On the effects from the simultaneous occurrence of the critical Casimir and dispersion forces between conical colloid particle and a thick plate immersed in nonpolar critical fluid

Here we study the interplay between the van der Waals (vdWF) and critical Casimir forces (CCF), as well as the total force (TF) between a conical colloid particle and a thick planar slab. We do that using general scaling arguments and mean-field type calculations utilizing the so-called “surface integration approach”, a generalization of the well known Derjaguin approximation. Its usage in the present research, requires knowledge on the forces between two parallel slabs, confining in between some fluctuating fluid medium characterized by its temperature T and chemical potential μ . The surfaces of the colloid particle and the slab are assumed coated by thin layers exerting strong preference to the liquid phase of a simple fluid, or one of the components of a binary mixture, modeled by strong adsorbing local surface potentials, ensuring the so-called (+,+) boundary conditions. On the other hand, the core region of the slab and the particle, influence the fluid by long-ranged competing dispersion potentials. We demonstrate that for a suitable set of colloid-fluid, slab-fluid, and fluid-fluid coupling parameters the competition between the effects due to the coatings and the core regions of the objects, result, when one changes T or μ , in sign change of the Casimir force (CF) and the TF acting between the colloid and the slab. Such an effect can provide a strategy for solving problems with handling, feeding, trapping and fixing of microparts in nanotechnology.