusion fluid flows out from contracted channel, heating member 6, and by the temperature of thermopair control contracted channel, heating member 6 and material storage tube, heating member 4, measure pressure P by the pressure transducer of installing on contracted channel, the heating member 6 1, P 2, and calculating pressure differential Δ p, the substitution experimental data just can obtain the real viscosity η of test material G
It should be noted that at last: above embodiment is only in order to illustrate the present invention and unrestricted technical scheme described in the invention; Therefore, although this instructions has been described in detail the present invention with reference to each above-mentioned embodiment,, those of ordinary skill in the art should be appreciated that still and can make amendment or be equal to replacement the present invention; And all do not break away from technical scheme and the improvement thereof of the spirit and scope of invention, and it all should be encompassed in the middle of the claim scope of the present invention.

Claims (9)

1. method of measuring unique real viscosity of generalized Newtonian fluid, utilization realizes with lower device, this device is comprised of head, charging barrel with visual, piston screw, servomotor and position sensing system, the head inner flow passage is the continuous gradation collapsed shape, and piston screw has axially directed groove structure; It is characterized in that: the method is the Viscosity Model that can comprehensively reflect the stickiness of polymer melt or solution, and this model can reflect the shear viscosity of material, can reflect again the elongational viscosity of material, and step comprises:
Step 1: the determining of rate of extension:
According to formula R 2(z-C 1)=C 2, at contracted channel three place's setting pressure sensors, and obtain rate of extension on the axle line:
ϵ · = 4 π · Q D 2 l c p - - - ( 1 )
Wherein,
Figure FSB00000930902000012
The U----contracted channel descends the melt velocity on place's central axis most, the average velocity of the melt on the Xia Chu cross section of V----contracted channel; Q----is through the volume flow rate (mm in the Xia Chu cross section of contracted channel 3/ s); The D----contracted channel descends place's diameter of section most; L----is the distance under from true origin to contracted channel; The even stable-state flow of melt, and incompressible; Wall is without slippage; Behind constant pressure differential, flow rate remains unchanged; Pressure only is the function of z;
After coordinate is fixing, determine constant C 1, C 2And surface equation, and l=z 3-C 1, D=2R 3, and flow rate is determined by the speed that piston moves, and by (1) formula, obtains shrinking the rate of extension on the curved sections central axis;
Step 2: the calculating of shear rate:
Shear rate
Figure FSB00000930902000013
For:
γ · = ∂ v Z ∂ r + ∂ v r ∂ z - - - ( 2 )
The constant strain rate section is at any point z=z 0On, there is continuity equation:
Q = 2 π ∫ 0 r z 0 v ( r , z 0 ) · r ( z 0 ) dr - - - ( 3 )
Its geometrical boundary condition is: R 2(z-c 1)=c 2At z=z 0The cross section on, its rate curve is para-curve; Therefore, at the central axis place, its velocity amplitude is maximum; And at the wall place, speed is 0, that is:
v ( R , z 0 ) = 0 v ( 0 , z 0 ) = v max - - - ( 4 )
Because the continuity that flows is at any one z 0The place, its flow rate is consistent with the former, therefore:
Q = ∫ 0 R v ( r , z ) · dA = 2 π ∫ 0 R v ( r , z ) · rdr ~ f ( r , z ) = Q - - - ( 5 )
Suppose that the rate curve equation is:
v=(Ar 2+B)·z (6)
Wherein, v----speed, the coordinate of r----radial direction, the z----axial coordinate, A, the B----undetermined constant, with (6) formula substitution (5), integration gets:
Q = 2 π z 0 ( 1 4 AR 4 + 1 2 BR 2 ) - - - ( 7 )
Obtain like this A, one group of experimental data of B, thus obtain rate curve, obtain shear rate
Step 3: the calculating of shear stress:
At the contracted channel of the 1-2mm of being separated by up and down a, b two places, measure the pressure of two sections, then Δ p Ab=p a-p b, establish: in dz infinitesimal section, fluid flows through with identical speed (1); (2) with Δ p=p a-p bExpression dz infinitesimal section central plane pressure differential is up and down then got by the shearing force on the dz infinitesimal section and external force balance:
τ = πr 2 ( z ) Δp 2 πr ( z ) Δz = r ( z ) Δp 2 Δz , - - - ( 8 )
Work as r=R WThe time, have:
τ w = RΔp 2 Δz - - - ( 9 )
Wherein: R is characteristic radius, is arithmetic mean or the logarithmic mean value of contracted channel top and middle place radius;
Step 4: the calculating of drawing stress:
The measured pressure differential of constant strain rate section is Δ p, and shear stress is shown in (9); Because rate of extension is constant, its tensile viscosity is constant, therefore drawing stress is constant,, ignores little variable Δ τ of shear stress here wThen:
p(A s+ΔA s)+σA s=τ wA w+(p+Δp)A s+σ(A s+ΔA s) (10)
Wherein: the pressure of p-------contracted channel a position; A sThe sectional area of------contracted channel a position; Δ A sThe cross section product moment of-----contracted channel a and b position; The drawing stress of σ-------contracted channel a position; The pressure differential of Δ p------contracted channel a and b position; τ wThe shearing force at-------wall place; A wThe lateral area of-------internal face; Its boundary condition:
σ| r=R=0,σ| r=0=σ max (11)
Equation (10) but abbreviation get:
(p-σ)ΔA s-ΔpA s=τ wA w (12)
Then have:
σ = Δp A s - τ w A w ΔA s + p - - - ( 13 )
With the above-mentioned σ that obtains, τ,
Figure FSB00000930902000032
Substitution:
η G = 1 2 ( II τ II d ) 1 2 = 1 / 3 σ 2 + τ 2 3 ϵ · 2 + γ · 2 - - - ( 14 )
Can obtain the real viscosity of material.
2. the method for measurement unique real viscosity of generalized Newtonian fluid according to claim 1, it is characterized in that: described rate of extension is the rate of extension on the pressure transducer axle line: comprising: the melt velocity on the central axis of pressure transducer right cylinder upper end; The average velocity of the melt on the pressure transducer cross section; Volume flow rate through pressure transducer right cylinder upper end cross section; Pressure transducer right cylinder upper end diameter of section; The distance of upper end from true origin to the pressure transducer right cylinder.
3. the method for measurement unique real viscosity of generalized Newtonian fluid according to claim 1, it is characterized in that: the viscosity of described generalized Newtonian fluid is unique, described viscosity comprises shear viscosity and elongational viscosity, and shear viscosity and elongational viscosity respectively characterize an aspect of fluid viscosity performance.
4. the method for measurement unique real viscosity of generalized Newtonian fluid according to claim 1 is characterized in that: set up the viscosity model of unique real viscosity of generalized Newtonian fluid, viscosity model and denseness m and power-law exponent are irrelevant.
5. the method for measurement unique real viscosity of generalized Newtonian fluid according to claim 1 is characterized in that: the strain rate scope that described viscosity is measured can be regulated; Change the diameter of machine head port mould, measure the real viscosity under the high strain rate.
6. device that utilizes each described method of claim 1-5 to measure unique real viscosity of generalized Newtonian fluid, it is characterized in that: this device is comprised of head, charging barrel with visual, piston screw, servomotor and position sensing system, the head inner flow passage is the continuous gradation collapsed shape, and piston screw has axially directed groove structure.
7. the device of measurement unique real viscosity of generalized Newtonian fluid according to claim 6, it is characterized in that: polymer solution body or melt enter charging barrel with visual through feeding device, under described driven by servomotor, described piston screw at the uniform velocity presses down material and extrudes from head, gather the pressure signal in the flow process, enter computer data system, calculate real viscosity.
8. the device of measurement unique real viscosity of generalized Newtonian fluid according to claim 6, it is characterized in that: when fluid was flowed through the head inner flow passage with large Reynold number, rate of extension was invariable on its central axis, can calculate the pure extension viscosity; Only have shear action at the barrel wall, can calculate the pure shear viscosity.
9. the device of measurement unique real viscosity of generalized Newtonian fluid according to claim 6, it is characterized in that: described device is Based Intelligent Control, the displacement of described position sensing system control piston screw rod, and real-time data collection import PC and carry out real viscosity calculating.
CN 200910076987 2009-01-16 2009-01-16 Device and method for measuring unique real viscosity of generalized Newtonian fluid Expired - Fee Related CN101556233B (en)

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