Critical and near critical phase behaviour and interplay between the thermodynamic Casimir and van der Waals forces in confined non-polar fluid medium with competing surface and substrate potentials

We study the behavior of the critical Casimir force and its interplay with the van der Waals force acting between two parallel slabs separated at a distance $L$ from each other confining a non-polar simple fluid or a binary liquid mixture. The surfaces of the slabs are coated by thin layers exerting strong preference to the liquid phase of the fluid, or one of the components of the mixture. The slabs influence the fluid by long-range competing dispersion potentials. Under such conditions one usually expects {\it attractive} Casimir force governed by universal scaling function to which the dispersion potentials provide only corrections to scaling. We demonstrate, however, that below a given $L<L_{\rm crit}$ the competition between the effects due to the coatings and the slabs can result in {\it sign change} of the Casimir force when one changes the temperature $T$, the chemical potential of the fluid $\mu$, or $L$. The last implies that by choosing specific materials for the slabs, coatings and the fluid for $L \lesssim L_{\rm crit}$ one can realize {\it repulsive} Casimir force with {\it non-universal} behavior which, upon increasing $L$, gradually turns into an {\it attractive} one described by an {\it universal} scaling function for $L\gg L_{\rm crit}$. We presented arguments and relevant data for specific substances in support of the experimental feasibility of the predicted behavior of the force.