This work discusses the sedimentation stability and aging of aqueous suspension of Laponite in the presence of cetyltrimethylammonium bromide (CTAB). The concentration of Laponite was fixed at the constant level $C_l=2$ %wt, which corresponds to the threshold between equilibrium gel IG$_1$ and repulsive gel IG$_2$ phases. The concentration of CTAB $C_s$ was within 0-0.3 %wt. In the presence of CTAB the Laponite aqueous suspensions were unstable against sedimentation and they separated out into upper and bottom layers (U- and B-layers, respectively). The dynamic light scattering technique revealed that the addition of CTAB even at rather small concentration, $C_s=0.0164$ %wt ($0.03 CEC$), induced noticeable changes in the aging dynamics of U-layer, and it was explained by equilibration of CTAB molecules that were initially non-uniformly distributed between different Laponite particles. Accelerated stability analysis by means of analytical centrifugation with rotor speed ${omega}=500-4000$ rpm revealed three sedimentation regimes: continuous (I, $C_s<0.14$ %wt), zone-like (II, $0.14<C_s<0.2$ %wt) and gel-like (III, $C_s >0.2$ %wt). It was demonstrated that B-layer was soft in the zone-like regime. The increase of ${omega}$ resulted in its supplementary compressing and the collapse of soft sediment above certain critical centrifugal acceleration.
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