Among the diversity of methods of water-soluble salts withdrawal from sediment the following can be pointed out: repulping, washing by filters, decantation.
Decantation is the easy and gentle cleaning method towards the pigment crystal structure, implying the process of hard and liquid phase´s separation by means of sedimentation
Aiming to define the quantity of cleaning cycles necessary for archiving the desired concentration of water-soluble salts in pigment paste the mathematical model of the process of water -soluble salts withdrawal from organic pigment suspension was developed.
When developing the mathematical model the following assumptions are taken into consideration: the mass of water-soluble salts is less than mass of water and hard particles; during the sequence period (mixing together with sedimentation) the gradient of water-soluble salts concentration in volume of suspension is considered as negligible; the character of dependence linking the equilibrium concentrations of water-soluble salts in paste and liquor is linear; the volume of paste in all cycles of washing is constant; pigment is a ball-type particle with radius r0.
Suspensions and sediments of pigments and colorants show electrokinetic potential that influences the process of water-soluble salts withdrawal [1-3]. Fine particles of hard phase (pigment) of some micron size bear electrical charge in relation to surrounding aqueous dispersion medium that appears as a result of preferential absorption of ions of a definite sign, surface ionization or due to absorption at the surface of polar molecules [2,4]. The system of spatial-split charges appeared at the phase border line (pigment-liquor (polar liquor)) represents a double electric layer [3,4]. Complex - a pigment particle in the dispersion phase with the double electric layer surrounding it represents micelle. Aggregate inside micelle represents a hard phase (pigment particle), pigment with potentialdefining ions, composed by ions of chlorine Cl-, represents a micelle core. Core together with the absorption layer form a particle, that surrounded by the diffuse layer. The micelle composition can be represented the following way:
{[(Pigment)nmCl-]xNa+}(m-x)Na+
where n - number of potentialdefining molecules, m-number of potentialdefining ions of chlorine, x - number of sodium ions.
The amount of water-soluble salts on the surface of micelle core is sum of quantity of water-soluble salts counterions in the micelle absorption and diffuse layers:
(1)
where v - quantity of water-soluble salts on the surface of a micelle core, kmol; 
- quantity of water-soluble salts in the micelle diffuse layer, kmol;
- quantity of water-soluble salts in the micelle absorption layer, kmol.
At diffuse layer the quantity of water-soluble salts counterions on the surface of a micelle particle in integral form:
(2)
where C - concentration of counterions in a diffuse area, kmol/m3; r - the interval from the surface of a pigment particle, m; r1 - the border of the absorption layer, m; r3 - the border of the diffuse layer, m.
At the absorption layer the quantity of water-soluble salts counterions on the surface of a micelle core with allowance for maximum possible quantity of counterions:
(3)
where r0 - radius of micelle core, m; 
- space occupied by one counterion, m2; 
- the change of substance chemical potential at transfer from liquor to absorption layer, J/mol; 
-the difference of potential in the given point and in the liquid volume (at the «endless» moving from the surface) J/C; 
- the thickness of the diffuse layer; m; 
- the thickness of the absorption layer; m;
- Faraday constant, C; z - ions charge.
Let´s bring into equation (1) equations (2-3):
(4)
where R - gas constant J/(mol C) ; T - absolute temperature, C.
The material balance of quantity of water-soluble salts for sedimentation and decantation processes appeared as a result of summing the quantity of water-soluble salts in hard material (pigment) and in liquor will have the following form:
(5)
- total quantity of the water-soluble salts in pigment suspension, kmol; 
- quantity of the water-soluble salts in liquor, kmol; 
- quantity of the water-soluble salts in the total pigment volume, kmol;
- quantity of the water-soluble salts on the surface of one pigment particle, kmol;
- volume of paste, m3; 
- number of pigment particles, p/m3; 
- pigment volume fraction in paste.
The paste layer obtained after decantation is brought to the volume of the initial suspension by adding water as a solvent, as a result the volume of water placed to the paste will be 
m3.
The quantity of water-soluble salts is not changed, the volume of paste is constant, the volume of water in liquor has grown up to .
Therefore, the material balance of the process of paste dilution by a solvent (water) can be represented the following way:
(6)
where V - volume of the initial suspension, m3;
- volume of liquor, m3.
The concentration of water-soluble salts in a solvent (water) becomes equal to 
while the quantity of substance of these salts doesn´t change.
The concentration of water -soluble salts in a solvent (water) is found out using integral way (method of successive approximation).
1-st approximation is based on the approximate dilution of liquor only.
First integral step. Let´s find the concentration of salt in liquor at the first dilution taking into consideration the concentration of salt in the initial liquor 
and volume of the initial suspension 
m3 and paste m3.
(7)
where 
- mole concentration of water-soluble salts in a solvent, kmol/m3.
Let´s calculate the quantity of water-soluble salts on the surface of pigment
(8)
where the quantity of one particle is defined according to the equation (4)
Second integral step. Let´s find the concentration of salts in liquor at the first dilution taking into consideration the quantity of water-soluble salts in a pigment suspension and on the pigment surface during the first dilution:
(9)
The process of successive approximation for the equations (7)-(9) is held up to the moment when the difference between the iterations for calculating by equation (7) and - calculating by equation (9) will exceed the desired number.
The concentration of water-soluble salts in liquor and at the pigment surface doesn´t change, the volume of liquor changes due to decantation influencing the total quantity of salts, as a result the material balance of the process of suspension sedimentation and dispersion phase (liquor) decantation can be represented the following way:
(10)
These findings are used for the next process of dilution. The calculation is repeated until the moment the concentration will take the value less or equal to the desired.
The procedure offered allows to calculate the technological parameters of the process of water- soluble salts withdrawal from azopigment suspension by method of decantation and sedimentation.
References
- Malinovskaya T.A. Suspension Separation in the Organic Synthesis Industry / T.A. Malinovskay. - M.: Chemistry, 1972. - 320 p.
- Lukomskiy U.Y., Gamburg, U.D. Phusic-chemical Fundamentals of Electrochemistry: text- book/ U.Y. Lukomskiy, U.D. Gamburg. - M.: ID Intellect, 2008. - 424 p.
- Damaskin B.B., Petriy O.A. Introduction to Electro-chemical Kinetics / B.B. Damaskin, O.A. Petriy, 2nd edition. - M.: Higher School, 1983. - 400 p.
- Zakharchenko V.N. Colloid Chemistry: text-book for universities / V.N. Zaharchenko. - M.: Higher School, 1989. - 238 p.
The work is submitted to Scientific Conference "The Problems of International Integration of Educational Standards", England (London) - France (Paris),
April 23 - May 1, 2010. Came to the editorial office on 15.02.2010.
Библиографическая ссылка
Subocheva M.U., Leontyeva A.I., Degtyarev A.A. MATHEMATICAL MODELING OF THE PROCESS OF WATER - SOLUBLE SALTS WITHDRAWAL FROM PIGMENT ORGANIC SUSPENSION BY DECANTATION // European Journal of Natural History. – 2010. – № 2. – С. 51-54;URL: https://world-science.ru/ru/article/view?id=20960 (дата обращения: 25.11.2024).