Pipe-flow viscoelasticity measurement method

Abstract

The present invention relates to a pipe-flow viscoelasticity measurement method for measuring the viscoelasticity of a measurement target material in a pipe, and provides a pipe-flow viscoelasticity measurement method which uses dynamic oscillation applied to the flow of the target material to measure the viscoelasticity of the target material in the pipe on the basis of the amplitude Qe of the measured flow rate of the target material, the amplitude △Pe of the pressure drop, and the frequency ω of the dynamic oscillation.

Description

Pipe flow viscoelasticity measurement method

[0001] The present invention relates to a method for measuring linear viscoelasticity and nonlinear viscoelasticity of a material using dynamic oscillatory motion in response to flow rate when there is a material (fluid) to be measured in a pipe.

[0002] The flow and deformation that a material undergoes during the process of manufacturing a product have a decisive impact on the quality and characteristics of the final product, and the unique properties that a material exhibits during the process of flowing and deforming are the representative rheological properties of that material.

[0003] Secondary battery materials, including plastics, films, adhesives, fibers, and cosmetics, which have recently attracted increasing industrial interest, are complex fluids with a very complex structure consisting of a mixture of organic and inorganic substances. Since they are processed into products through complex flow and deformation processes, understanding the material's inherent rheological properties is essential in the processing process.

[0004] The method of measuring rheological properties is to use a rheometer, which is a device that measures rheological properties with high accuracy by implementing various types of flow fields, to apply deformation or stress to a material and measure the resulting stress or deformation to obtain a unique material function (rheological property).

[0005] Among various types of flow, the most commonly used experiment for measuring the intrinsic viscoelastic properties of materials is dynamic oscillatory shear. Unlike steady shear flow, which is applied in one direction, this method applies oscillatory shear deformation with a sinusoidal periodicity in both directions while fixing the angular frequency or strain amplitude, and measures the resulting stress change as a function of frequency (ω) or amplitude (γ0) as a rheological property.

[0006] When viscoelastic shear deformation is applied, the strain energy is stored as stress inside the material, which represents the elasticity of the material, and the energy given to the material is lost through energy dissipation, which represents the viscosity of the material, which is expressed as the storage modulus (G´).

[0007] Especially in industries that utilize various polymer composites, including secondary batteries, various processes exist, including mixing, coating, and printing. Therefore, changes in material properties under each process condition are a highly sensitive issue. From this perspective, real-time monitoring of the viscoelastic rheological properties (linear and nonlinear) of composite fluids can be of great help in actual process analysis and optimization.

[0008] However, conventional methods can only measure using specific rheometer fixtures (Cone and Plate: CP, Parallel Plate: PP), limiting the ability to sample and measure materials after the process is complete. Furthermore, rheometers are prohibitively expensive for installation in all industrial settings, and significant restrictions on equipment size and installation location make them unsuitable for real-time viscoelasticity monitoring across a wide range of processes.

[0009] The related technology for a method for easily predicting the pressure drop or flow rate in the corresponding flow field has been presented by the applicant in Republic of Korea Patent Publication No. 10-2018-0115606 (October 23, 2018).

[0010] The purpose of the present invention is to provide a method for measuring the viscoelasticity of a pipe flow, which can be directly installed in an actual industrial process for process control and enables real-time monitoring of the viscoelastic behavior of a fluid during the process.

[0011] The present invention relates to a pipe flow viscoelasticity measurement method for measuring the viscoelasticity of a measurement target substance in a pipe, wherein the amplitude size Q of the measured flow rate of the measurement target substance is measured by using dynamic vibration for the flow rate of the measurement target substance. e and the amplitude of the pressure drop △P e And a pipe flow viscoelasticity measurement method is provided for measuring the viscoelasticity of a measurement target material in a pipe through the frequency ω of dynamic vibration.

[0012] The pipe flow viscoelasticity measurement method according to the present invention obtains an effective energy dissipation rate coefficient and an effective shear rate coefficient based on the flow rate and pressure drop information (magnitude, phase difference) measured in the flow of the target substance in the pipe, and predicts the linear and nonlinear storage modulus and loss modulus of the target substance based on these, thereby enabling real-time monitoring of the viscoelastic behavior of the target substance.

[0013] Figure 1 is a drawing showing a pipe shape applied to a pipe flow viscoelasticity measurement method according to one embodiment of the present invention.

[0014] Figure 2 is a frequency analysis graph according to single mode and multimode of flow rate and pressure drop of a pipe flow viscoelasticity measurement method according to one embodiment of the present invention.

[0015] FIG. 3 is a diagram showing the shear rate according to an arbitrary waveform of a pipe flow viscoelasticity measurement method according to one embodiment of the present invention.

[0016] FIG. 4 is a graph comparing the results of the storage modulus G´ and the loss modulus G˝ measured according to the pipe shape in the pipe flow viscoelasticity measurement method according to one embodiment of the present invention with the values ​​of the Single-mode Maxwell fluid theory under the linear region.

[0017] FIG. 5 is a graph comparing the results of measuring the storage modulus G´ and the loss modulus G˝ according to each frequency of the ratio of each pipe length and diameter in a pipe flow viscoelasticity measurement method according to one embodiment of the present invention with the values ​​of the Single-mode Maxwell fluid theory.

[0018] Figure 6 is a simulation result comparing the storage modulus G´ and loss modulus G˝ results according to the shear rate of pipe flow according to the pipe flow viscoelasticity measurement method according to one embodiment of the present invention with the Giesekus model theoretical values.

[0019] Figure 7 is a schematic diagram showing a method for measuring pipe flow viscoelasticity according to one embodiment of the present invention.

[0020] Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the attached drawings. Prior to this, it should be noted that the terms and words used in this specification and claims should not be construed as limited to their conventional or dictionary meanings. Based on the principle that the inventor can appropriately define the concept of a term to best explain his or her invention, they should be construed as meanings and concepts consistent with the technical spirit of the present invention.

[0021] A method for measuring pipe flow viscoelasticity according to one embodiment of the present invention uses dynamic oscillatory motion for flow rate when there is a material (fluid) to be measured in the pipe as shown in FIG. 7, and measures the amplitude size Q of the flow rate in the pipe measurement section. e and the amplitude of the pressure drop △P e And the linear viscoelasticity and nonlinear viscoelasticity of a material can be measured using the frequency ω of dynamic vibration.

[0022] Here, dynamic oscillatory flow applies a sinusoidal periodic deformation to the measuring device, and the resulting stress change is measured as a function of frequency, as shown in Equation 1. The measured stress reflects a phase difference due to the material's inherent viscoelastic properties, which is known to be an intermediate form between an elastic body and a viscous fluid.

[0023]

[0024] Here, γ represents strain, γ0 represents strain amplitude, ω represents angular frequency, τ represents shear stress, τ0 represents shear stress amplitude, t represents time, and δ represents phase difference.

[0025] The measured stress can be divided into two material functions: the storage modulus G´, which represents the elasticity of the viscoelastic material, and the loss modulus G˝, which represents the viscosity, and can be expressed as in mathematical equation 2.

[0026]

[0027]

[0028] [Viscoelasticity Measurement Techniques in Pipe Flow: Linear Viscoelasticity Measurement]

[0029] Let us look at the viscoelasticity measurement technique in a pipe in more detail. A fluid with viscosity η is placed in a pipe at a flow rate Q [m 3 When the fluid flows at [ / s], the pressure drop △p in the pipe is proportional to the product of viscosity and flow rate. That is, △p∝ηQ, which can be expressed as in mathematical equation 3. If the proportionality constant of this relationship is α, α is a value determined by the shape of the pipe.

[0030]

[0031] There are various ways to obtain the shape factor α. For example, for a Newtonian fluid with experimentally known viscosity, the shape factor α can be easily obtained by measuring the pressure drop in relation to the flow rate in a pipe. Similarly, it can be easily obtained using numerical analysis methods.

[0032] At this time, shear stress and shear rate can be obtained using a flow quantification technique based on energy dissipation rate in the pipe.

[0033] The method for measuring viscoelasticity and nonlinear viscoelasticity using the above shape factor α are explained as follows.

[0034] When the flow rate Q(t) of the fluid in the pipe oscillates periodically, the mean flow rate Q0 is sufficiently small, and the fluctuating flow rate Q ε If this average flow rate is less than Q0, the pressure drop △p(t) measured in the pipe has a phase difference δ and can be expressed as in mathematical equation 4.

[0035]

[0036] Here, the relationship between the fluctuating flow rate Q´(t) and the fluctuating pressure drop △p´(t) follows the equation in mathematical formula 3. That is, the viscosity at this time is the complex viscosity η. * It can be expressed as , and can be expressed as mathematical formula 5 as follows.

[0037]

[0038] In mathematical expression 5, the amplitude of the flow rate Q ε If this is sufficiently small, the complex point η * can be expressed using the pressure drop behavior, and for the convenience of calculation, a complex number expression as in Equation 6 is introduced to obtain a complex number expression of complex viscosity as in Equation 7.

[0039]

[0040]

[0041] Using the general relationship between complex viscosity and complex modulus in linear viscoelasticity of Equation 8, expressed in Equation 7, the storage modulus G´ and the loss modulus G˝ can be obtained as in Equation 9, where G´ and G˝ are the amplitudes of the flow rate Q. ε Since is sufficiently small, it is a function of only the frequency ω.

[0042]

[0043]

[0044] Mathematical expression 9 can be used to obtain the linear viscoelasticity of a fluid by utilizing the flow rate oscillation of the fluid in the pipe.

[0045] In the problem of determining the storage modulus G´ and the loss modulus G˝, the amplitude of the flow rate Q ε This large case is called the nonlinear region, and the storage modulus G´ and the loss modulus G˝ are the amplitudes of the flow rate Q. ε It is a function of both the frequency ω and the strain, and is called nonlinear viscoelasticity.

[0046]

[0047] [Measurement of Nonlinear Viscoelasticity in Pipe Flow]

[0048] In order to obtain nonlinear viscoelasticity, the correlation between the pressure drop measured in the pipe flow and the representative shear stress of the system and the flow rate of the pipe flow and the representative shear strain of the system is obtained, and the storage modulus and loss modulus can be obtained by substituting the representative shear stress and the representative shear rate into the above mathematical equation 2.

[0049] There are various methods for obtaining representative shear stress and representative shear rate in pipe flow, but in one embodiment of the present invention, energy dissipation rate-based flow quantification, which is generally used in pipe flow, is introduced, and in this case, the shape factor α of mathematical expression 3 can be expressed more specifically.

[0050] Energy dissipation rate-based flow quantification is a dimensionless power number N. p By using the Reynolds number Re as a method to obtain the characteristic curve of pipe flow, the characteristic curve can be determined for the shape of the pipe system.

[0051] A fluid with viscosity η flows through a pipe at a flow rate Q [m 3 / s] and the pressure drop in the pipe is △p, the power P applied to the system is calculated as P=△p·Q, and this amount is equal to the total energy dissipation rate within the system in the laminar flow region. (At this time, the power is not the motor power, but the net power excluding the power loss due to friction in the seal or reducer among the motor power, and is called the total energy dissipation rate.)

[0052] Power number N p is the total energy dissipation rate divided by the characteristic energy dissipation rate in the turbulent region, and the average velocity in the pipe [m / s] ( =Q / πR 2 ), apparent shear rate of the pipe ( =4Q / πR 3 ) is expressed using the Reynolds number Re of the pipe, and if the density of the fluid is ρ, it can be expressed as in mathematical equation 10 using the variables above.

[0053]

[0054] In the laminar flow region of a Newtonian fluid with constant viscosity, the power number N p is proportional to the reciprocal of the Reynolds number Re, (i.e. N p ~Re -1) proportionality constant K p If defined as such, the correlation between the Power number and the Reynolds number can be expressed as in mathematical equation 11.

[0055]

[0056] Here, the proportionality constant K p is determined by the shape of the piping system.

[0057] If the definitions of the Power number and Reynolds number defined in Equation 10 are substituted into Equation 11, the pipe shape factor α is K as in Equation 12. p It can be expressed using , which is another method for obtaining the pipe shape factor.

[0058]

[0059] Let's look at how to obtain the effective shear stress and effective shear rate of a piping system. The effective shear stress τ of the piping eff is expressed as mathematical equation 13, and the effective shear rate γ eff is the effective shear rate velocity can be obtained from

[0060]

[0061] For steady-state flow in a piping system, flow rate Q and effective shear rate is the effective shear rate coefficient K s It can be determined proportionally to the apparent shear rate.

[0062]

[0063] The correlation in Equation 14 can be viewed as a purely geometric relationship, and can be applied in the same way to pipe flow oscillating at a frequency ω. Furthermore, since integrating the shear rate velocity over time yields the shear rate (strain), it can be expressed as in Equation 15.

[0064]

[0065] In steady-state flow in a piping system, the viscosity η and the effective shear rate velocity can be expressed as a function of flow rate.

[0066]

[0067] If we organize Equation 12 for viscosity η, It is expressed as , and when substituted into Equation 16 as in Equation 14, the effective shear stress τ eff can be obtained as in mathematical equation 17.

[0068]

[0069] We now present a method to obtain the correlation between the flow rate Q(t), the shear rate γ(t), the shear stress τ(t), and the pressure drop △p(t) in an oscillatory pressure driven flow.

[0070] Here, the effective shear rate velocity is the flow rate Q(t)=Q0+Q ε Like sin(ωt) It is expressed as , and can be expressed as a function of flow rate as in mathematical equation 18.

[0071]

[0072] Since the shear rate (strain) is obtained by integrating the shear rate over time, it can be expressed as in mathematical equation 19.

[0073]

[0074] In mathematical expression 19, the strain amplitude γ0 is the pulsating flow rate Q ε It can be seen that it can be expressed as a function of frequency ω.

[0075] Pressure drop △p(t) and effective shear stress τ effThe relationship between (t) is basically a balance of power and can be expressed by Equations 20 and 21.

[0076]

[0077]

[0078] Therefore, the effective shear stress can be obtained as follows using Equation 17.

[0079]

[0080] Shear stress τ´ of Equation 22 eff and shear rate γ of mathematical expression 19 eff,ε Using the method used in Equations 1 and 2, the complex elastic modulus G of Equation 23 is obtained. * can be obtained, and in this case, the assumption of linear viscoelasticity is not necessary, so it corresponds to a general relationship that can be applied to the case of nonlinear viscoelasticity with a large shear rate.

[0081]

[0082] For the convenience of calculation, we can organize it by introducing a complex number representation as in Equation 24.

[0083]

[0084] Then, the storage modulus G´ and loss modulus G˝ that can be applied to the nonlinear region can be obtained as follows.

[0085]

[0086] The formulas for the storage modulus G´ and the loss modulus G˝ presented in Equation 25 are obtained by substituting the shape factor α of Equation 9 into K p It is consistent with the formulas for the storage modulus G´ and the loss modulus G˝ in linear viscoelasticity expressed using , and the strain γ0 is determined by the amplitude of the flow rate pulsation as in Equation 19 or Equation 25.

[0087] That is, it can be seen that mathematical expression 9 can be applied not only to the linear region but also to the nonlinear region.

[0088]

[0089] [Example, Application to General Pipe Shapes]

[0090] The following is a look at the measurement of viscoelasticity using a general pipe such as that shown in Fig. 1.

[0091] Here, the applied pipe can be a shape with a circular cross-section and no change in shape in the longitudinal direction as in (a) of Fig. 1, a shape with a pipe that expands or contracts in the longitudinal direction as in (b) of Fig. 1, and a shape with a square cross-section as in (c) of Fig. 1, so that the viscoelasticity of the material can be measured. In addition, it goes without saying that the pipe can have any cross-sectional shape including a circle or a square, or a cross-sectional shape that changes or is bent along the length, so that the viscoelasticity of the material can be measured.

[0092] This is done by using the shape factor α used in Equation 3, or by using K instead of the pipe shape factor α as in Equation 12. p Using this, a formula can be derived as in Equation 25, and in this case, it can be applied not only to the storage modulus G´ and the loss modulus G˝ in linear viscoelasticity, but also to the nonlinear region.

[0093] First, let's look at the method of measuring the viscoelasticity of a material when the cross-section of the pipe is square using the pipe shape factor α of mathematical equation 3. As explained above, the shape factor α can be easily obtained by measuring the pressure drop for the flow rate of the pipe for a Newtonian fluid whose viscosity is experimentally known, and can also be easily obtained using a numerical analysis method in the same way.

[0094] Using the obtained shape coefficient α in Equation 9, the viscoelasticity of the fluid can be measured.

[0095] And, briefly explaining the method of obtaining the storage modulus G´ and the loss modulus G˝ when the pipe is expanded and contracted in the longitudinal direction, the flow quantification technique based on the energy dissipation rate described above is used in the same way, and the deformation imposed through the complex viscosity expression can be obtained by dividing it into the In phase and Out of phase.

[0096] For expansion / reduction pipes, Power number N is based on the pipe inlet shape. p and Reynolds number, apparent shear rate velocity It is defined as in mathematical equation 26.

[0097]

[0098] In this piping system, a fluid with viscosity η flows through the pipe at a flow rate Q [m 3 / s] and the pressure drop in the pipe is △p, the power P applied to the system is calculated as P=△p·Q, and the power per unit volume can be expressed as in mathematical equation 27.

[0099]

[0100] By substituting Equation 26 into Equation 11, which is the relationship between the Power number and the Reynolds number, and organizing it for the pressure drop △p, it can be written as Equation 28.

[0101]

[0102] Equation 28 can be written for the fluctuating flow rate Q´(t) and the fluctuating pressure drop △p´(t), and the complex viscosity η * can be expressed using the pressure drop behavior. For the convenience of calculation, a complex number expression is introduced as in Equation 29, and a complex number expression of the complex viscosity can be obtained as in Equation 30.

[0103]

[0104]

[0105] Using the general correlation between complex viscosity and complex modulus in linear viscoelasticity of Equation 31, expressed in Equation 30, the storage modulus G´ and the loss modulus G˝ can be obtained as in Equation 32, where G´ and G˝ are the amplitudes of the flow rate Q. ε Since is sufficiently small, it is a function of only the frequency ω.

[0106]

[0107]

[0108] Mathematical expression 32 can be used to obtain the viscoelasticity of a fluid by utilizing the flow rate oscillation of the fluid in the expansion / contraction pipe.

[0109] And, the viscoelasticity measurement technique in the pipe flow of the present invention showed that viscoelasticity measurement is possible when the flow rate Q(t) and the pressure drop △p(t) are a single frequency and a complete sine wave (single mode), as shown in Fig. 2 (a). The viscoelasticity measurement method in the case where multiple frequencies are synthesized (multimode) in a pipe system, as shown in Fig. 2 (b), is described as follows.

[0110] Figure 2 (a) is a diagram showing a single mode, which is a single frequency and a complete sine wave, and Figure 2 (b) is a diagram showing a multimode, which is a composite of multiple frequencies. In the case of a single mode, measurement is possible using the viscoelasticity measurement technique in pipes presented above, and in the case of a multimode, since multiple frequencies are composited, frequency analysis must be performed using FFT (Fast Fourier Transform).

[0111] The frequency ω is synthesized by performing FFT (Fast Fourier Transform) on both the flow rate Q(t) and the pressure drop △p(t). i , the magnitude of the frequency component Q ε,i ,△p ε,i and phase difference δ ican be obtained, and the flow rate Q(t) and pressure drop △p(t) can be obtained using mathematical expression 33.

[0112]

[0113] Frequency ω i , the magnitude of the frequency component Q ε,i ,△p ε,i and phase difference δ i Since all of them are obtained, we use mathematical expression 9 using the shape factor α of the pipe, or the energy dissipation rate coefficient K. p Using mathematical equation 25, the storage modulus G´ and the loss modulus G˝ corresponding to each frequency can be calculated simultaneously.

[0114] And, as shown in Fig. 3, the method for measuring viscoelasticity in an arbitrary wave in a piping system is described as follows.

[0115] Any waveform with a period like that of Fig. 3 can be expressed as a Fourier series by decomposing it into the weights of trigonometric functions. If Fig. 3 is expressed using a Fourier series, the shear rate magnitude γ is as in Equation 34. n,0 , expressed as frequency ηㆍω.

[0116]

[0117] The stress change due to the shear rate as in Equation 34 is the stress magnitude γτ as in Equation 35. n,0 , frequency nㆍω, phase difference δ n It is expressed as . Theoretically, it can be expressed using a Fourier series and extended to infinity. However, for the convenience of calculation and to implement a viscoelastic monitoring system in practice, a range other than infinity must be specified.

[0118]

[0119] Frequency nㆍω, magnitude of frequency component γ n,0, τ n,0 and phase difference δ nSince all of them are obtained, we use Equation 2 or obtain the shape factor α or energy dissipation rate coefficient K by obtaining the correlation between the flow rate Q(t) and shear rate γ(t), shear stress τ(t) and pressure drop △p(t) in the oscillatory pressure driven flow described above. p The storage modulus G´ and loss modulus G˝ can be obtained using .

[0120] As explained above, in the viscoelastic monitoring system, when a flow rate input of an arbitrary waveform with a period is given, the phase difference δ is output similar to Equation 35. n A pressure waveform with is shown. In order to obtain the viscoelastic properties in the viscoelastic monitoring system, an arbitrary waveform given as input is used as a Fourier series to obtain the shear rate magnitude γ within a certain frequency range. n,0 , the frequency nㆍω can be known, and the Fourier series can be used to derive the stress magnitudeτ within the same constant frequency range for the arbitrary waveform response displayed as the output. n,0 , frequency nㆍω, phase difference δ n can be obtained. In this way, the input and output are expressed as arbitrary waveforms with a period, and the input and output can be used to obtain information within a certain frequency range using the Fourier series, thereby obtaining the viscoelastic characteristics. In the case of a viscoelastic monitoring system, a low-pass filter can be used to attenuate signals with frequencies above a specific cutoff frequency, allowing only signals with frequencies below the cutoff frequency to pass.

[0121] Shape factor α or energy dissipation rate coefficient K in these various pipe shapes (straight pipes with circular, square, and rectangular cross sections, pipes that expand / contract in the longitudinal direction) p We performed a viscoelasticity measurement simulation to obtain the result, and compared the linear viscoelasticity simulation results and theoretical values ​​for each shape.

[0122] α and K of the used pipep The values ​​are presented in Table 1, and the linear viscoelasticity data measured using them are presented in Fig. 4. Fig. 4 also presents the linear viscoelasticity theory values ​​using a single-mode Maxwell fluid. Here, Fig. 4 is a comparison data of the single-mode Maxwell fluid theory values ​​and the storage modulus G´ and loss modulus G˝ measurement results according to each frequency of each pipe shape. Fig. 4 (a) shows a circular cross-section straight pipe, Fig. 4 (b) shows a pipe that expands / contracts in the longitudinal direction, Fig. 4 (c) shows a square cross-section straight pipe, and Fig. 4 (d) shows a rectangular cross-section straight pipe.

[0123] Figure 4 compares the storage modulus G´ and loss modulus G˝ measured in the linear region (small amplitude oscillatory shear, SAOS) with the single-mode Maxwell fluid theory values ​​and four types of pipe shapes (straight pipes with circular, square, and rectangular cross-sections, and pipes that expand / contract in the longitudinal direction), and shows very high consistency.

[0124] Circular expansion / contraction square rectangle α--7.13×10 9 6.24×10 8 K p 42.06--K s 0.8020.17--

[0125] Table 1 shows the shape factor α and effective energy dissipation rate coefficient K according to the shape of each pipe (straight pipe with circular, square, and rectangular cross-sections, and extended pipe with R2 / R1=2) measured through simulation. p , effective shear rate coefficient K s This is a table showing the values. At this time, Table 2 shows the parameter values ​​of the model used in the simulation.

[0126] η s [P a ·s]η p [P a·s]λ[s]α[-]sing-mode Maxwell0.50.50.5-Giesekus0.50.50.50.5

[0127] Linear viscoelasticity data for various pipe shapes were presented previously, and in the case of Fig. 5, viscoelasticity measurement simulations were performed according to the length of the pipe, and the linear viscoelasticity simulation results were compared with the Single-mode Maxwell fluid theory values. Fig. 5 is a comparison data of the Single-mode Maxwell fluid theory values ​​and the storage modulus G´ and loss modulus G˝ measurement results according to each frequency of the ratio of each pipe length and diameter.

[0128] Here, (a) of Fig. 5 is the storage elastic modulus G´ when the relaxation time is 0.5 [s], and (b) of Fig. 5 is the loss elastic modulus G˝ when the relaxation time is 0.5 [s].

[0129] Figure 5 shows linear viscoelasticity data according to each frequency of each pipe length, and even if the length increases, each frequency is 10. 1 It can be confirmed that the storage modulus G´ and the loss modulus G˝ show high consistency with the theoretical values. In addition, as can be seen from the results in Figure 5, it can be confirmed that the length of the pipe has a minimal effect on the linear viscoelasticity measurement.

[0130] The above results support the fact that linear and nonlinear viscoelastic data measured under oscillatory shear flow, which was considered to be the exclusive property of expensive, state-of-the-art equipment such as rheometers, can very accurately predict viscoelastic rheological properties of fluids used in pipe flow using one embodiment of the present invention without a rheometer.

[0131] Additionally, by selecting a variety of pipe shapes and lengths, problems such as end collapse, difficulty in sample loading, and high-shear region problems can all be solved.

[0132] The Giesekus model, a viscoelastic fluid model, was used for simulations to measure the nonlinear viscoelasticity of pipe flow. Figure 6 compares the theoretical values ​​of the Giesekus model used with the nonlinear viscoelasticity (LAOS) data according to the shear rate of pipe flow.

[0133] In the case of the Giesekus model theoretical values ​​presented in Fig. 6, the constitutive equations of the Giesekus model in simple shear flow were expanded for each component and solved by establishing a system of ordinary differential equations. Afterwards, the storage modulus G´ and the loss modulus G˝ were presented using the previously described mathematical expression 2, and the storage modulus G´ and the loss modulus G˝ according to the shear rate of the pipe flow with a circular cross-section were presented.

[0134] In the case of the storage modulus G´ and the loss modulus G˝ in a pipe with a circular cross-section, the nonlinear viscoelasticity mathematical equation 19 described above was used, and this equation is consistent with the equations for the storage modulus G´ and the loss modulus G˝ in linear viscoelasticity of mathematical equation 9. That is, Fig. 6 shows that it can be applied not only in the linear region but also in the nonlinear region.

[0135] While the present invention has been described with reference to the embodiments illustrated in the drawings, these are merely exemplary, and those skilled in the art will appreciate that various modifications and equivalent alternative embodiments are possible. Therefore, the true scope of technical protection of the present invention should be determined by the technical spirit of the appended claims.

Claims

1. In a pipe flow viscoelasticity measurement method for measuring the viscoelasticity of a target material in a pipe, Using the dynamic vibration of the flow rate of the above-mentioned measurement target substance, the amplitude size Q of the flow rate of the above-mentioned measurement target substance is measured. e and the amplitude of the pressure drop △p e A pipe flow viscoelasticity measurement method for measuring the viscoelasticity of a target material in the pipe through the frequency ω of dynamic vibration.

2. In claim 1, The viscosity of the above-mentioned measured material is η, and the flow rate Q [m in the pipe 3 When flowing with [ / s], The pressure drop △p of the above pipe is derived from the shape factor α of the pipe, and the complex viscosity η of the material to be measured is calculated using the fluctuating pressure drop △p´(t) calculated through the fluctuating flow rate Q´(t). * Steps to derive, The above complex point η * A step of deriving the storage modulus G´ and the loss modulus G˝ from Effective shear stress τ of the above pipe eff , effective shear rate velocity and the effective shear rate γ eff A method for measuring pipe flow viscoelasticity, comprising the steps of deriving a .

3. In claim 2, The above pressure drop △p is derived through the mathematical formula △p=αηQ, The above fluctuating flow rate Q´(t) is expressed by the mathematical formula Q´(t)=Q ε It is derived through sin(ωt), The above variable pressure drop △p´(t) is expressed by the mathematical formula △p´(t) = △p ε sin(ωt+δ)=αη * A method for measuring pipe flow viscoelasticity derived through Q´(t).

4. In claim 2, The above complex point η * is a mathematical formula is derived through, The above storage modulus G´ and loss modulus G˝ are expressed by mathematical formulas A method for measuring the pipe flow viscoelasticity derived through .

5. In claim 2, Effective shear stress τ of the above pipe eff is a mathematical formula is derived through, The above effective shear rate velocity is a mathematical formula is derived through, The effective shear rate γ above eff is a mathematical formula A method for measuring the pipe flow viscoelasticity derived through .

6. In claim 2, The shape factor α and pressure drop △p of the above pipe are proportional constants K through flow quantification based on energy dissipation rate. p A method for measuring pipe flow viscoelasticity derived using .

7. In claim 6, The above pressure drop △p is given by the mathematical formula is derived through, The shape factor α of the above pipe is given by the mathematical formula A method for measuring the pipe flow viscoelasticity derived through .

8. In claim 1, The above pipe is a method for measuring the flow viscoelasticity of a pipe having a circular cross-section.

9. In claim 1, The above pipe is a method for measuring the flow viscoelasticity of a pipe having a rectangular cross-section.

10. In claim 1, The above pipe is a method for measuring the flow viscoelasticity of a pipe having a cross-sectional shape in which the diameter expands or contracts in the longitudinal direction.

11. In claim 1, The above pipe is a method for measuring the flow viscoelasticity of a pipe having an arbitrary cross-sectional shape including a circle or a square.

12. In claim 1, The above pipe is a method for measuring the flow viscoelasticity of a pipe having a cross-sectional shape that changes along its length or has a curved shape.

13. In claim 2, A method for measuring pipe flow viscoelasticity by performing frequency analysis of the flow rate Q(t) and pressure drop △p(t) using FFT (Fast Fourier Transform) in a multi-mode where the flow rate in the above pipe is synthesized at multiple frequencies.

14. In claim 2, A method for measuring pipe flow viscoelasticity using a Fourier series when the flow rate in the above pipe is expressed as an arbitrary waveform having a period.

15. In claim 14, A method for measuring pipe flow viscoelasticity by using a Fourier series within a certain frequency range for input and output in the above pipe when the input and output are expressed as arbitrary waveforms.

16. In claim 14, A pipe flow viscoelasticity measurement method that uses a low-pass filter to attenuate signals with frequencies higher than a specific cutoff frequency when implementing a viscoelasticity monitoring system, thereby passing only signals with frequencies lower than the cutoff frequency.

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