RU2522805C1 - Method of determining wettability of finely-disperse powders - Google Patents

Abstract

FIELD: chemistry.

SUBSTANCE: suspension of evenly distributed in air powder particles with a diameter not larger than 5 mcm with an initial concentration of a particle suspension, selected on condition T₀≤0.2, is created in a cuvette with transparent flat-parallel walls, and a spectral coefficient of the suspension transmittance is measured. After that, a flow of monodisperse drops with a diameter 0.8÷2.5 mm is supplied from an evenly distributed on the transverse section of the cuvette drop counters within the specified time interval t_k, determined from condition T_k>2T₀, with re-measurement of the spectral coefficient of the suspension transmittance. A parameter of the powder wettability is calculated by formula $$\beta =\frac{4V\ln \left[\left(\ln \frac{1}{T_0}\right){\left(\ln \frac{1}{T_k}\right)}^{-1}\right]}{\eta \pi D^{2}hnf{t}_k},$$

where V is the cuvette volume; T₀, T_k is the spectral coefficient of transmittance before and after precipitation of drops; η is the capture coefficient; D is the drop diameter; h is the cuvette height; n is a number of drop counters; f is frequency of drop falling; t_k is a time interval of supplying drops into the cuvette.

EFFECT: increased accuracy of determining characteristics of the powder material wettability and provision of measurement carrying out directly in a dust-air mixture.

3 tbl, 7 dwg

Description

The invention relates to the field of studies of the characteristics of powders, in particular their wettability. The wettability of powders plays an important role in the effectiveness of a number of technological processes - wet dust collection, dust suppression, flotation, filtering, clumping of powder materials, the formation of ceramic compositions, impregnation, etc. [one].

The wettability of carbon black, for example, determines the granulation process and regulates the yield of carbon black used in the rubber industry in the manufacture of varnishes and paints, as well as in the production of rubbers. The wettability of coal powders is one of the indicators that determine the efficiency of the process of separating minerals from gangue during coal processing [2] and the technology of neutralizing coal dust in mines [3].

The main characteristic of the wettability of a flat surface of a solid by a liquid is the contact angle θ [4], which is measured from the tangent to the free surface of a liquid droplet drawn at the interface of three phases (liquid, solid, gaseous), towards the liquid (Figure 1). Known methods for determining the wettability of solid materials [1, 5], based on the measurement of the contact angle by the profile of a liquid droplet y (r) located on a flat surface of a solid, by tangent to the point of three-phase contact R (Figure 1). Here y (r) is the distance of point A of the droplet profile from the flat substrate for the radial coordinate r.

For powder materials, this method of determining the contact angle is difficult due to the small size of the powder particles (up to submicron) and the absence of generally flat surfaces of the particles. A number of indirect methods are known for powders for determining the wettability characteristics based on measuring values associated with the wettability phenomenon.

A known method for determining the contact angle for powders, which consists in placing a drop of liquid on a plate with a thin layer of a binder solution and a monolayer of powder deposited on it [1]. In this case, the powder forms a layer of adhering particles. This method has low accuracy due to surface roughness due to the heterogeneity of the dispersed composition of the powder and the presence of gaps between the particles.

Known methods for determining the contact angle of powder materials based on measuring the droplet profile y (r) placed on the briquette obtained by pressing the powder [6, 7]. The disadvantages of these methods include the problem of obtaining a stationary droplet associated with the leakage of fluid into the pores and the deformation of the powder particles during the briquette pressing, as a result of which the identity of the powder particles in the briquette may violate the original particles.

A known method for determining the wettability of powder materials by measuring the rate of absorption of moisture by a layer of powder upon contact with a wet surface [8]. In this case, the kinetics of the wetting of the powder layer are built according to the measurement results; wettability is greater, the greater the amount of absorbed moisture. This method provides only a qualitative assessment of wettability.

The closest in technical essence is a method for determining the wettability of powders by film flotation [9]. This method is based on determining the mass fraction of powder particles sunk in a certain time, sprinkled with a thin even layer on the surface of the liquid. The mass fraction of settled powder particles (wetted particles) or the wettability parameter is determined by the formula

, $$\beta =\frac{m_c}{m}\cdot \mathrm{one\; hundred}\%$$

,

where m _c is the mass of settled particles;

m is the mass of the initial sample of the powder.

This method also allows one to obtain only a qualitative assessment of the wettability and to divide the powders into three groups - poorly wettable (β <30%), medium wettable (β = 30 ÷ 80%) and well wettable (β> 80%).

The technical result of the present invention is the development of a more accurate method for determining the wettability of powders, providing measurements directly in the dust-air mixture.

The technical result of the invention is achieved by the fact that a method for determining the wettability of fine powders based on the calculation of the fraction of wetted powder particles is developed. In a cuvette with transparent plane-parallel walls, a suspension of uniformly distributed powder particles with a maximum diameter of not more than 5 μm is created and the spectral transmittance of the probe laser radiation of the suspension is measured, a flow of monodispersed droplets with a diameter of 0.8 ÷ 2.5 mm is fed into the cuvette from droppers uniformly distributed over the cross section and re-measured spectral transmittance, the initial concentration of the powder particles is selected from the condition of T ₀ ≤0.2, interspace supply op droplets time edelyayut conditions of T _k> 2T _0. The wettability parameter β is calculated by the formula

, $$\beta =\frac{\mathrm{four}V\ln \left[\left(\ln \frac{\mathrm{one}}{T_0}\right){\left(\ln \frac{\mathrm{one}}{T_k}\right)}^{-\mathrm{one}}\right]}{\eta \pi D^{2}hnf{t}_k}$$

,

where V is the volume of the cell;

T ₀ , T _k - spectral transmittance before and after the deposition of droplets;

- коэффициент захвата; $$\eta ={\left(\frac{Stk}{Stk+0.125}\right)}^2$$

- capture coefficient;

- осредненное число Стокса; $$Stk=\frac{{\rho }_p{D}_{\mathrm{twenty}}u}{\mathrm{eighteen}\mu D}$$

- averaged Stokes number;

ρ _p is the density of powder particles;

D ₂₀ is the rms diameter of the powder particles;

u is the speed of gravitational precipitation of the droplet;

µ is the coefficient of dynamic viscosity of air;

D is the diameter of the droplet;

h is the height of the cell;

n is the number of droppers;

f is the frequency of drops falling;

t _k is the time interval for dropping drops into the cell.

Consider the rationale for the proposed method. As a characteristic of wettability, we take the mass fraction of powder particles (wetted particles) deposited on a single drop

$$\beta =\frac{m_c}{m},\left(\text{one}\right)$$

where m _c is the mass of wetted powder particles (deposited per drop); m is the mass of powder particles colliding with the drop during its gravitational deposition in the cell.

When a liquid droplet is deposited with a diameter D in a cell of height h, the value of m is calculated by the formula (Figure 2)

, $$m=\frac{\mathrm{<figure-callout\; id="2"\; label="\pi \; D"\; filenames="00000038.png,00000042.png"\; state="\{\{state\}\}">\pi \; </figure-callout>}{D}^{}{}^2}{\mathrm{four}}hc\eta$$

,

where c is the mass concentration of powder particles in the cell;

η≤1 - capture coefficient.

The mass of wetted powder particles, taking into account (1), is equal to

$$m_c=\beta m=\mathrm{<figure-callout\; id="2"\; label="\beta \; \pi \; D"\; filenames="00000038.png,00000042.png"\; state="\{\{state\}\}">\beta \; </figure-callout>}\frac{\pi D^{}}{}\frac{{}^2}{\mathrm{four}}hc\eta .\left(\text{2}\right)$$

When analyzing the deposition of powder particles on a moving drop, it is necessary to take into account the curvature of the streamlines of a dusty dusty air stream (Figure 2). The capture coefficient η is the ratio of the number of particles colliding with an obstacle (drop) to the number of particles that would collide if the streamlines did not deviate by the obstacle. As a result of this effect, not all particles located in the cross section S = nD ^2/4 (midship section drops) collide with it. The fraction of colliding particles is determined (for potential flow) by the Langmuir-Blodgett formula [10]

$$\eta ={\left(\frac{Stk}{Stk+0.125}\right)}^2,\left(\text{3}\right)$$

where Stk is the Stokes number.

For monodisperse powder particles with a diameter of D _p, the Stokes number is determined by the expression

. $$Stk=\frac{{\rho }_p{D}_p^{2}u}{\mathrm{eighteen}\mu D}$$

.

Since the powder suspension is a collection of polydisperse particles, it is necessary to use the averaged Stokes number [10]:

, $$Stk={\displaystyle \underset{0}{\overset{\infty }{\int }}\frac{{\rho }_{\mathrm{<figure-callout\; id="2"\; label="p\; D\; p"\; filenames="00000038.png,00000042.png"\; state="\{\{state\}\}">p\; </figure-callout>}}{D}_p^{}{}_2^{}\varphi \left(D_p\right)u}{\mathrm{eighteen}\mu D}d{D}_p=\frac{{\rho }_{p}u}{\mathrm{eighteen}\mu D}{\displaystyle \underset{0}{\overset{\infty }{\int }}{\mathrm{<figure-callout\; id="2"\; label="D\; p"\; filenames="00000038.png,00000042.png"\; state="\{\{state\}\}">D\; </figure-callout>}}_p^{}\varphi \left(D_p\right)d{D}_p=\frac{{\rho }_{p}u}{\mathrm{eighteen}\mu D}{D}_{\mathrm{twenty}}}}$$

,

where φ (D _p ) is the differential function of the countable size distribution of powder particles;

- среднеквадратичный диаметр частиц порошка. $$D_{\mathrm{twenty}}={\displaystyle \underset{0}{\overset{\infty }{\int }}{\mathrm{<figure-callout\; id="2"\; label="D\; p"\; filenames="00000038.png,00000042.png"\; state="\{\{state\}\}">D\; </figure-callout>}}_p^{}\varphi \left(D_p\right)d{D}_p}$$

is the rms diameter of the powder particles.

To feed a stream of monodispersed drops in the upper part of the cuvette (Figure 3), n droppers are installed that are evenly distributed in the cross section of the cuvette. All droppers form droplets of the same diameter D with a feed frequency f (the number of droplets formed per second). Thus, over a period of time t N drops will pass through the cuvette:

N = nft.

Since the mass of powder particles settled on one drop is determined by formula (2), for N drops the total mass of wetted particles is

$$M_c=\beta \frac{\pi {\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="00000038.png,00000042.png"\; state="\{\{state\}\}">D</figure-callout>}}^2}{\mathrm{four}}hcN\eta =\beta \frac{\pi {\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="00000038.png,00000042.png"\; state="\{\{state\}\}">D</figure-callout>}}^2}{\mathrm{four}}hcnft\eta .\left(\text{four}\right)$$

To determine the wettability parameter β, it is necessary to take into account the time variation of the mass concentration of powder particles in the cuvette, since a certain fraction of particles is deposited on the droplets. To do this, we write equation (4) in the form

$$d{M}_c(t)=\beta \frac{\pi {\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="00000038.png,00000042.png"\; state="\{\{state\}\}">D</figure-callout>}}^2}{\mathrm{four}}hc(t)nf\eta dt,\left(\text{5}\right)$$

where dM _c (t) is the mass of wetted particles during the time dt.

The wetted particles, together with the droplets, are deposited on the bottom of the cuvette; therefore, the decrease in the total mass of particles M (t) suspended in the cuvette is

$$dM\left(t\right)=-d{M}_c\left(t\right).\left(\text{6}\right)$$

In view of (6), equation (5) takes the form

$$dM\left(t\right)=-\mathrm{<figure-callout\; id="2"\; label="\beta \; \pi \; D"\; filenames="00000038.png,00000042.png"\; state="\{\{state\}\}">\beta \; </figure-callout>}\frac{\pi D^{}}{}\frac{{}^2}{\mathrm{four}}hc\left(t\right)nf\eta dt.$$

Dividing this equation term by term by the volume of the cell V, we obtain:

$$dc\left(t\right)=-\beta Bc\left(t\right)dt,\left(\text{7}\right)$$

Where

$$B=\frac{\mathrm{<figure-callout\; id="2"\; label="\pi \; D"\; filenames="00000038.png,00000042.png"\; state="\{\{state\}\}">\pi \; </figure-callout>}{D}^{}{}^2}{\mathrm{four}V}hnf\eta =const.\left(\text{8}\right)$$

We represent equation (7) in the form

$$\frac{dc\left(t\right)}{c\left(t\right)}=-\beta Bdt.\left(\text{9}\right)$$

Integrating (9) in the range from t = 0 to t, we obtain:

. $$\ln \left[\frac{c\left(t\right)}{c_0}\right]=-\beta Bt$$

.

It follows that

$$c\left(t\right)={\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="00000039.png,00000041.png"\; state="\{\{state\}\}">c</figure-callout>}}_0\exp \left(-\beta Bt\right),\left(\text{10}\right)$$

where c (t) is the mass concentration of powder particles at an arbitrary instant of time t> 0;

c ₀ is the initial mass concentration of powder particles.

From equation (10) it is possible to determine the wettability parameter β:

$$\beta =\frac{\ln \left[{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="00000039.png,00000041.png"\; state="\{\{state\}\}">c</figure-callout>}}_0/c\left(t\right)\right]}{Bt}.\left(\text{eleven}\right)$$

Substituting in (11) the expression for B from equation (8), we obtain:

, $$\beta =\frac{\mathrm{four}V\ln \left[{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="00000039.png,00000041.png"\; state="\{\{state\}\}">c</figure-callout>}}_0/c_k\right]}{\pi D^{2}hnf{t}_k\eta },\left(\text{12}\right)$$

,

where c _k is the concentration at time t _k corresponding to the cessation of the supply of drops.

To determine the wettability parameter β by the formula (12), it is necessary to determine the mass concentration of powder particles in the cell at the initial time point c ₀ (the beginning of the droplet supply) and after the precipitation of droplets c _k .

For this, a suspension of powder particles evenly distributed in air is created in a cuvette with plane-parallel walls made of a transparent material, for example, optical glass (Figure 3). Using a probe radiation source (laser) and a radiation receiver measure the spectral transmittance in the cell

, $$T=\frac{I}{I_0}$$

,

where I is the intensity of the radiation transmitted through the suspension of particles;

I ₀ is the radiation intensity of the incoming beam.

In accordance with the law of Bouguer [11]

T = exp (-τ),

where τ = Kcl is the spectral optical density of the layer of powder particles;

K is the spectral attenuation index, which characterizes the attenuation of light by a single volume of medium containing independently scattering particles;

l is the width of the cell (the thickness of the layer of powder particles).

For a layer of polydisner particles with a distribution function φ (D _p ), the attenuation coefficient is [11]

, $$K=\frac{3\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="00000038.png,00000042.png"\; state="\{\{state\}\}">c</figure-callout>}}{2{\rho }_p}\frac{{\displaystyle \underset{0}{\overset{\infty }{\int }}Q\left(\alpha ,\overline{m}\right){\mathrm{<figure-callout\; id="2"\; label="D\; p"\; filenames="00000038.png,00000042.png"\; state="\{\{state\}\}">D\; </figure-callout>}}_p^{}\varphi \left(D_p\right)d{D}_p}}{{\displaystyle \underset{0}{\overset{\infty }{\int }}{\mathrm{<figure-callout\; id="3"\; label="D\; p"\; filenames="00000040.png,00000042.png"\; state="\{\{state\}\}">D\; </figure-callout>}}_p^{}\varphi \left(D_p\right)d{D}_p}}$$

,

Where

- фактор эффективности ослабления; $$Q\left(\alpha ,\overline{m}\right)$$

- attenuation efficiency factor;

α = πD _p / λ is the dimensionless diffraction parameter (Mie parameter);

λ is the wavelength of the probe radiation;

- комплексный показатель преломления материала частиц. $$\overline{m}$$

- a complex refractive index of the particle material.

Assuming that during the deposition of powder particles onto a drop, the distribution function φ (D _p ) does not change, we can write

$$\frac{c_0}{c_k}=\frac{{\mathrm{<figure-callout\; id="0"\; label="\tau "\; filenames="00000039.png,00000041.png"\; state="\{\{state\}\}">\tau </figure-callout>}}_0}{{\tau }_k}=\frac{\ln \left(\frac{\mathrm{one}}{T_0}\right)}{\ln \left(\frac{\mathrm{one}}{T_0}\right)},\left(\text{13}\right)$$

where τ ₀ , τ _k is the spectral optical density of the layer of powder particles before and after the deposition of droplets, respectively.

Substituting (13) into (12), we obtain the working formula for calculating β

$$\beta =\frac{\mathrm{four}V\ln \left[\left(\ln \frac{\mathrm{one}}{T_0}\right){\left(\ln \frac{\mathrm{one}}{T_k}\right)}^{-\mathrm{one}}\right]}{\pi D^{2}hnf{t}_k\eta }.\left(\text{fourteen}\right)$$

The resulting positive effect of the invention is associated with the following factors:

1. The measurement of the wettability of the powder particles is carried out directly in the dust-air mixture. During measurements, powder materials are not subjected to mechanical stress (briquetting, polishing, etc.).

2. The choice of droplet diameter in the range of 0.8–2.5 mm is due to the fact that during deposition in the cuvette, the drop must retain a spherical shape. According to the experimental data [12, 13], the drop does not deform and retains its spherical shape at Weber numbers We <0.15. In [13], the experimental data on the drop deformation are approximated by the expression

$$\psi =\sqrt{\exp \left(0.03W{e}^{1.5}\right)}\cdot \mathrm{one\; hundred}\%,\left(\text{fifteen}\right)$$

where ψ is the measure of deformation.

[10], где Re=ρuD/µ - число Рейнольдса; ρ - плотность воздуха; µ - коэффициент динамической вязкости воздуха.The rate of stationary deposition of water droplets was determined by solving the equation of gravitational deposition of a spherical particle for the value of the drag coefficient $$C_D=24/\mathrm{Re}+\mathrm{four}/\sqrt[3]{\mathrm{Re}}$$

[10], where Re = ρuD / µ is the Reynolds number; ρ is the air density; µ is the coefficient of dynamic viscosity of air.

The Weber number was calculated by the formula [10] We = ρu ² D / σ, where σ is the coefficient of surface tension of the liquid. The calculations were carried out for the following parameter values: ρ = 1.205 kg / m ³ ; ρ _l = 1000 kg / m ³ is the density of water; µ = 1.808 · 10 ^-5 kg / (m · s). The calculation results (table 1) showed that for water droplets with a diameter of 0.8 mm and 2.5 mm during precipitation in air, the value of the Weber number is We = 0.13 and We = 2.5, respectively. According to (15), for given values of the Weber number, the measure of deformation of the droplet shape does not exceed ψ≈0.1 ÷ 5%. The use of smaller diameter droplets is associated with the technical problem of producing finely divided droplets. Table 1 also shows the experimentally determined values of the rate of deposition of water droplets in air at a pressure p = 100 kPa and a temperature T = 20 ° C [14], which are in good agreement with the calculated data.

Table 1 Parameters of precipitation of a drop of water in air D mm 0.1 0.5 0.8 one 1.5 2 2.5 3 u, m / s 0.25 2.01 3.15 3.9 5.5 7 7.8 8.6 u _exp , m / s 0.27 - - 4.03 - 6.49 - 8.06 We 10 ^-4 0.03 0.13 0.25 0.75 1.6 2.5 3.7

3. The choice of the diameter of the powder particles D _p ≤5 μm is due to the fact that when D _p > 5 μm, the time of deposition of particles is short and the particles quickly settle to the bottom of the measuring volume. The results of the calculations for the speed and time of deposition of particles of coal powder are shown in table 2.

The rate and time of deposition of coal particles were calculated using the formulas for the Stokes regime [10]

, t_p=h/u_p, $$u_p=g\frac{{\rho }_{\mathrm{<figure-callout\; id="2"\; label="p\; D\; p"\; filenames="00000038.png,00000042.png"\; state="\{\{state\}\}">p\; </figure-callout>}}{D}_p^{}{}_2^{}}{\mathrm{eighteen}\mu }$$

, t _p = h / u _p ,

where h = 0.2 m is the height of the measuring volume;

ρ _p = 1200 kg / m ³ - the density of coal particles.

When the particle diameter D _p = 5 μm, the time of their deposition is more than 2 minutes This time is sufficient to measure the transmittance before and after the supply of a set of drops.

, из которых видно, что при значении T₀≤0.2 наблюдается большая чувствительность оптической плотности от коэффициента пропускания.4. The choice of the initial transmittance T ₀ ≤0.2 is due to the fact that the error in the calculation of the optical density τ is the smaller, the greater the sensitivity τ from the transmittance. Figure 4 shows the dependences τ (T) and $$\frac{d\tau }{dT}\left(T\right)$$

, from which it can be seen that at a value of T ₀ ≤0.2, a greater sensitivity of the optical density from the transmittance is observed.

5. The choice of T _k > 2T ₀ is determined from the condition of maximum accuracy of transmittance measurement.

table 2 The parameters of the deposition of particles of coal powder in the air D _p = 20 μm Stk 5.8 5.7 5.4 5.2 4.6 η 0.96 0.96 0.96 0.95 0.95 t _p , s fourteen fourteen fourteen fourteen fourteen D _p = 10 μm Stk 1.5 1.4 1.4 1.3 1.2 η 0.85 0.85 0.84 0.83 0.81 t _p , s 55 55 55 55 55 D _p = 5 μm Stk 0.36 0.36 0.34 0.32 0.29 η 0.55 0.55 0.53 0.52 0.49 t _p , s 221 221 221 221 221 D _p = 4 μm Stk 0.23 0.23 0.22 0.21 0.18 η 0.42 0.42 0.40 0.39 0.35 t _p , s 346 346 346 346 346 D _p = 3 μm Stk 0.13 0.13 0.12 0.12 0.10 η 0.26 0.26 0.24 0.23 0.21 t _p , s 615 615 615 615 615 D _p = 2 μm Stk 0.06 0.06 0.05 0.05 0.05 η 0.1 0.01 0.09 0.09 0.07 t _p min 23 L ²³ L ²³ 23 23 D _p = 1 μm Stk CL02 | 0.01 0.01 0.01 0.01 η 0.01 0.01 0.009 0.008 0.007 t _p min 92 92 92 92 92

The invention is illustrated by drawings and graphs.

Figure 1 shows the equilibrium shape of a drop placed on a horizontal hard surface.

Figure 2 shows the deposition scheme of the drop.

Figure 3 shows a diagram of an experimental setup for determining the wettability of powder materials.

Figure 4 shows the dependence of the optical density τ and its derivative dτ / dT on the transmittance.

Figure 5 shows the differential function of the countable distribution of particles of coal powder in size.

Figure 6 shows the dependence of the concentration of coal dust particles with a distribution (16) on the time of droplet supply for the wettability parameter β = 0.8, calculated by the formula (10).

Figure 7 shows the dependence of the ratio of the optical densities τ ₀ and τ _{k of} particles with distribution (16) on the time of drop supply for the wettability parameter β = 0.8, calculated by the formula (13).

An example implementation of the proposed method (Figure 3). In cell 1 with transparent plane-parallel walls create a uniform suspension of 2 powder particles. Using a laser 3 and a radiation receiver 4, a spectral transmittance T _{0 of} particle suspension is measured. From the droplet supply system 5, a stream of droplets enters the cuvette over a period of time t _k . Then re-measure the spectral transmittance T _k and determine the wettability parameter of the powder particles by the formula (14).

The effectiveness of the proposed method, the circuit of which is shown in FIG. 2, was determined by direct calculations of changes in the concentration and optical density of the medium using coal dust particles as an example when they are deposited in air when water droplets are supplied for the parameter values given in table 3. The distribution function of coal particles, obtained using the installation Mastersizer 2000 (MALVERN, UK), is shown in Figure 5. The rms particle diameter is D ₂₀ = 1.9 μm. The resulting function is approximated by gamma distribution

$$\varphi \left(D_p\right)=15.9D_p^{5.5}\exp \left(-3.6D_p\right),\left(\text{16}\right)$$

where [φ (D _p )] = μm ^-1 ; [D _p ] = μm.

Table 3 The values of the parameters for calculating β ρ _p = 1200 kg / m ³ µ = 1.808 · 10 ^-5 kg / m · s n = 50 f = 2c ^-1 ρ = 1.205 kg / m ³ h = 0.2 m V = 0.002 m ³ η = 0.53 ρ _l = 1000 kg / m ³ D = l.5 mm c ₀ = 1000 kg / m ³

The calculation results are presented in Fig.6, 7. Fig.6 shows the dependence of the concentration of suspended particles of coal dust from the time of supply of droplets for the wettability parameter β = 0.8. Figure 7 shows the dependence of the optical density on the time of supply of droplets to the cell with a value of β = 0.8. The verification of the adequacy of the method can be carried out using Fig.6 and Fig.7.

We select the time interval for droplet delivery t _k = 100 s, at which a change in the initial concentration of the suspension is noticeable and the condition T _k > 2T ₀ is fulfilled for the spectral transmittance (Fig. 6, 7). When the value of time t _k = 100 s, the suspension concentration and the ratio of optical densities are equal to c _k = 470 kg / m ³ , τ ₀ / τ _k = 2.1, respectively.

We substitute the found values into the final formula (14) for calculating the parameter β

. $$\beta =\frac{\mathrm{four}\cdot 0.002\cdot \ln \left(2.1\right)}{3.14\cdot {\left(1.5\cdot {10}^{-3}\right)}^2\cdot 0.2\cdot \mathrm{fifty}\cdot 2\cdot \mathrm{one\; hundred}\cdot 0.53}=0.8$$

.

As can be seen from the above example, the specified and calculated values of the wettability parameter coincide (β = 0.8). Similar results are obtained for any wettability parameter in the range β = 0 ÷ 1.0. Thus, the proposed method allows to increase the accuracy of determining the wettability characteristics of fine powders and to measure directly in a dusty air mixture. This method can find application for research of a wide class of organic and inorganic powder materials.

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Claims (1)

A method for determining the wettability of finely dispersed powders, based on the calculation of the fraction of wetted powder particles, characterized in that in a cuvette with transparent plane-parallel walls a suspension of powder particles uniformly distributed in air with a maximum diameter of not more than 5 μm is created and the spectral transmittance of the probe laser radiation of the suspension is measured , a flow of monodispersed droplets with a diameter of 0.8 ÷ 2.5 mm is fed into the cuvette from droppers uniformly distributed over the cross section of the cuvette and remeasured ktralny transmittance, the initial concentration of the powder particles is selected from the condition of T ₀ ≤0.2, gob delivery time interval is determined from the condition T _k> 2T _0, a parameter of wettability is calculated by the formula

where V is the volume of the cell;
T ₀ , T _k - spectral transmittance before and after the deposition of droplets;

- capture coefficient;

ρ _p is the density of powder particles;
D ₂₀ is the rms diameter of the powder particles;
u is the speed of gravitational precipitation of the droplet;
µ is the coefficient of dynamic viscosity of air;
D is the diameter of the drop;
h is the height of the cell;
n is the number of droppers;
f is the frequency of drops falling;
t _k is the time interval for dropping drops into the cell.

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