The Effect of Electrostatic Double Layer Repulsion on Gravitational Coagulation

Can colloidal particles flocculate at two energy minima simultaneously in a quiescent medium?

“…2. The above three flocculation regions were shown in the papers of Melik and Folger [2] and Qiao and Wen [7], but not for the fourth region of simultaneous flocculation at both the primary and secondary minima in the total interaction energy curve. The evidence for the existence of this narrow strip region of "combined" flocculation enclosed by curves BB OC as shown in Fig.…”

“…2 in Ref. [7]) which is caused by the repulsive force induced by the electron clouds around particles.…”

“…3 below), located at (1) flocculation at the primary minimum of the total interaction energy curve; (2) flocculation at the secondary minimum of the total interaction energy curve; (3) an extremely narrow region of simultaneous flocculation at both the primary minimum and the secondary minimum of the total interaction energy profile; and (4) a region of deflocculation where colloidal suspension remains stable. Both Melik and Fogler [2] and Qiao and Wen [7] ignored the third narrow flocculation region in their analyses. We shall now prove the existence of this narrow region in details as follows.…”

“…But Spielman and Cukor [1] found four distinct regions of flocculation, and Melik and Fogler [2] only found three. Later on, Qiao and Wen [7] adopted Jeffrey and Onishi's mobility functions [8] and took the electron-cloudinduced repulsive force into consideration; they also found that the colloidal suspension can be stable against gravityinduced coagulation at intermediate gravity forces. However, in our previous work [9], using the same concept of determining the limiting trajectory and detailed calculation, we confirmed Spielman and Cukor's result [1] that there are four distinct regions of flocculation in the stability diagram (see Fig.…”

Gravity-induced flocculation of Brownian particles in quiescent media under weak gravity

“…In their model, the relative particle velocity due to Brownian motion was formulated in terms of the relative diffusion coefficient and the probability density [10]. Then, by using the same perturbation method, Qiao and Wen [11] and Qiao et al [12] also determined the flocculation rates of Brownian particles in a quiescent media at various ionic strengths. From the contours of related magnitudes of the probability density in both the upstream and the downstream regions around the referenced particle a 1 shown in Fig.…”