CN102967539A - Method for determining shape factor of particle swarm - Google Patents

Abstract

The invention provides a method for determining a shape factor of a particle swarm, comprising the following steps of: 1) establishing a particle swarm condensation liquid-solid reaction model; 2) determining grain diameter distribution of a solid particle swarm to realize mathematic expression; carrying out reaction with a liquid solution on the particle swarm under the conditions of constant temperature and constant solution concentration; weighing and determining a dissolving rate of the solid particle swarm; and fitting to realize the mathematic expression; 3) on the basis of the particle swarm condensation liquid-solid reaction model, utilizing measurement fitting data to calculate to obtain a comprehensive chemical reaction coefficient k and a change rule thereof of a liquid-solid two-phase chemical reaction; 4) when the shape factor phi of the particle swarm is about 1, carrying out experiment calculation to obtain the comprehensive chemical reaction coefficient k of the liquid-solid two-phase chemical reaction, namely a k0 value; and 5) calculating a specific value of the k value obtained by test calculation to a theoretical comprehensive chemical reaction coefficient k0 to obtain the value of the shape factor phi of the particle swarm. The determining method disclosed by the invention has the very important meanings on the mutual correlation of macroscopic experiment data and chemical reaction parameters aiming to the completion of a theoretical system of solid characteristics and a liquid-solid two-phase reaction.

Description

A kind of method of measuring the particle swarm form factor

Technical field

The invention belongs to solid particle feature and liquid solid chemical reaction field, be specifically related to a kind of method of measuring particle shape factor.

Background technology

Solid particle has the style characteristic of more complicated, in experimental study, generally be considered Utopian spherical the processing, the ratio of the surface area of the real surface area of solid particle and Utopian equal-volume equivalent ball, be defined as the form factor of solid particle, have great importance for experimental study, but be difficult to directly measure by existing experimental technique.The liquid-solid two-phase chemical reaction is a very complicated process, except chemical reaction process, also is accompanied by the mobile and mixing of reactant and the transmittance process of heat and matter.The former belongs to the problem of Chemical Kinetics; The latter relates to is physical influence or is called macroscopical transmission effects.The method of research liquid-solid two-phase reaction mainly is to participate in the reactant quality of reaction and the characteristics that the reaction rate parameter on the solid reactant surface area is investigated its reaction by mensuration at present.Solid particle has the surface configuration of more complicated, but in the model of former studies liquid-solid two-phase reaction, it is spherical that solid particle often is regarded as desirable equal-volume equivalent, so that theoretical prediction has larger difference with real response characteristic, this species diversity can be considered the ratio by the surface area of the real surface area of solid particle and Utopian equal-volume equivalent ball, and namely form factor φ causes.But form factor φ directly measures by existing experimental technique is very difficult, therefore realizes the mensuration of form factor φ is had very important significance for the response characteristic of studying liquid-solid two-phase reaction and description solid particle.

Summary of the invention

For solving above-mentioned problems of the prior art, order of the present invention is to provide a kind of method of measuring the particle swarm form factor, be the mensuration of ratio of the surface area of the real surface area of particle swarm and idealized equal-volume equivalent ball, solid particle group character is described and the theoretical system of liquid-solid two-phase reaction for improving for this, realizes that the interrelated of macroscopical experimental data and chemical reaction parameters has great importance.

For achieving the above object, the technical solution adopted in the present invention is a kind of method of measuring the particle swarm form factor, comprises the steps:

Step 1: according to diffusivity and the chemical reaction rate of solid reactant in fluid, determine the molten rate of disappearing of individual particle, the molten rate that disappears of individual particle is synthetic chemistry reaction coefficient k, the function of reaction conditions and particle initial particle; Introduce the particle diameter distributed model of particle swarm on the basis that individual particle disappears molten, set up the liquid-solid reaction model of particle swarm condensation, see formula (1);

$X_T\left(t\right)={\∫}_0^{\∞}x(D,t)f_M(D,0)\mathrm{dD}---\left(1\right)$

In the formula (1): X _T(t) be the molten rate of disappearing of solid particle group; X (D, t) is the molten speed of disappearing of individual particle; f _M(D, 0) is the initial particle distribution function of particle swarm;

Step 2: the particle diameter of measuring solid particle group distributes, and realizes mathematical expression; Carry out particle swarm under the condition of constant temperature, constant solution concentration with the reaction of liquid solution, weigh, measure the molten rate that disappears of solid particle group, and realize mathematical expression by match;

Molten rate X disappears _TDefinition: in batch (-type) liquid-solid two-phase reaction experiment, definition has participated in the mass M of the solid particle that reacts ' be the molten rate that disappears with the ratio of the mass M that adds particle sometime in the section, sees formula (2);

$X_T=\frac{M^{\′}}{M}---\left(2\right)$

Step 3: on the basis of the liquid-solid reaction model of particle swarm condensation that step 1 is set up, see formula (1), use step 2 to measure the data of match, calculate synthetic chemistry reaction coefficient k and the Changing Pattern thereof of liquid-solid two-phase chemical reaction; The synthetic chemistry reaction coefficient k of experimental calculation and synthetic chemistry reaction coefficient k in theory ₀There are differences, the synthetic chemistry reaction coefficient k of experimental calculation has comprised particle swarm form factor φ and synthetic chemistry reaction coefficient k in theory ₀, see formula (3);

k=φ(D ₀,t)*k ₀ (3）

In the formula (3): k is the synthetic chemistry reaction coefficient of the liquid-solid two-phase chemical reaction of experimental calculation; φ (D ₀, t) being the form factor of particle, it is particle initial particle D ₀Function with reaction time t; k ₀It is liquid-solid two-phase chemical reaction synthesis in theory chemical reaction coefficient;

Step 4: theoretical analysis knows, if solid particle is desirable spherical, and when particle swarm reacts with liquid solution under the condition of constant temperature, constant solution concentration, the theoretic synthetic chemistry reaction coefficient k of liquid-solid two-phase chemical reaction ₀Be a constant value, so in long-time reacted terminal stage, namely particle swarm form factor φ is about at 1 o'clock, the synthetic chemistry reaction coefficient k value of the liquid-solid two-phase chemical reaction of experimental calculation is theoretic synthetic chemistry reaction coefficient k ₀

Step 5: the synthetic chemistry reaction coefficient k and the synthesis in theory chemical reaction coefficient k that use the liquid-solid two-phase chemical reaction of following formula experiment with computing calculating ₀Ratio, namely get the value of particle shape factor φ in the liquid-solid two-phase reaction, see formula (4).

φ(D ₀,t)=k/k ₀ （4）

In experimental study, we suppose that particle all is the sphere of rule, and in fact the original shape of particle swarm is not spherical completely, in addition, a small amount of hole that also may exist in the inside of particle swarm is so that actual surface area is greater than the calculated value that adopts spherical hypothesis, so, at the initial stage of whole particle swarm and solution reaction process, it is larger that the shape of particle swarm departs from sphere, and form factor φ is larger; And along with the carrying out that reacts, disappearing the molten later stage, and the shape of particle swarm has moved closer to sphere, and form factor φ levels off to 1 gradually.

Because in experimental study (comprising liquid-solid reaction), solid particle group often is regarded as Utopian equal-volume equivalent ball and processes, the ratio of its real surface area and Utopian equal-volume equivalent ball surface area, be form factor φ and at the ongoing Changing Pattern of reaction, have very important significance for the research feature of solid particle group and liquid-solid two-phase reaction.So, the mensuration of particle swarm form factor φ, the theoretical system for the description of improving the solid particle feature and liquid-solid two-phase reaction realizes that the interrelated of macroscopical experimental data and chemical reaction parameters has great importance.

Description of drawings

Fig. 1 is disappear molten lime stone experiment constant temperature, constant solution concentration system of hydrochloric acid.

Fig. 2 is with the disappear partial fitting design sketch of molten lime stone experimental data of double-exponential function formula match hydrochloric acid.

Fig. 3 is under three kinds of operating modes, the synthetic chemistry reaction constant k of limestone particle group and acid reaction.

Fig. 4 is under three kinds of operating modes, the form factor φ of limestone particle.

Three kinds of concrete operating modes are as follows:

Operating mode one: under 50 ℃ of conditions, size-grade distribution is

The lime stone of n=2.47011 and the hydrochloric acid reaction of pH=4.6;

Operating mode two: under 50 ℃ of conditions, size-grade distribution is

The lime stone of n=3.07528 and the hydrochloric acid reaction of pH=5.4;

Operating mode three: under 50 ℃ of conditions, size-grade distribution is

The lime stone of n=2.56954 and the hydrochloric acid reaction of pH=6.2;

Embodiment

Below in conjunction with the drawings and specific embodiments the present invention is described in further detail.

According to assay method of the present invention, limestone particle group's form factor is measured.In experimental system shown in Figure 1, carried out the limestone particle group under the condition of constant temperature, constant solution concentration with the molten reaction of disappearing of hydrochloric acid, obtain solid disappear molten and the reaction rule time.In system shown in Figure 1, reaction bulb 1 places on the constant temperature magnetic force heating stirrer 8, reaction bulb 1 usefulness rubber plug 2 seals, insert thermometer 3, pH value probe 6 and acid buret 4 in it, pH value probe 6 other ends are connected connection with automatical potentiometric titrimeter, the solenoid valve 5 that is connected with automatical potentiometric titrimeter 7 is set on the acid buret 4, and hydrochloric acid and lime stone react in reaction bulb 1.The design of thermometer 3 and constant temperature magnetic force heating stirrer 8 in the pilot system has guaranteed that temperature of reaction keeps constant in the experimental system; The design of acid buret 4, solenoid valve 5, pH value probe 6 and automatical potentiometric titrimeter 7 has guaranteed pH value ie in solution concentration in the experimental system, keeps constant.

Step 1: use the liquid-solid reaction model of particle swarm condensation, see formula (1), according to diffusivity and the chemical reaction rate of limestone particle group in hydrochloric acid solution, determine the molten rate of disappearing of individual particle, see formula (5); On this basis, introduce limestone particle group particle diameter distributed model, obtain the molten rate that disappears in hydrochloric acid to the limestone particle group, see formula (6);

$x({\mathrm{<figure-callout\; id="0"\; label="D"\; filenames="HDA00002552706400012.png,HDA00002552706400021.png"\; state="\{\{state\}\}">D</figure-callout>}}_0,t)=1-{\left(\frac{R}{R_0}\right)}^3=1-{(1-\frac{k}{D_0}t)}^3---\left(5\right)$

$X_T\left(t\right)={\&Integral;}_0^{\&infin;}x(D,t)f_M(D,0)\mathrm{dD}={\&Integral;}_0^{\&infin;}[1-{(1-\frac{k}{D}t)}^3]f_M(D,0)\mathrm{dD}---\left(6\right)$

In formula (5) and the formula (6): x (D ₀, t) being the molten rate of disappearing of individual particle lime stone, it is synthetic chemistry reaction coefficient k, limestone particle initial particle D ₀Function with time t; f _M(D, 0) is limestone particle group's initial particle distribution and expression formula.

Step 2: use the laser particle size measurement instrument to record under three kinds of operating modes, limestone particle group's particle diameter distributes, and realizes mathematical expression with Rosin-Rammler distribution function formula (7); Carry out the limestone particle group under the condition of constant temperature, constant solution concentration with the reaction of hydrochloric acid solution, use the balance check weighing, measure the molten rate that disappears of solid particle group, and with double-exponential function formula (8) match experimental data, in operating mode once, the molten data fitting that disappears is suc as formula (9), operating mode three times, disappear molten data fitting suc as formula (10), and the effect of match is seen Fig. 2;

$f\left(D\right)=n\frac{D^{n-1}}{{\stackrel{\&OverBar;}{D}}^n}{e}^{-{\left(\frac{D}{\stackrel{\&OverBar;}{D}}\right)}^n}---\left(7\right)$

$X_T\left(t\right)=A_1\&times;(1-e^{-t/B_1})+(1-A_1)\&times;(1-e^{-t/B_2})---\left(8\right)$

In the formula (7):

Be characteristic parameter, n is characteristic parameter;

In the formula (8): A ₁Be characteristic parameter, B ₁, B ₂Be characteristic parameter, t is the reaction time;

X(t)=0.2809×(1-e ^-t/260.96)+0.7191×(1-e ^-t/1974.4) （9）

X(t)=0.0854×(1-e ^-t/353.5)+0.9146×(1-e ^-t/4122.5) （10）

Step 3: the liquid-solid reaction model of particle swarm condensation that uses step 1 to set up, see formula (6), the substitution of step 2 fitting data, calculate synthetic chemistry reaction coefficient k and the Changing Pattern thereof of liquid-solid two-phase chemical reaction, wherein comprised form factor φ and synthetic chemistry reaction coefficient k in theory ₀, suc as formula (3), as shown in Figure 3, be the synthetic chemistry reaction coefficient k of limestone particle group and acid reaction under three kinds of operating modes in the liquid-solid two-phase chemical reaction;

Step 4: it is last to be recorded in reaction, and particle shape factor φ is about at 1 o'clock, and experimental calculation obtains the synthetic chemistry reaction coefficient k value of liquid-solid two-phase chemical reaction, namely for this reason under the device reaction condition, and theoretic synthetic chemistry reaction coefficient k ₀Value;

Step 5: the synthetic chemistry reaction coefficient k of the liquid-solid two-phase chemical reaction that experiment with computing calculates and synthetic chemistry reaction coefficient k in theory ₀Ratio, suc as formula (4), namely get the value of particle shape factor φ in the liquid-solid two-phase reaction and with the Changing Pattern of reaction, as shown in Figure 4, be the value of limestone particle form factor φ under three kinds of operating modes in the liquid-solid two-phase reaction.

Claims (1)

1. a method of measuring the particle swarm form factor is characterized in that comprising the steps:

Step 1: according to diffusivity and the chemical reaction rate of solid reactant in fluid, determine the molten rate of disappearing of individual particle, the molten rate that disappears of individual particle is synthetic chemistry reaction coefficient k, the function of reaction conditions and particle initial particle; Introduce the particle diameter distributed model of particle swarm on the basis that individual particle disappears molten, set up the liquid-solid reaction model of particle swarm condensation, see formula (1);

$X_T\left(t\right)={\&Integral;}_0^{\&infin;}x(D,t)f_M(D,0)\mathrm{dD}---\left(1\right)$

In the formula (1): X _T(t) be the molten rate of disappearing of solid particle group; X (D, t) is the molten speed of disappearing of individual particle; f _M(D, 0) is the initial particle distribution function of particle swarm.

Step 2: the particle diameter of measuring solid particle group distributes, and realizes mathematical expression; Carry out particle swarm under the condition of constant temperature, constant solution concentration with the reaction of liquid solution, weigh, measure the molten rate that disappears of solid particle group, and realize mathematical expression by match;

Molten rate X disappears _TDefinition: in batch (-type) liquid-solid two-phase reaction experiment, definition has participated in the mass M of the solid particle that reacts ' be the molten rate that disappears with the ratio of the mass M that adds particle sometime in the section, sees formula (2);

$X_T=\frac{M^{\&prime;}}{M}---\left(2\right)$

Step 3: on the basis of the liquid-solid reaction model of particle swarm condensation that step 1 is set up, see formula (1), use step 2 to measure the data of match, calculate synthetic chemistry reaction coefficient k and the Changing Pattern thereof of liquid-solid two-phase chemical reaction; The synthetic chemistry reaction coefficient k of experimental calculation and synthetic chemistry reaction coefficient k in theory ₀There are differences, the synthetic chemistry reaction coefficient k of experimental calculation has comprised particle swarm form factor φ and synthetic chemistry reaction coefficient k in theory ₀, see formula (3);

k=φ(D ₀,t)*k ₀ （3)

In the formula (3): k is the synthetic chemistry reaction coefficient of the liquid-solid two-phase chemical reaction of experimental calculation; φ (D ₀, t) being the form factor of particle, it is particle initial particle D ₀Function with reaction time t; k ₀It is liquid-solid two-phase chemical reaction synthesis in theory chemical reaction coefficient.

Step 4: theoretical analysis knows, if solid particle is desirable spherical, and when particle swarm reacts with liquid solution under the condition of constant temperature, constant solution concentration, the theoretic synthetic chemistry reaction coefficient k of liquid-solid two-phase chemical reaction ₀Be a constant value, so in long-time reacted terminal stage, namely particle swarm form factor φ is about at 1 o'clock, the synthetic chemistry reaction coefficient k value of the liquid-solid two-phase chemical reaction of experimental calculation is theoretic synthetic chemistry reaction coefficient k ₀

Step 5: the synthetic chemistry reaction coefficient k and the synthesis in theory chemical reaction coefficient k that use the liquid-solid two-phase chemical reaction of following formula experiment with computing calculating ₀Ratio, namely get the value of particle shape factor φ in the liquid-solid two-phase reaction, see formula (4).

φ(D ₀,t)=k/k ₀ （4）

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