Prediction method of adhesive shelf life

The critical centrifugal conditions of the adhesive were measured by centrifugation and converted into storage period, which solved the problem of long time to determine the adhesive storage stability and the inability to predict the storage period, and achieved a fast and accurate storage period evaluation.

CN114965250BActive Publication Date: 2025-02-14TECHSTORM MATERIAL TECH SHANGHAI CO LTD
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Patent Information

Application Number
CN202210545871.6
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2022-05-19
Publication Date
2025-02-14
Estimated Expiration
2042-05-19

AI Technical Summary

Technical Problem

In the prior art, the adhesive storage stability measurement time is long, and the adhesive storage period cannot be clearly predicted.

Method used

Critical centrifugal conditions (critical centrifugal time and rotation speed) were measured by placing the adhesive sample in a centrifugal tube and converting the critical centrifugal time into storage period.

Benefits of technology

It realizes rapid acquisition of the storage time of adhesive samples, and provides more accurate data for the performance evaluation of adhesives, solving the problem of long measurement time and unpredictable storage period.

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Abstract

The present invention provides a method for predicting the storage period of an adhesive, comprising the following steps: placing an adhesive sample in a centrifuge tube, placing the centrifuge tube in a centrifuge for centrifugal operation to measure the critical centrifugal condition of the adhesive sample, wherein the critical centrifugal condition includes a critical centrifugal time and a critical centrifugal speed; and multiplying the critical centrifugal time by a conversion coefficient to obtain the storage period of the adhesive sample. The present invention solves the problem that the measurement time of the adhesive storage stability in the prior art is relatively long, and the measurement method of the adhesive storage stability cannot clearly obtain the adhesive storage period.
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Description

Technical Field

[0001] The invention relates to the technical field of adhesives, and in particular to a method for predicting the storage period of an adhesive. Background Art

[0002] The composition of adhesive includes main part and additive part. The main part includes cross-linkable high molecular oligomer and curing agent. The additive part is mainly added according to different performance requirements, among which inorganic mineral fillers are the main ones. The addition of fillers can improve the physical properties of the cured product and reduce the production cost. The most common preparation method of adhesive is to first add fillers to oligomer liquid, and then add curing agent to cure it.

[0003] Storage stability is an important indicator for evaluating the quality of adhesives. In the prior art, there are a variety of methods for measuring the storage stability of adhesives. The adhesive storage stability detection method usually observes the appearance after a certain period of storage or applies it to measure the changes in viscosity and strength, which requires natural placement for 3 months, 6 months or 12 months, which is very uneconomical. Although storage stability can also be tested by accelerated thermal aging, this method still takes a long time to measure the storage stability of the adhesive, and the method for measuring the storage stability of the adhesive cannot clearly determine the shelf life of the adhesive, and there is no method in the prior art that can predict the shelf life of the adhesive.

[0004] Therefore, it is necessary to develop a method for predicting the shelf life of adhesives to solve the above problems existing in the prior art. Summary of the invention

[0005] The purpose of the present invention is to provide a method for predicting the storage period of an adhesive, which solves the problem in the prior art that the determination time of the adhesive storage stability is long and the determination method of the adhesive storage stability cannot clearly determine the adhesive storage period.

[0006] To achieve the above object, the present invention provides a method for predicting the shelf life of an adhesive, comprising the following steps:

[0007] S100: placing an adhesive sample in a centrifuge tube, placing the centrifuge tube in a centrifuge for centrifugation to measure a critical centrifugation condition of the adhesive sample, wherein the critical centrifugation condition includes a critical centrifugation time and a critical centrifugation speed;

[0008] S200: converting the critical centrifugation time into the adhesive sample storage period.

[0009] The beneficial effect of the adhesive storage stability evaluation method of the present invention is that the critical centrifugation time is converted into the adhesive sample storage period, the storage time of the adhesive sample can be quickly obtained, and more accurate data is provided for the evaluation of adhesive performance. The present invention solves the problem that the measurement time of adhesive storage stability in the prior art is long and the measurement method of adhesive storage stability cannot clearly derive the adhesive storage period.

[0010] Optionally, in step S200, the step of converting the critical centrifugation time into the adhesive sample storage period includes: multiplying the critical centrifugation time by a conversion coefficient to obtain the adhesive sample storage period.

[0011] Optionally, an average rotation radius calculation step is also included between step S100 and step S200, and the average rotation radius calculation step includes: measuring the minimum rotation radius of the adhesive sample in the centrifuge tube under the critical centrifugal conditions and the maximum rotation radius of the adhesive sample, and calculating the arithmetic mean of the minimum rotation radius and the maximum rotation radius to obtain the average rotation radius.

[0012] Optionally, the step S200 also includes the conversion coefficient calculation step, and the conversion coefficient calculation step includes: dividing the critical centrifugal sedimentation velocity by the gravitational sedimentation velocity to obtain the conversion coefficient.

[0013] Optionally, step S200 also includes the critical centrifugal sedimentation velocity calculation step, and the critical centrifugal sedimentation velocity calculation step includes: multiplying the square of the critical centrifugal angular velocity, the sedimentation velocity conversion coefficient and the average rotation radius to obtain the critical centrifugal sedimentation velocity, and the critical centrifugal angular velocity is converted from the critical centrifugal rotation speed.

[0014] Optionally, the step S200 also includes the gravitational sedimentation velocity calculation step, and the gravitational sedimentation velocity calculation step includes: multiplying the sedimentation velocity conversion coefficient by the gravitational acceleration to obtain the gravitational sedimentation velocity.

[0015] Optionally, the critical centrifugal speed ranges from 1000 to 10000 r / min, and the critical centrifugal time ranges from 5 to 60 min.

[0016] Optionally, the sedimentation velocity conversion coefficient is calculated by a sedimentation velocity conversion coefficient calculation formula, and the sedimentation velocity conversion coefficient calculation formula is as follows:

[0017]

[0018] Wherein, the adhesive sample is composed of filler and liquid, wherein, A is the sedimentation velocity conversion coefficient; dp is the diameter of the packing; the ρ p is the density of the filler; the ρ m is the density of the liquid; and η is the viscosity of the adhesive sample.

[0019] Optionally, the calculation formula for the storage period of the adhesive sample is:

[0020]

[0021] Among them, in the formula, the t g is the shelf life of the adhesive, and v s is the critical centrifugal sedimentation velocity, the v g is the gravity sedimentation velocity, and t s is the critical centrifugal time, ω is the critical centrifugal angular velocity, and r av is the average rotation radius, g is the gravitational acceleration, and N is the critical centrifugal speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 is a flow chart of a prediction method in an embodiment of the present invention;

[0023] Figure 2 Schematic diagram of the structure of the centrifuge tube and the centrifuge in the embodiment of the present invention. DETAILED DESCRIPTION

[0024] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention. Unless otherwise defined, the technical terms or scientific terms used herein should be understood by people with general skills in the field to which the present invention belongs. "Including" and similar words used in this article mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects.

[0025] Figure 1 Flow chart of the prediction method in an embodiment of the present invention.

[0026] In an embodiment of the present invention, a method for predicting the shelf life of an adhesive is provided, referring to Figure 1 , including the following steps:

[0027] S100: placing an adhesive sample in a centrifuge tube, placing the centrifuge tube in a centrifuge for centrifugation to measure a critical centrifugation condition of the adhesive sample, wherein the critical centrifugation condition includes a critical centrifugation time and a critical centrifugation speed;

[0028] S200: converting the critical centrifugation time into the adhesive sample storage period.

[0029] Specifically, by converting the critical centrifugation time into the storage period of the adhesive sample, the storage period of the adhesive sample can be quickly obtained, and more accurate data can be provided for the evaluation of adhesive performance. The present invention solves the problem in the prior art that the determination time of adhesive storage stability is long and the determination method of adhesive storage stability cannot clearly deduce the adhesive storage period.

[0030] In some possible embodiments of the present invention, the criterion for determining the critical centrifugation condition is: the centrifugation condition of the centrifuge corresponding to when obvious liquid precipitation occurs in the adhesive sample in the centrifuge tube is the critical centrifugation condition.

[0031] In some other possible embodiments of the present invention, the criterion for judging the critical centrifugal condition is: the centrifugal condition of the centrifuge corresponding to when liquid precipitation occurs in the adhesive sample in the centrifuge tube and the filler in the adhesive sample settles is the critical centrifugal condition.

[0032] In some possible embodiments of the present invention, in the step S200, the step of converting the critical centrifugation time into the adhesive sample storage period includes: multiplying the critical centrifugation time by a conversion coefficient to obtain the adhesive sample storage period.

[0033] In some possible embodiments of the present invention, the storage period of the adhesive sample is calculated by a storage period calculation formula, and the storage period calculation formula is as follows:

[0034]

[0035] Among them, in the formula, the t g is the shelf life of the adhesive, and v s is the critical centrifugal sedimentation velocity, the v g is the gravity sedimentation velocity, and t s is the critical centrifugal time, ω is the critical centrifugal angular velocity, and r av is the average rotation radius, and g is the gravitational acceleration.

[0036] In some possible embodiments of the present invention, an average rotation radius calculation step is also included between step S100 and step S200, and the average rotation radius calculation step includes: measuring the minimum rotation radius of the adhesive sample in the centrifuge tube under the critical centrifugal conditions and the maximum rotation radius of the adhesive sample, and calculating the arithmetic mean of the minimum rotation radius and the maximum rotation radius to obtain the average rotation radius.

[0037] Figure 2 Schematic diagram of the structure of the centrifuge tube and the centrifuge in the embodiment of the present invention.

[0038] In some possible embodiments of the present invention, referring to Figure 2 The centrifuge tube 2 is placed in the centrifuge 1, the angle between the central axis 3 of the centrifuge 1 and the center line 4 of the centrifuge tube 2 is α, and the shortest distance from the centrifuge tube 2 to the central axis 3 is the minimum rotation radius, which is r min The farthest distance from the centrifuge tube 2 to the central axis 3 is the maximum rotation radius, which is r max The average rotation radius from the centrifuge tube 2 to the central axis 3 is the arithmetic mean of the minimum rotation radius and the maximum rotation radius, that is, r av .

[0039] In some embodiments of the present invention, the angle α between the central axis 3 of the centrifuge 1 and the central line 4 of the centrifuge tube 2 can affect the obvious liquid precipitation of the adhesive sample.

[0040] In some other specific embodiments of the present invention, the angle α between the central axis 3 of the centrifuge 1 and the center line 4 of the centrifuge tube 2 is in the range of 25° to 45°.

[0041] In some specific embodiments of the present invention, the angle α between the central axis 3 of the centrifuge 1 and the center line 4 of the centrifuge tube 2 is any one of 25°, 27°, 29°, 30°, 33°, 35°, 37°, 39°, 41°, 43° and 45°.

[0042] In some more specific embodiments of the present invention, the angle α between the central axis 3 of the centrifuge 1 and the center line 4 of the centrifuge tube 2 is 30°.

[0043] In some possible embodiments of the present invention, the step S200 further includes the conversion coefficient calculation step, and the conversion coefficient calculation step includes: dividing the critical centrifugal sedimentation velocity by the gravitational sedimentation velocity to obtain the conversion coefficient.

[0044] In some possible embodiments of the present invention, the conversion coefficient is calculated by a conversion coefficient calculation formula, and the conversion coefficient calculation formula is as follows:

[0045]

[0046] Wherein, B is the conversion coefficient, v s is the critical centrifugal sedimentation velocity, the v g is the gravity sedimentation velocity, ω is the critical centrifugal angular velocity, and r av is the average rotation radius, and g is the gravitational acceleration.

[0047] In some possible embodiments of the present invention, step S200 also includes the critical centrifugal sedimentation velocity calculation step, and the critical centrifugal sedimentation velocity calculation step includes: multiplying the square of the critical centrifugal angular velocity, the sedimentation velocity conversion coefficient and the average rotation radius to obtain the critical centrifugal sedimentation velocity, and the critical centrifugal angular velocity is converted from the critical centrifugal rotation speed.

[0048] In some possible embodiments of the present invention, the critical centrifugal sedimentation velocity is calculated by a critical centrifugal sedimentation velocity calculation formula, and the critical centrifugal sedimentation velocity calculation formula is as follows:

[0049]

[0050] Among them, in the formula, the v s is the critical centrifugal sedimentation velocity, the d p is the diameter of the packing; the ρ p is the density of the filler; the ρ m is the density of the liquid; η is the viscosity of the adhesive sample, ω is the critical centrifugal angular velocity, and r av is the average radius of rotation.

[0051] In some possible embodiments of the present invention, the critical centrifugal angular velocity is obtained by converting the critical centrifugal speed, and the critical centrifugal angular velocity conversion formula is as follows:

[0052]

[0053] Wherein, in the formula, ω is the critical centrifugal angular velocity, and N is the critical centrifugal speed.

[0054] In some possible embodiments of the present invention, the step S200 further includes the gravitational settling velocity calculation step, and the gravitational settling velocity calculation step includes: multiplying the settling velocity conversion coefficient by the gravitational acceleration to obtain the gravitational settling velocity.

[0055] In some possible embodiments of the present invention, the gravity settling velocity is calculated by a gravity settling velocity calculation formula, and the gravity settling velocity calculation formula is as follows:

[0056]

[0057] Among them, in the formula, the v g is the gravity sedimentation velocity, the d p is the diameter of the packing; the ρ p is the density of the filler; the ρ m is the density of the liquid; η is the viscosity of the adhesive sample, and g is the acceleration due to gravity.

[0058] In some possible embodiments of the present invention, the sedimentation velocity conversion coefficient is calculated by a sedimentation velocity conversion coefficient calculation formula, and the sedimentation velocity conversion coefficient calculation formula is as follows:

[0059]

[0060] Wherein, the adhesive sample is composed of filler and liquid, wherein, A is the sedimentation velocity conversion coefficient; d p is the diameter of the packing; the ρ p is the density of the filler; the ρ m is the density of the liquid; and η is the viscosity of the adhesive sample.

[0061] In some possible embodiments of the present invention, the critical centrifugal angular velocity conversion formula is substituted into the storage period calculation formula to obtain the calculation formula for the adhesive storage period. The calculation formula for the adhesive sample storage period is as follows:

[0062]

[0063] Among them, in the formula, the t g is the shelf life of the adhesive, and v s is the critical centrifugal sedimentation velocity, the v g is the gravity sedimentation velocity, and t s is the critical centrifugal time, ω is the critical centrifugal angular velocity, and r av is the average rotation radius, g is the gravitational acceleration, and N is the critical centrifugal speed.

[0064] In some possible embodiments of the present invention, the critical centrifugal speed ranges from 1000 to 10000 r / min, and the critical centrifugal time ranges from 5 to 60 min.

[0065] Example

[0066] The manufacturers and models or brands of the instruments used in the embodiments of the present invention are shown in Table 1.

[0067] Table 1 Manufacturer and model or brand of the instrument

[0068]

[0069] In some specific embodiments of the present invention, the adhesive sample used is selected from the TS 385 series products of Daosheng Tianhe Materials Technology (Shanghai) Co., Ltd.

[0070] Adhesive sample 1 is TS 385H; adhesive sample 2 is TS 385M; and adhesive sample 3 is TS385L. They are referred to as sample 1, sample 2, and sample 3 below.

[0071] The gravity settling velocity calculation formula is: Among them, in the formula, the v g is the gravity sedimentation velocity, the d p is the diameter of the packing; the ρ p is the density of the filler; the ρ m is the density of the liquid; η is the viscosity of the adhesive sample, and g is the acceleration due to gravity.

[0072] The critical centrifugal sedimentation velocity calculation formula is: Among them, in the formula, the v s is the critical centrifugal sedimentation velocity, the d p is the diameter of the packing; the ρ p is the density of the filler; the ρ m is the density of the liquid; η is the viscosity of the adhesive sample, ω is the critical centrifugal angular velocity, and r av is the average radius of rotation.

[0073] The calculation formula of the sedimentation velocity conversion coefficient is: Wherein, A is the sedimentation velocity conversion coefficient; d p is the diameter of the packing; the ρ p is the density of the filler; the ρ m is the density of the liquid; and η is the viscosity of the adhesive sample.

[0074] The conversion coefficient calculation formula is: Among them, in the formula, the v g is the gravity sedimentation velocity, the v s is the critical centrifugal sedimentation velocity, ω is the critical centrifugal angular velocity, and r av is the average rotation radius, and g is the gravitational acceleration.

[0075] The storage period calculation formula is: Among them, in the formula, the t g is the shelf life of the adhesive, and v s is the critical centrifugal sedimentation velocity, the v gis the gravity sedimentation velocity, and t s is the critical centrifugal time, ω is the critical centrifugal angular velocity, and r av is the average rotation radius, and g is the gravitational acceleration.

[0076] The critical centrifugal angular velocity conversion formula is: Wherein, in the formula, ω is the critical centrifugal angular velocity, and N is the critical centrifugal speed.

[0077] Accurately measure sample 1, sample 2 and sample 3 respectively, and put them into three sample cups respectively, then put the three sample cups into the sample mixer, and mix them evenly by vacuuming to eliminate the influence of bubbles on the subsequent test. The mixing speed is 2000 rpm and the time is 2 minutes. After mixing, take out sample 1 to be evaluated, sample 2 to be evaluated and sample 3 to be evaluated;

[0078] Weigh the same mass of the sample to be evaluated and water and put them into a centrifuge tube, tighten the tube cover, and symmetrically put the two centrifuge tubes into the centrifuge sleeve, set the centrifugation condition as follows: centrifuge at 1000rpm for 30min, take out the sample 1 to be evaluated, the sample 2 to be evaluated and the sample 3 to be evaluated in the centrifuge tube to observe whether obvious liquid precipitation occurs, if the sample to be evaluated does not have obvious liquid precipitation, then put the corresponding sample to be evaluated into a new centrifuge tube and re-centrifuge, wherein the speed of the centrifuge is increased until the sample to be evaluated that has not had obvious liquid precipitation has obvious liquid precipitation, and record the centrifugation condition of the centrifuge corresponding to the obvious liquid precipitation of the sample to be evaluated, which is the critical centrifugation condition of the sample to be evaluated, and the critical centrifugation condition includes critical centrifugation speed and critical centrifugation time, and the data are recorded in Table 2;

[0079] The minimum rotation radius of the sample 1 to be evaluated and the maximum rotation radius of the sample 1 to be evaluated, the minimum rotation radius of the sample 2 to be evaluated and the maximum rotation radius of the sample 2 to be evaluated, the minimum rotation radius of the sample 3 to be evaluated and the maximum rotation radius of the sample 3 to be evaluated in the centrifuge tube under the critical centrifugal condition are measured, and the average rotation radius is obtained by calculating the arithmetic mean of the minimum rotation radius and the maximum rotation radius, and the average rotation radius of the sample 1 to be evaluated, the average rotation radius of the sample 2 to be evaluated and the average rotation radius of the sample 3 to be evaluated are recorded in Table 2;

[0080] The gravitational acceleration, the measured critical centrifugal time, the measured critical centrifugal speed and the calculated average rotation radius are substituted into the calculation formula of the adhesive storage period, thereby calculating the storage period of sample 1, the storage period of sample 2 and the storage period of sample 3. The calculation results are shown in Table 2.

[0081] The calculation formula for the storage period of the adhesive sample is:

[0082]

[0083] Among them, in the formula, the t g is the shelf life of the adhesive, and v s is the critical centrifugal sedimentation velocity, the v g is the gravity sedimentation velocity, and t s is the critical centrifugal time, ω is the critical centrifugal angular velocity, and r av is the average rotation radius, g is the gravitational acceleration, and N is the critical centrifugal speed.

[0084] Table 2 Test data and storage period of samples after centrifugation test

[0085] Sample 1 Sample 2 Sample 3 Critical centrifugal speed N (rpm) 10000 6000 4000 <![CDATA[Critical centrifugation time t s (min)]]> 30 30 30 <![CDATA[Minimum rotation radius r min (cm)]]> 6.1 5.3 5.5 <![CDATA[Maximum rotation radius r max (cm)]]> 9.9 9.9 9.9 <![CDATA[Average radius of rotation r av (cm)]]> 8.0 7.6 7.7 <![CDATA[Storage period t of the adhesive g (days)]]> 171 67 29 Actual values ​​for the shelf life of adhesives 179 71 32

[0086] The storage stability of the sample can be judged by the critical centrifugal speed of each sample. From the test results in Table 2, it can be seen that the critical centrifugal speed of sample 1 is 10000rpm, the critical centrifugal speed of sample 2 is 6000rpm, and the critical centrifugal speed of sample 3 is 4000rpm. It can be seen that the storage stability of sample 1 is the best, the storage stability of sample 2 is poor, and the storage stability of sample 3 is the worst; at the same time, the adhesive storage period is calculated by the formula, and the calculated value of the adhesive storage period is that the adhesive storage period of sample 1 is the longest, which can reach 171 days, the adhesive storage period of sample 2 is poor, which is 67 days, and the adhesive storage period of sample 3 is the worst, which is 29 days. By comparing the calculated value of the adhesive storage period with the actual value of the adhesive storage period shown in Table 2, it can be seen that the calculated value of the adhesive storage period is very close to the actual value of the adhesive storage period. It can be seen that the adhesive storage period prediction method provided by the present invention can predict the adhesive storage period more accurately.

[0087] Although the embodiments of the present invention are described in detail above, it is obvious to those skilled in the art that various modifications and variations can be made to these embodiments. However, it should be understood that such modifications and variations are within the scope and spirit of the present invention as described in the claims. Moreover, the present invention described herein may have other embodiments and may be implemented or realized in a variety of ways.

Claims

1. A method for predicting the shelf life of an adhesive, characterized in that: The method comprises the following steps: S100: placing an adhesive sample in a centrifuge tube, placing the centrifuge tube in a centrifuge for centrifugation to measure the critical centrifugation condition of the adhesive sample, wherein the critical centrifugation condition includes a critical centrifugation time and a critical centrifugation speed; S200: converting the critical centrifugation time into a storage period of the adhesive sample; In step S200, the step of converting the critical centrifugation time into the adhesive sample storage period includes: multiplying the critical centrifugation time by a conversion coefficient to obtain the adhesive sample storage period; The step S100 and the step S200 further include an average rotation radius calculation step, which includes: measuring the minimum rotation radius of the adhesive sample in the centrifuge tube under the critical centrifugal condition and the maximum rotation radius of the adhesive sample, and calculating the arithmetic mean of the minimum rotation radius and the maximum rotation radius to obtain the average rotation radius; The step S200 also includes the conversion coefficient calculation step, which includes: dividing the critical centrifugal sedimentation velocity by the gravitational sedimentation velocity to obtain the conversion coefficient; The step S200 further includes a critical centrifugal sedimentation velocity calculation step, wherein the critical centrifugal sedimentation velocity calculation step includes: multiplying the square of the critical centrifugal angular velocity, the sedimentation velocity conversion coefficient and the average rotation radius to obtain the critical centrifugal sedimentation velocity, wherein the critical centrifugal angular velocity is converted from the critical centrifugal rotation speed; The step S200 also includes the gravitational settling velocity calculation step, which includes: multiplying the settling velocity conversion coefficient by the gravitational acceleration to obtain the gravitational settling velocity.

2. The method for predicting the adhesive shelf life according to claim 1, characterized in that: The critical centrifugal speed ranges from 1000 to 10000 r / min, and the critical centrifugal time ranges from 5 to 60 min.

3. The method for predicting the adhesive shelf life according to claim 1, characterized in that: The sedimentation velocity conversion coefficient is calculated by the sedimentation velocity conversion coefficient calculation formula, and the sedimentation velocity conversion coefficient calculation formula is as follows: Wherein, the adhesive sample is composed of filler and liquid, wherein, A is the sedimentation velocity conversion coefficient; d p is the diameter of the packing; the ρ p is the density of the filler; the ρ m is the density of the liquid; and η is the viscosity of the adhesive sample.

4. The method for predicting the shelf life of an adhesive according to any one of claims 1 to 3, characterized in that: The calculation formula for the storage period of the adhesive sample is: Among them, in the formula, the t g is the shelf life of the adhesive, and v s is the critical centrifugal sedimentation velocity, the v g is the gravity sedimentation velocity, and t s is the critical centrifugal time, ω is the critical centrifugal angular velocity, and r av is the average rotation radius, g is the gravitational acceleration, and N is the critical centrifugal speed.

Citation Information

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