Method for detecting deformation of flexible particles

Abstract

The application discloses a kind of flexible particle deformation quantity detection methods.For any deformed flexible particle, the centroid position of the flexible particle is determined, a three-dimensional Cartesian coordinate system is established with the centroid position as the origin, and the inertia tensor of the flexible particle can be obtained by calculating the moment of inertia and the product of inertia;The three principal moments of inertia of the inertia tensor of the flexible particle are taken as eigenvalues, and the three eigenvalues are sequentially arranged from large to small, the deformed flexible particle is equivalent to an ellipsoid, and the three-axis length of the ellipsoid is calculated;According to the three-axis length of the ellipsoid, the deformation of the flexible particle is calculated.The application can accurately obtain the deformation of the flexible particle, solve the problem that the micro-particle deformation cannot be accurately obtained in three-dimensional conditions, and has wide application.

Description

Technical Field

[0001] This invention relates to a particle physics measurement method in the field of microparticle mechanics, specifically a method for detecting the deformation of flexible particles. Background Technology

[0002] The motion of flexible particles has a wide range of applications in natural environments and industrial production, such as the movement of variable elements like red blood cells in blood, the settling of droplets in air, the movement of bubbles in liquids, and, on a larger timescale, the growth process of nuts and the evolution of celestial bodies. For flexible particles, the amount of deformation is a very important indicator, usually defined using Taylor deformation, as shown in the following formula:

[0003]

[0004] Where L is the deformed major axis and H is the deformed minor axis.

[0005] This is more intuitive in a two-dimensional plane, such as Figure 1 As shown, after a circle is deformed into an ellipse, the major axis is L and the minor axis is H. The Taylor deformation amount defined by the above formula has a value range of [0, 1). When the deformation amount is 0, the corresponding shape is a circle, and when the deformation amount is 1, the corresponding shape is a line (considering that if the area needs to remain the same before and after deformation, this situation will not occur).

[0006] However, when applying Taylor deformation to the three-dimensional case, in addition to the major axis L and the minor axis H, there is another dimension, the length of which lies between the two, that is not reflected in the above formula. Therefore, in the three-dimensional case, the existing technology lacks a method that can effectively reflect the influence of this other dimension of length while accurately reflecting the deformation of the flexible particles. Summary of the Invention

[0007] To address the aforementioned issues, this invention proposes a novel method for detecting the deformation of flexible particles, which solves the problem of inaccurately obtaining the deformation of micro-particles in three-dimensional cases.

[0008] The specific solution of this invention is as follows:

[0009] 1) For any deformed flexible particle, determine the centroid position of the flexible particle, establish a three-dimensional Cartesian coordinate system with the centroid position as the origin, and obtain the inertia tensor of the flexible particle by calculating the moment of inertia and the product of inertia.

[0010] The centroid of the flexible particle is its geometric center. For a flexible particle with uniform mass, the geometric center is equivalent to its center of mass.

[0011] 2) Obtain the three principal moments of inertia of the inertia tensor of the flexible particle as eigenvalues, arrange the three eigenvalues ​​in order and perform ellipsoidal equivalent calculation to obtain the lengths of the three axes of the ellipsoid or the proportional relationship between them.

[0012] 3) The deformation of the flexible particles is calculated by processing the lengths of the three axes of the ellipsoid or the proportional relationship between them.

[0013] After obtaining the deformation amount of the flexible particles, this deformation amount can be applied to industrial production or everyday life.

[0014] The inertia tensor of the flexible particle is obtained by first calculating the moment of inertia and product of inertia of the flexible particle through integral calculation based on the motion of the flexible particle, and then assembling the moment of inertia and product of inertia into a matrix to obtain the inertia tensor.

[0015] The moment of inertia and product of inertia of flexible particles are obtained through simulation of their motion.

[0016] As flexible particles move through a fluid, they deform, a process that can be achieved through numerical simulations or experiments. Once the shape of the flexible particle is determined, i.e., the coordinates of its surface are known, the moment of inertia and product of inertia can be determined using integral formulas.

[0017] In step 1), a three-dimensional xyz coordinate system is established [centered on the centroid of the flexible particle], and the inertial tensor A of the flexible particle is... I Represented as:

[0018]

[0019] Among them, I xx I represents the moment of inertia of the flexible particle about the x-axis. yy I represents the moment of inertia of the flexible particle about the y-axis. zz I represents the moment of inertia of the flexible particle about the z-axis; xy I represents the product of inertia of the flexible particles about the xy plane. xz I represents the product of inertia of the flexible particles about the xz plane. yz This represents the product of inertia of the flexible particle about the yz plane.

[0020] In one embodiment, step 2) specifically includes:

[0021] Arrange the three eigenvalues ​​from largest to smallest to obtain I′ xx ≥I′ yy ≥I′ zz , where I′ xx 、I′ yy 、I′ zzThese represent the largest, middle, and smallest eigenvalues, respectively.

[0022] Calculate based on the following formula using three eigenvalues ​​arranged from largest to smallest:

[0023]

[0024] Where L represents the length of the longest axis of the ellipsoid, W represents the length of the intermediate major axis of the ellipsoid, and H represents the length of the shortest axis of the ellipsoid, i.e., L≥W≥H; V represents the volume of the flexible particle.

[0025] In step 3), the deformation D of the flexible particle is calculated according to the following formula based on the triaxial length of the ellipsoid. xyz :

[0026]

[0027] Where L represents the length of the longest axis of the ellipsoid, W represents the length of the intermediate major axis of the ellipsoid, and H represents the length of the shortest axis of the ellipsoid, satisfying L≥W≥H.

[0028] In practice, it is not necessary to directly calculate the specific values ​​of the three axis lengths. It is only necessary to calculate the proportional relationship between the three axis lengths, i.e., L / L, W / L, H / L, and then obtain the deformation amount D of the flexible particle. xyz The specific processing method is as follows:

[0029] In another embodiment, step 2) specifically refers to:

[0030] Arrange the three eigenvalues ​​from largest to smallest to obtain I′ xx ≥I′ yy ≥I′ zz , where I′ xx 、I′ yy 、I′ zz These represent the largest, middle, and smallest eigenvalues, respectively.

[0031] Calculate based on the proportional relationship between the three eigenvalues ​​arranged from largest to smallest using the following formula:

[0032]

[0033] Where L represents the length of the longest axis of the ellipsoid, W represents the length of the intermediate major axis of the ellipsoid, and H represents the length of the shortest axis of the ellipsoid, that is, L≥W≥H.

[0034] Step 3) specifically includes:

[0035] Without needing to calculate the specific values ​​of L, W, H, and V, we obtained L / L, W / L, and H / L. Dividing both the numerator and denominator of the formula by L yields the following formula: The deformation D is obtained using the following formula. xyz :

[0036]

[0037] Where L represents the length of the longest axis of the ellipsoid, W represents the length of the intermediate major axis of the ellipsoid, and H represents the length of the shortest axis of the ellipsoid, satisfying L≥W≥H.

[0038] The deformation can then be calculated.

[0039] [The flexible particles described include cells in blood, droplets in air, bubbles in liquid, and, on a larger timescale, the growth process of nuts and the evolution of celestial bodies, etc.]

[0040] The beneficial effects of this invention are:

[0041] Taylor deformation only considers the influence of the longest and shortest axis lengths, without considering the influence of the axis lengths between the long and short axes. This invention also takes into account the axis lengths between the long and short axes, making the obtained deformation amount contain richer information and more quantitatively expressing the shape of the actual three-dimensional flexible particles after deformation.

[0042] Meanwhile, the range of values ​​for the deformation amount described in this invention is consistent with that of the Taylor deformation amount. The closer the value is to 0, the closer the corresponding shape is to a sphere; in this case, the conclusions obtained by the two calculation methods are consistent. However, the closer the value is to 1, the shape corresponding to the Taylor deformation amount could be either an elongated ellipsoid or an oblate spheroid, but the deformation amount described in this invention corresponds to only one shape: an elongated ellipsoid. For an oblate spheroid, the deformation amount described in this invention will be close to 0.5.

[0043] Therefore, the deformation amount described in this invention can more accurately quantify the shape of flexible particles, and can be better used to guide industrial applications, such as separating and classifying the health status of cells, screening nuts such as almonds and peanuts, and studying the evolution of celestial shapes. Attached Figure Description

[0044] Figure 1 This is a schematic diagram showing the transformation of a circle into an ellipse in a two-dimensional plane.

[0045] Figure 2 This is a schematic diagram showing the deformation of a sphere into an elongated ellipsoid and an oblate ellipsoid in three dimensions.

[0046] Specific implementation methods

[0047] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0048] The specific embodiments and implementation process of the present invention are as follows:

[0049] The example uses cells from the blood as flexible particles.

[0050] 1) For any deformed flexible particle, determine the centroid position of the flexible particle, establish a three-dimensional Cartesian coordinate system with the centroid position as the origin, and obtain the moment of inertia and product of inertia of the flexible particle by calculating the moment of inertia and product of inertia. Then, the inertia tensor can be obtained by assembling the moment of inertia and product of inertia into matrices.

[0051] The inertial tensor AI of flexible particles is represented as:

[0052]

[0053] 2) Obtain the three principal moments of inertia of the inertia tensor of the flexible particle, which are the eigenvalues ​​of the inertia tensor. Arrange these three eigenvalues ​​in descending order, and use an ellipsoid to represent the deformed flexible particle. Calculate the lengths of the three axes of the ellipsoid.

[0054] Arrange the three eigenvalues ​​from largest to smallest to obtain I′ xx ≥I′ yy ≥I′ zz , where I′ xx 、I′ yy 、I′ zz These represent the largest, middle, and smallest eigenvalues, respectively.

[0055] Calculate the lengths of the three axes based on the three eigenvalues ​​arranged from largest to smallest using the following formula:

[0056]

[0057] 3) The deformation of the flexible particles is calculated by processing the three-axis length of the ellipsoid.

[0058] The deformation D of the flexible particle is calculated using the following formula, based on the triaxial length of the ellipsoid. xyz :

[0059]

[0060] Where L represents the length of the longest axis of the ellipsoid, W represents the length of the intermediate major axis of the ellipsoid, and H represents the length of the shortest axis of the ellipsoid, satisfying L≥W≥H.

[0061] Application Scenario 1: In blood cells, healthy cells are more elastic and, without the influence of other cells, will move along the centerline of the blood vessel. Unhealthy cells, on the other hand, are less elastic and tend to move closer to the vessel wall, potentially accumulating and causing blockages, thus affecting blood flow and endangering life. In a shear flow field, healthy cells deform more than unhealthy cells. By calculating the amount of deformation, the health status of cells can be quantified, and they can be separated and classified.

[0062] Application Scenario 2: If we increase the time scale, many things in nature can be regarded as flexible particles, such as nuts during their growth process and celestial bodies during their evolution. For nuts such as almonds and peanuts, more accurate quantification can be achieved by calculating the amount of deformation and combining it with other shape parameters, thus enabling separation and classification; while for celestial bodies such as the Earth, quantitative research on their shape evolution can be conducted by calculating the amount of deformation.

[0063] The application of deformation calculation is not limited to the two application scenarios mentioned above.

[0064] The specific implementation also compares the deformation amounts obtained by Taylor deformation and the method of the present invention for several representative cell shapes, as shown in the table below:

[0065] Table 1 compares the calculation results of several shapes using Taylor's deformation calculation formula and the deformation calculation formula of this invention.

[0066]

[0067] Table 1 shows that the deformation parameters of the present invention provide more information than existing Taylor deformation parameters. Many different shapes yield the same results using Taylor deformation, while those of the present invention do not.

[0068] Furthermore, the deformation calculated using both Taylor deformation and the method of this invention has a value range of [0, 1), that is, when the shape of the flexible particle is spherical and L = W = H, D xy =D xyz =0; while when the shape of the flexible particle is a line, L>W=H=0, D xy =D xyz =1. The shape can be determined from the amount of deformation. For example, the closer the deformation is to 0, the closer the shape of the flexible particle is to a sphere.

[0069] After taking into account the length W of the third axis, which lies between the major and minor axes, and considering an extreme case where the flexible particle is flattened into a circle, i.e., L = W > H = 0, D xyz =0.5, while D xy=1. Using Taylor deformation, the result is always 1 for both a line and a circle, but its drawback is that it doesn't consider the axial length W. The deformation result of this invention is 0.5. Clearly, a circle is closer to a sphere than a line; therefore, the flexible particle deformation method described in this invention is superior to existing Taylor deformation methods.

Claims

1. A method for detecting the deformation of flexible particles, characterized in that: 1) For any deformed flexible particle, determine the centroid position of the flexible particle, establish a three-dimensional Cartesian coordinate system with the centroid position as the origin, and obtain the inertia tensor of the flexible particle by calculating the moment of inertia and the product of inertia. 2) Obtain the three principal moments of inertia of the inertia tensor of the flexible particle as eigenvalues, arrange the three eigenvalues ​​in order and perform ellipsoidal equivalent calculation to obtain the lengths of the three axes of the ellipsoid or the proportional relationship between them. Step 2) specifically includes: Arrange the three eigenvalues ​​from largest to smallest to obtain I′ xx ≥I′ yy ≥I′ zz , where I′ xx I yy I zz These represent the largest, middle, and smallest eigenvalues, respectively. Calculate based on the following formula using three eigenvalues ​​arranged from largest to smallest: Where L represents the length of the longest axis of the ellipsoid, W represents the length of the intermediate major axis of the ellipsoid, and H represents the length of the shortest axis of the ellipsoid, i.e., L≥W≥H; V represents the volume of the flexible particle. Step 2) specifically includes: Arrange the three eigenvalues ​​from largest to smallest to obtain I′ xx ≥I′ yy ≥I′ zz , where I′ xx 、I′ yy 、I′ zz Let represent the largest, middle, and smallest eigenvalues, respectively; calculate the eigenvalues ​​based on the proportional relationship between the three eigenvalues ​​arranged from largest to smallest using the following formula: Where L represents the length of the longest axis of the ellipsoid, W represents the length of the intermediate major axis of the ellipsoid, and H represents the length of the shortest axis of the ellipsoid, that is, L≥W≥H. 3) The deformation of the flexible particles is calculated by processing the lengths of the three axes of the ellipsoid or the proportional relationship between them.

2. The method for detecting the deformation of flexible particles according to claim 1, characterized in that: The inertia tensor of the flexible particle is obtained by first calculating the moment of inertia and product of inertia of the flexible particle through integral calculation, and then assembling the moment of inertia and product of inertia into a matrix to obtain the inertia tensor.

3. The method for detecting the deformation of flexible particles according to claim 1, characterized in that: In step 1), a three-dimensional xyz coordinate system is established, and the inertial tensor A of the flexible particle is... I Represented as: Among them, I xx I represents the moment of inertia of the flexible particle about the x-axis. yy I represents the moment of inertia of the flexible particle about the y-axis. zz I represents the moment of inertia of the flexible particle about the z-axis; xy I represents the product of inertia of the flexible particles about the xy plane. xz I represents the product of inertia of the flexible particles about the xz plane. yz This represents the product of inertia of the flexible particle about the yz plane.

4. The method for detecting the deformation of flexible particles according to claim 1, characterized in that: In step 3), the deformation D of the flexible particle is calculated according to the following formula based on the triaxial length of the ellipsoid. xyz : Where L represents the length of the longest axis of the ellipsoid, W represents the length of the intermediate major axis of the ellipsoid, and H represents the length of the shortest axis of the ellipsoid, satisfying L≥W≥H.

5. The method for detecting the deformation of flexible particles according to claim 1, characterized in that: Step 3) specifically involves obtaining the deformation amount D according to the following formula. xyz : Where L represents the length of the longest axis of the ellipsoid, W represents the length of the intermediate major axis of the ellipsoid, and H represents the length of the shortest axis of the ellipsoid, satisfying L≥W≥H.

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