Galin Valchev

Surface integration approach: a new technique for evaluating geometry dependent forces between objects of various geometry and a plate.

We present a new approach, which can be considered as a generalization of the Derjaguin approximation, that provides exact means to determine the force acting between a three-dimensional body of any shape and a half-space mutually interacting via pairwise potentials. Using it, in the cases of the Lennard-Jones, standard and the retarded (Casimir) van der Waals interactions we derive exact expressions for the forces between a half-space or a slab of finite thickness and an ellipsoid in a general orientation, which in the simplest case reduces to a sphere, a tilted fully elliptic torus, and a body obtained via rotation of a single loop generalized Cassini oval, a particular example of which mimics the shape of a red blood cell. The results are obtained for the case when the object is separated from the plane via a non-polar continuous medium that can be gas, liquid or vacuum. Specific examples of biological objects of various shapes interacting with a plate like substrates are also considered.

On the Forces Between Micro and Nano Objects and a Gripper

The authors study the van der Waals force, between the gripper jaw and an object-cubical, spherical and conical in shape, situated at a distance L of closest approach from it. The generic and most general case is considered, when the materials of the working jaw of the gripper and the particle are made of different materials strongly preferring the liquid phase of the fluid being at temperature T and chemical potentialm. The contributions due to the standard van der Waals, as well as of the retarded Casimir van der Waals interactions are considered. They concluded that strongly depends on the contrast, at given fixed T and m, between the physical properties of the fluid and the material of the arms of the gripper and the particle. In addition, as expected, strongly depends on the shape of the object, its size, and the distance L between it and the working jaw of the gripper. Their approach can be applied to any nonpolar fluid.

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

We study, using general scaling arguments and mean-field type calculations, 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 some fluctuating fluid medium, say a nonpolar one-component 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, modeled by strong adsorbing local surface potentials ensuring the so-called (+,+) boundary conditions. The slabs, on the other hand, influence the fluid by long-range competing dispersion potentials, which represent irrelevant interactions in renormalization-group sense. Under such conditions, one usually expects attractive Casimir force governed by universal scaling function, pertinent to the extraordinary surface universality class of Ising type systems, to which the dispersion potentials provide only corrections to scaling. We demonstrate, however, that below a given threshold thickness of the system L(crit) for a suitable set of slabs-fluid and fluid-fluid coupling parameters the competition between the effects due to the coatings and the slabs can result in sign change of the Casimir force acting between the surfaces confining the fluid when one changes the temperature T, the chemical potential of the fluid μ, or L. The last implies that by choosing specific materials for the slabs, coatings, and the fluid for L≲L(crit) one can realize repulsive Casimir force with nonuniversal behavior which, upon increasing L, gradually turns into an attractive one described by a universal scaling function, depending only on the relevant scaling fields related to the temperature and the excess chemical potential, for L≫L(crit). We present arguments and relevant data for specific substances in support of the experimental feasibility of the predicted behavior of the force. It can be of interest, e.g., for designing nanodevices and for governing behavior of objects, say colloidal particles, at small distances. We formulate the corresponding criterion for determination of L(crit). The universality is regained for L≫L(crit). We also show that for systems with L≲L(crit), the capillary condensation phase diagram suffers modifications which one does not observe in systems with purely short-ranged interactions.

On the Interaction of a Micro Object with the Working Arm of a Gripper Immersed in a Nonpolar Fluid

We study the total force tot F between the working plate of a gripper and an object – cubical or spherical in shape, situated at a distance L of closest approach to each other and both immersed in a nonpolar fluid, which can be liquid or gas, with temperature T and chemical potential μ. For comparison, we also present results when the fluid is replaced by a vacuum. We consider the most general case when the materials of the working jaw of the gripper are made of different materials with both strongly preferring the liquid phase of the fluid. In our approach we take into account the direct particle-jaw van der Waals interaction ~ s J , the van der Waals interactions between the molecules of the fluid with i) other molecules of the fluid ~ l J ; ii) with the constituent elements of the particle , ~ , l p J and iii) the constituents of the plate , ~ l s J . We consider both the contribution due to the standard van der Waals, as well as of the retarded van der Waals-Casimnir interactions. We conclude that tot F strongly depends on the contrast, at given fixed T and , between the physical properties of the fluid and the material of the arms of the gripper and the particle, and is proportional to ,p ,s p / / l l l l l l s l J J J J J , where ( , ) l T is the density of the fluid, s is the density of the substrate, and p is that one of the particle. In addition, as expected, tot F strongly depends on the shape of the object, its size, and the distance between it and the working jaw of the gripper. Our approach can be applied to any nonpolar fluid.