CN101308076A - Method for using forced resonance torsional pendulum instrument for measuring liquid continuous frequency conversion viscoelasticity - Google Patents

Abstract

The invention provides a method for measuring liquid continuous frequency-changing viscoelasticity by using a forced resonance torsion pendulum instrument, which firstly measures resonance curves after unloading and loading liquid to be measured through the forced resonance torsion pendulum instrument, and the resonance curves include an angular displacement-frequency curve (Theta-Omega) and a phase-frequency curve (Phi-Omega), then the viscoelasticity of the corresponding liquid under the driving frequency (Omega) can be directly obtained through each pair of data points of the resonance curves, namely, the viscoelasticity (G1, G2 or Eta) of liquid can be calculated through the corresponding angular displacement (Theta) and phase (Phi) of each driving frequency (Omega). The invention provides a completely new method to overcome the defect that the existing forced resonance torsion pendulum instrument can only measure the liquid viscoelasticity under a specific frequency, and the new method realizes the continuous frequency-changing measurement of liquid viscoelasticity by the forced resonance torsion pendulum instrument in a real sense.

Description

The viscoelastic method of a kind of use forced resonance torsional pendulum instrument for measuring liquid continuous frequency conversion

Technical field

The invention belongs to liquid viscoelasticity measurement technical field, particularly relate to and a kind ofly measure the viscoelastic method of liquid continuous frequency conversion based on forced resonance torsional pendulum instrument.

Technical background

Soft material is ubiquitous in daily life: liquid crystal, polymkeric substance, surfactant, biological membrane, colloid, emulsion, foam, particulate matter and life system or the like all belong to soft material.The viscoelastic measurement Research of soft material not only can help people to explore the material of large nature profundity, and helps to promote manufacturing industry, medicine and food industry, and petroleum industry, agricultural or the like development in field has crucial relation for people's life.

At present, the most popular measurement Research instrument of soft material viscoelasticity mainly contains, and commercial flow graph rocks instrument and miniflow and becomes or the like.The survey frequency scope of rocking instrument has covered the frequency measurement scope of general commercial flow graph, and high frequency can have very high measuring accuracy up to tens megahertzes, is a kind of method of very important complex fluid viscoelasticity measurement.

Rock instrument and generally can be divided into two kinds of measurement patterns, free damping and forced vibration, the latter has higher measuring accuracy, and is widely used.

The forced vibration torsional pendulum instrument is by measuring the resonance curve of unloaded and Load System respectively, obtaining the velocity resonance frequency f of Load System ₀, the passband frequency f ₁And f ₂With respect to the skew of zero load, or the velocity resonance frequency f of Load System ₀With maximum strain speed

With respect to the variation of spaceborne system, obtain measuring under the resonant frequency liquid then and put on the plane wave feature complex impedance that rocks oscillator, calculate the viscoelastic coefficient of liquid at last again.But the shortcoming of forced resonance torsional pendulum instrument is once to measure the liquid viscoelastic coefficient of one or several frequencies.

How realizing rocking the high-precision continuous frequency conversion of instrument, to measure liquid viscoelasticity be that scientists is paid close attention to but the problem of solution fully not also always.

Summary of the invention

The objective of the invention is to overcome the deficiencies in the prior art, the continuous frequency conversion that provides a kind of convenient-to-running method to realize forced resonance torsional pendulum instrument is measured liquid viscoelasticity.

In order to realize the foregoing invention purpose, the technical scheme of employing is as follows:

The viscoelastic method of a kind of use forced resonance torsional pendulum instrument for measuring liquid continuous frequency conversion, earlier unloaded and load resonance curve behind the fluid to be measured by forced resonance torsional pendulum instrument for measuring, described resonance curve comprise angular displacement～frequency curve (θ～ω) and phase place～frequency curve (

～ω), directly obtain the viscoelasticity of corresponding liquid under this driving frequency (ω) again, promptly by each driving frequency (ω) corresponding angular displacement (θ) and phase place by every pair of data point of resonance curve

Calculate liquid viscoelasticity (G ', G " or η).

The present invention is by the resonance curve with the torsional pendulum instrument for measuring gained, frequency in its effective frequency section and angular displacement, frequency and the corresponding parameter of phase place are calculated the viscoelasticity of fluid to be measured, by measuring and calculating automatically and realized in required driving frequency, the viscoelasticity of the pairing liquid of different frequency, thus realize continuous frequency conversion liquid viscoelasticity.

In the technique scheme, behind the torsional pendulum instrument for measuring resonance curve, the viscoelastic detailed process of calculating liquid is as follows:

Calculate the real part (R that measurement liquid puts on the plane wave feature complex impedance that rocks oscillator by (1) and (2) formula _Pl) and imaginary part (X _Pl)

Wherein

θ _0air, θ _0lBe respectively the phase place and the angular displacement that measure under unloaded and the loading liquid situation, the angular frequency of ω for changing, A ₄, E ₄And E ₅Be respectively instrument parameter;

Calculate the viscoelasticity G ' and the G of liquid again by (3) and (4) formula "

$G^{\′}\left(\mathrm{\ω}\right)=\frac{{\left(R_{\mathrm{pl}}\left(\mathrm{\ω}\right)\right)}^2-{\left(X_{\mathrm{pl}}\left(\mathrm{\ω}\right)\right)}^2}{\mathrm{\ρ}}---\left(3\right)$

$G^{\′\′}\left(\mathrm{\ω}\right)=\frac{2\left(R_{\mathrm{pl}}\left(\mathrm{\ω}\right)\right)\left(X_{\mathrm{pl}}\left(\mathrm{\ω}\right)\right)}{\mathrm{\ρ}}---\left(4\right)$

Wherein, " be respectively the storage modulus and the loss modulus of liquid, ρ is a density of liquid for G ' and G.

When calculating fluid to be measured viscoelasticity,, also calculate its viscosity (η) by formula (5) if the liquid of surveying is Newtonian liquid

$\mathrm{\η}=\frac{2R_{\mathrm{pl}}\left(\mathrm{\ω}\right)X_{\mathrm{pl}}\left(\mathrm{\ω}\right)}{\mathrm{\ω\ρ}}---\left(5\right).$

In order to make the best results of measuring and calculating, measure used angular frequency and be chosen for ω ∈ [200,550] rad/s.

Further, measured liquid is the Glycerine-Aqueous Solution of variable concentrations, or the polyoxyalkylene aqueous solution of variable concentrations.Calculate by measurement, and verify, confirmed the accuracy of measurement and result of calculation with the measurement result of commercial flow graph to Glycerine-Aqueous Solution and polyoxyalkylene aqueous solution.

The present invention proposes a kind of new method, overcome existing forced resonance torsional pendulum instrument and can only on specific frequency, measure viscoelastic this defective of liquid, directly obtain the viscoelasticity of corresponding measurement liquid under this driving frequency by every pair of data point of the resonance curve of the principal oscillation pattern of unloaded and Load System, by the homemade forced resonance torsional pendulum instrument in application experiment chamber, measured the viscoelasticity of polyoxyalkylene (PEO) aqueous solution of the viscosity of Glycerine-Aqueous Solution of variable concentrations and variable concentrations thereof, and the reliability of PEO-aqueous solution experiment of having used commercial flow graph repeated authentication.Experimental result has been verified the feasibility of this method exactly, and the application that has shown this method has realized that the continuous frequency conversion of the forced resonance torsional pendulum instrument of real meaning measures liquid viscoelasticity.

Description of drawings

Fig. 1 is the structural representation of the used type that the rocks viscosity resonance measuring instrument of the present invention;

Fig. 2 is measured zero load, the resonance curve of adding variable concentrations Glycerine-Aqueous Solution, and wherein (a) is angular displacement-survey frequency curve, (b) is phase place-survey frequency curve;

Fig. 3 is curve and the related data measured according to Fig. 2, the real part (R of the plane wave feature complex impedance of the measurement liquid that calculates by (1) and (2) formula _Pl: △) and imaginary part (X _Pl: ☆) synoptic diagram, wherein (--) be according to R _Pl=X _Pl=ω ρ η _Theo/ 2 calculate the theoretical resistance value of attaining the Way, and C is the glycerol concentration of Glycerine-Aqueous Solution;

Fig. 4 is the data according to Fig. 3, and (a) of the different Glycerine-Aqueous Solution that calculate by (5) formula measures viscosities il ^MAnd (b) corresponding relative error | η ^M-η _Theo|/η _Theo, η wherein _TheoViscosity number for theory;

Fig. 5 for measure concentration be (a) C=2.0% and (b) viscoelasticity of the PEO-aqueous solution of C=4.0% (G ' and G ") with the curve synoptic diagram of survey frequency variation.

Embodiment

The present invention is described further below in conjunction with accompanying drawing.

Forced resonance torsional pendulum instrument structure of the present invention as shown in Figure 1, comprise torsion wire 1, fixed chuck 2, rotate chuck with rock bar 3, nylon wire 4, counterpoise 5, drive coil to 6, permanent magnet 7, light source and optical alignment pipe 8, base and support 9, differential photocell 10, catoptron 11, runner 12, thermopair 13, be inverted revolving cup 14, fluid to be measured and liquid holding cup 15, temperature controlled water bath pond 16, insulation foamed plastic lid 17.

Adopt above-mentioned torsional pendulum instrument for measuring unloaded and load the resonance curve of variable concentrations Glycerine-Aqueous Solution, described resonance curve comprise angular displacement～frequency curve (θ～ω) and phase place～frequency curve (

～ω), as shown in Figure 2, calculate the real part (R that the variable concentrations Glycerine-Aqueous Solution puts on the plane wave feature complex impedance that rocks oscillator by (1) and (2) formula then _Pl) and imaginary part (X _Pl), as shown in Figure 3, being accompanying drawing 2 pairing complex impedance figure, concrete computing formula and computing module are arranged in the software module of rocking instrument:

Wherein

θ _0air, θ _0lBe respectively the phase place and the angular displacement that measure under unloaded and the loading liquid situation, the angular frequency of ω for changing; A ₄, E ₄And E ₅Be respectively instrument parameter (the instrument parameter value can obtain by the standard model calibration).

Calculate the viscoelasticity (G ' and G ") of liquid at last again by (3) and (4) formula.

$G^{\′}\left(\mathrm{\ω}\right)=\frac{{\left(R_{\mathrm{pl}}\left(\mathrm{\ω}\right)\right)}^2-{\left(X_{\mathrm{pl}}\left(\mathrm{\ω}\right)\right)}^2}{\mathrm{\ρ}}---\left(3\right)$

$G^{\′\′}\left(\mathrm{\ω}\right)=\frac{2\left(R_{\mathrm{pl}}\left(\mathrm{\ω}\right)\right)\left(X_{\mathrm{pl}}\left(\mathrm{\ω}\right)\right)}{\mathrm{\ρ}}---\left(4\right)$

If the liquid of measuring is Newtonian liquid, then the viscosity of Ce Lianging (η) is obtained by (5) formula

$\mathrm{\η}=\frac{2R_{\mathrm{pl}}\left(\mathrm{\ω}\right)X_{\mathrm{pl}}\left(\mathrm{\ω}\right)}{\mathrm{\ω\ρ}}---\left(5\right)$

In (3), (4) and (5) formula, " be respectively the storage modulus and the loss modulus of liquid, ρ is a density of liquid, and ω is for driving angular frequency, R for G ' and G _Pl(ω) and X _Pl(ω) be the real part and the imaginary part of the feature complex impedance under this frequency.

Accompanying drawing 4 (a) and (b) (, calculate) experimental result and the corresponding relative error of measuring thereof that has provided respectively by the variable concentrations Glycerine-Aqueous Solution of torsional pendulum instrument for measuring shown in the accompanying drawing 1 by (5) formula by the data of Fig. 3 impedance diagram.This experimental result has proved the feasibility of this method exactly, and has shown, is ω ∈ [200 in the measured angular frequency, 550] rad/s, measure liquid viscosity in 10～1420cp scope, the complex impedance measurement precision of instrument can reach 1～2%, and the precision of viscosity measurement is about 4.0%.

Accompanying drawing 5 provided concentration for (a) C=2.0% and (b) experimental result of rocking instrument of the polyoxyalkylene aqueous solution (PEO) of C=4.0% (experimental result of solid line among the figure (G ') and dotted line data (G ")) and commercial flow graph thereof (the hollow dots data among the figure, (G ':; G ": zero)) contrast.Concrete measurement and the computation process of PEO are similar to above-mentioned Glycerine-Aqueous Solution, and the measurement result of rocking instrument and commercial flow graph is fine in the repeatability as a result of crossover frequency section, have verified the feasibility of this method once more.The phase measurement accuracy of this instrument is ± 0.0003 °, and the angle displacement measurement precision is 1%.

Claims (5)

1, the viscoelastic method of a kind of use forced resonance torsional pendulum instrument for measuring liquid continuous frequency conversion, it is characterized in that earlier unloaded and load resonance curve behind the fluid to be measured by forced resonance torsional pendulum instrument for measuring, described resonance curve comprise angular displacement～frequency curve (θ～ω) and phase place～frequency curve ( ), directly obtain the viscoelasticity of corresponding liquid this driving frequency (ω) under again by every pair of data point of resonance curve, promptly angular displacement (θ) by each driving frequency (ω) correspondence and phase place (

) calculate liquid viscoelasticity (G ', G " or η).

2, the viscoelastic method of use forced resonance torsional pendulum instrument for measuring liquid continuous frequency conversion according to claim 1, the viscoelastic detailed process that it is characterized in that calculating liquid is as follows:

Calculate the real part (R that measurement liquid puts on the plane wave feature complex impedance that rocks oscillator by (1) and (2) formula _Pl) and imaginary part (X _Pl)

Wherein

θ _0air, θ _0lBe respectively the phase place and the angular displacement that measure under unloaded and the loading liquid situation, the angular frequency of ω for changing, A ₄, E ₄And E ₅Be respectively instrument parameter;

Calculate the viscoelasticity G ' and the G of liquid again by (3) and (4) formula "

$G^{\′}\left(\mathrm{\ω}\right)=\frac{{\left(R_{\mathrm{pl}}\left(\mathrm{\ω}\right)\right)}^2-{\left(X_{\mathrm{pl}}\left(\mathrm{\ω}\right)\right)}^2}{\mathrm{\ρ}}---\left(3\right)$

$G^{\′\′}\left(\mathrm{\ω}\right)=\frac{2\left(R_{\mathrm{pl}}\left(\mathrm{\ω}\right)\right)\left(X_{\mathrm{pl}}\left(\mathrm{\ω}\right)\right)}{\mathrm{\ρ}}---\left(4\right)$

Wherein, " be respectively the storage modulus and the loss modulus of liquid, ρ is a density of liquid for G ' and G.

3, the viscoelastic method of use forced resonance torsional pendulum instrument for measuring liquid continuous frequency conversion according to claim 2 is characterized in that also passing through the viscosity (η) that formula (5) calculates Newtonian liquid

$\mathrm{\η}=\frac{2R_{\mathrm{pl}}\left(\mathrm{\ω}\right)X_{\mathrm{pl}}\left(\mathrm{\ω}\right)}{\mathrm{\ω\ρ}}---\left(5\right).$

4,, it is characterized in that measured angular frequency is ω ∈ [200,550] rad/s according to claim 1 or the viscoelastic method of 2 or 3 described use forced resonance torsional pendulum instrument for measuring liquid continuous frequency conversion.

5, the viscoelastic method of use forced resonance torsional pendulum instrument for measuring liquid continuous frequency conversion according to claim 4 is characterized in that measured liquid is the Glycerine-Aqueous Solution of variable concentrations, or the polyoxyalkylene aqueous solution of variable concentrations.

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