2015
DOI: 10.1063/1.4934594
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Approach to theoretical estimation of the activation energy of particle aggregation taking ionic nonclassic polarization into account

Abstract: The activation energy of particle aggregation in suspensions is a very important kinetic parameter in a wide range of science and engineering applications. At present, however, there is no theory that can theoretically predict the activation energy. Because the activation energy is often less than 10 kT (where k is the Boltzmann constant and T is the temperature), it is difficult to experimentally measure. In this study, a theory for calculating the activation energy is established. Experimental measurements o… Show more

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Cited by 37 publications
(50 citation statements)
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“…The relative values of cationic non‐classical polarizability of a monovalent cation, taking Li + as the reference, have been obtained previously (Liu et al , , ; Xu et al , ; Hu et al , ), and the estimated effective charges of Na + and K + arising from NCP were approximately +1.110 and +1.827, respectively (with the charge of Li + equal to +1), at concentrations of 0.001–0.02 mol l −1 of a 1:1‐type electrolyte (Liu et al , , ). Recently, Li et al () obtained the absolute value of effective charge by comparison with the measured and calculated activation energy of clay particle aggregation; that for Na + arising from NCP was +1.180 under 1:1‐type electrolyte concentrations of 0.035–0.214 mol l −1 . Considering that Na + is a weak polarization cation species, it is reasonable to assume that the absolute effective charge of Na + that arises from NCP is +1.180 under 1:1‐type electrolyte concentrations of 0.00001–0.10 mol l −1 .…”
Section: Theory For Calculating Surface Potential Of Soil Particles Tmentioning
confidence: 99%
“…The relative values of cationic non‐classical polarizability of a monovalent cation, taking Li + as the reference, have been obtained previously (Liu et al , , ; Xu et al , ; Hu et al , ), and the estimated effective charges of Na + and K + arising from NCP were approximately +1.110 and +1.827, respectively (with the charge of Li + equal to +1), at concentrations of 0.001–0.02 mol l −1 of a 1:1‐type electrolyte (Liu et al , , ). Recently, Li et al () obtained the absolute value of effective charge by comparison with the measured and calculated activation energy of clay particle aggregation; that for Na + arising from NCP was +1.180 under 1:1‐type electrolyte concentrations of 0.035–0.214 mol l −1 . Considering that Na + is a weak polarization cation species, it is reasonable to assume that the absolute effective charge of Na + that arises from NCP is +1.180 under 1:1‐type electrolyte concentrations of 0.00001–0.10 mol l −1 .…”
Section: Theory For Calculating Surface Potential Of Soil Particles Tmentioning
confidence: 99%
“…We characterized the rate of aggregation using the rate of total average aggregation (TAA) (Jia et al, ), which is defined by the equation given below (Jia et al, ; Tian et al, , ; Li et al, ): truev˜Tf0=1t00t0νtrue˜tf0dt=1t00t0DtD0tdt, where νtrue˜ T ( f 0 ) (nm minute −1 ) is the TAA rate, D ( t ) is the mean hydrodynamic diameter of clusters at time t (as shown in Figure ), D 0 is the initial mean hydrodynamic diameter of soil particles at t = 0 and t 0 is equal to 60 minutes in this study.…”
Section: Resultsmentioning
confidence: 99%
“…Repulsive electrostatic energy can be defined as the work required for a particle with a head area S (nm 2 ) to move from λ = b to λ = a in a repulsive space with the pressure distribution P E ( λ ) (Li et al ., ). Therefore, the repulsive electrostatic energy can be calculated with Equation : Ec0=101SabPnormalEλdλ=101S×A where E ( c 0 ) is the repulsive electrostatic energy (J mol −1 ); a = 2 nm, b = 10 nm.…”
Section: Discussionmentioning
confidence: 97%
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“…(), the charge number of cation Z in the equations can be replaced by γZ (Li et al . ), and the surface potentials of the two soils under different electrolyte concentrations could be estimated; the results are given in Table . On the other hand, to calculate the long‐range van der Waals attractive force, the Hamaker constant must also be given; for soil we take the Hamaker constant to be 7.8 × 10 −20 J (Yu et al ., ).…”
Section: Discussionmentioning
confidence: 99%