Method for determining surface tension of a comminuted solid

Process for determining the numeric value of the surface tension γ of a comminuted solid starting from different experimental measurements and different mathematical equations consisting of:

• taking a tube, the lower end of which is hermetically sealed by a membrane permeable to the liquid,
• filling it to about 80% of its total volume with the said comminuted solid,
• dipping the lower part closed by the membrane in a liquid,
• allowing the liquid to rise freely in a first phase in the tube,
• measuring the liquid mass that rose in the tube as a function of time by monitoring the variation of the remaining mass of the liquid, in order to obtain the slope 1 of the straight line described by equation (I) below:
• m2=f(t) (equation I)
• characterized in that:
• in a second phase, when 10 to 20% of the total height of the powder is in contact with the liquid, a first back pressure is applied to the upper part of the tube so as to stop the capillary rise of the liquid in the tube through the comminuted solid, and to measure the numeric value of the remaining liquid mass after the liquid has risen so as to determine the mass of the liquid that rose into the tube by mathematical calculation, as soon as the pair consisting of the pressure and the mass variation has stabilized, and then after using the mathematical equation:
• ΔP=(A−Δγ)−(εpgh) (equation II)
• to obtain the numeric value of (A−Δγ)
• where
• A is the specific area of the comminuted solid (m2/m3)
• Δγ=γs−γsL is the difference between the surface tension of the solid (Ys) and the solid-liquid interface energy (YSL),
• ε is the porosity of the solid,
• p is the density of the liquid,
• g is the acceleration due to gravity (9.81),
• h is the height of the comminuted solid in the tube,
• ΔP is the pressure variation applied on the tube,
• in a third phase, to stop applying the first back pressure so as to allow the liquid to rise freely in the tube until the comminuted solid is fully immersed in the liquid present in the tube, and to regularly measure the variation of the remaining mass of liquid after the liquid has risen in the tube, as a function of time, to afterwards deduce the total mass of liquid risen in the tube and after a mathematical calculation, and then to make a mathematical equation (I) to obtain the slope 2 and then the porosity ε according to equation (III) below:
• 11 ϵ = liquid ⁢ ⁢ volume ⁢ ⁢ at ⁢ ⁢ saturation powder ⁢ ⁢ volume ⁢ ⁢ in ⁢ ⁢ the ⁢ ⁢ tube (equation III)
• and then to use the mathematical equation (IV):
• 12 Q exp = ( ϵ · π · R 2 ) 2 β × ( A · Δγ ) (equation IV)
• where
• Qexp (kg.m/s2) is equal to [1/(2×Γliq)]×slope 2
• where Γliq=ρ/η, where η is the viscosity of the probe liquid in Pa.s,
• R is the internal radius of the tube,
• ε is the porosity of the comminuted solid,
• the numeric value of β where β is the tortuousness coefficient,
• in a fourth step, to apply a negative pressure on the top part of the tube, kept constant for a period varying from 300 to 1000 seconds, to measure the numeric value of the remaining liquid mass after the liquid has risen in the tube, and then to use a mathematical calculation to deduce the rate of variation of the liquid mass risen in the tube, and then the numeric value of the specific area A(m2/m3) of the powder in the tube, using Kozeny-Carman's equation (V) defined below:
• 13 A 2 = Δ ⁢ ⁢ P 5 · η · h · v × ϵ 3 ( 1 - ϵ ) ( equation ⁢ ⁢ V )
• where
• ΔP is the pressure variation applied to the tube,
• η is the viscosity of the liquid,
• h is the powder height in the tube,
• v is the rise velocity of the liquid,
• ε is the porosity of the comminuted solid,
• and to apply a second back pressure in a fifth step, on the top part of the tube and held constant for a duration of about 300 to 1000 seconds, to make another calculation of the numeric value of the specific area A (m2/m3) as defined in step 4.