Competing interaction fluids have become ideal model systems to study a large number of phenomena, for example, the formation of intermediate range order structures, condensed phases not seen in fluids driven by purely attractive or repulsive forces, the onset of particle aggregation under in- and out-of-equilibrium conditions, which results in the birth of reversible and irreversible aggregates or clusters whose topology and morphology depend additionally on the thermodynamic constrictions, and a particle dynamics that has a strong influence on the transport behaviour and rheological properties of the fluid. In this contribution, we study a system of particles interacting through a potential composed by a continuous succession of a short-ranged square-well, an intermediate-ranged square-shoulder and a long-ranged square-well. This potential model is chosen to systematically analyse the contribution of every component of the interaction potential on the phase behaviour, the microstructure, the morphology of the resulting aggregates and the transport phenomena of fluids described by competing interactions. Our results indicate that the inclusion of a barrier and a second well leads to new and interesting effects, which in addition result in variations of the physical properties associated to the competition among interactions.

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The gravitational effects in gel-forming patchy colloidal systems are studied. We focus on how the gel structure is modified by gravity. Through Monte Carlo computer simulations of gel-like states recently identified by the rigidity percolation criterion, the influence of the gravitational field, characterized by the gravitational P\'eclet number, $Pe$, on patchy colloids is studied in terms of the patchy coverage, $\chi$. We find that there exists a threshold P\'eclet number, $Pe_{g}$, that depends on $\chi$ above which the gravitational field enhances the particle bonding and promotes the aggregation or clustering of particles. Interestingly, when $\chi \sim 1$, our results are consistent with an experimentally determined threshold $Pe$ value where gravity affects the gel formation in short-range attractive colloids. The cluster size distribution and the density profile undergo variations that lead to changes in the percolating cluster. These changes have an important impact on the structural rigidity of the patchy colloidal dispersion; the percolating cluster goes from a uniform spatially network to a heterogeneous percolated structure; depending on the $Pe$ value, the new heterogeneous gel-like states can coexist with both diluted and dense phases. In the isotropic case, the increase in the $Pe$ number can shift the critical temperature to higher temperatures, however, when $Pe > 0.01$ the binodal disappears and the particles sediment at the bottom of the sample cell. Furthermore, gravity moves the rigidity percolation threshold to lower densities. Finally, we also notice that within the values of the P\'eclet number here explored, the cluster morphology is barely altered.