Hydrodynamic theory of de-wetting

A prototypical problem in the study of wetting phenomena is that of a solid plunging into or being withdrawn from a liquid bath. In the latter, de-wetting case, a critical speed exists above which a stationary contact line is no longer sustainable and a liquid film is being deposited on the solid. Demonstrating this behavior to be a hydrodynamic instability close to the contact line, we provide the first theoretical explanation of a classical prediction due to Derjaguin and Levi: instability occurs when the outer, static meniscus approaches the shape corresponding to a perfectly wetting fluid

Long range polarization attraction between two different likely charged macroions

It is known that in a water solution with multivalent counterions (Z-ions), two likely charged macroions can attract each other due to correlations of Z-ions adsorbed on their surfaces. This "correlation" attraction is short-ranged and decays exponentially with increasing distance between macroions at characteristic distance A/2\pi, where A is the average distance between Z-ions on the surfaces of macroions. In this work, we show that an additional long range "polarization" attraction exists when the bare surface charge densities of the two macroions have the same sign, but are different in absolute values. The key idea is that with adsorbed Z-ions, two insulating macroions can be considered as conductors with fixed but different electric potentials. Each potential is determined by the difference between the entropic bulk chemical potential of a Z-ion and its correlation chemical potential at the surface of the macroion determined by its bare surface charge density. When the two macroions are close enough, they get polarized in such a way that their adjacent spots form a charged capacitor, which leads to attraction. In a salt free solution this polarization attractive force is long ranged: it decays as a power of the distance between the surfaces of two macroions, d. The polarization force decays slower than the van der Waals attraction and therefore is much larger than it in a large range of distances. In the presence of large amount of monovalent salt, when A/2\pi<< d<< r_s (r_s is the Debye-H\"{u}ckel screening radius), this force is still much stronger than the van der Waals attraction and the correlation attraction mentioned above.Comment: 12 pages, 7 figures. Small change in the text, no change in result

Ionic conductivity on a wetting surface

Recent experiments measuring the electrical conductivity of DNA molecules highlight the need for a theoretical model of ion transport along a charged surface. Here we present a simple theory based on the idea of unbinding of ion pairs. The strong humidity dependence of conductivity is explained by the decrease in the electrostatic self-energy of a separated pair when a layer of water (with high dielectric constant) is adsorbed to the surface. We compare our prediction for conductivity to experiment, and discuss the limits of its applicability.Comment: 5 pages, 3 figures; one section and two illustrations added; figures updated and discussion added; typo fixe

The interaction between colloids in polar mixtures above Tc

We calculate the interaction potential between two colloids immersed in an aqueous mixture containing salt near or above the critical temperature. We find an attractive interaction far from the coexistence curve due to the combination of preferential solvent adsorption at the colloids' surface and preferential ion solvation. We show that the ion-specific interaction strongly depends on the amount of salt added as well as on the mixture composition. Our results are in accord with recent experiments. For a highly antagonistic salt of hydrophilic anions and hydrophobic cations, a repulsive interaction at an intermediate inter-colloid distance is predicted even though both the electrostatic and adsorption forces alone are attractive.Comment: 9 pages, 6 figure

Casimir Energies: Temperature Dependence, Dispersion, and Anomalies

Assuming the conventional Casimir setting with two thick parallel perfectly conducting plates of large extent with a homogeneous and isotropic medium between them, we discuss the physical meaning of the electromagnetic field energy $W_{\rm disp}$ when the intervening medium is weakly dispersive but nondissipative. The presence of dispersion means that the energy density contains terms of the form $d[\omega\epsilon(\omega)] /d\omega$ and $d[\omega\mu(\omega)] /d\omega$. We find that, as $W_{\rm disp}$ refers thermodynamically to a non-closed physical system, it is {\it not} to be identified with the internal thermodynamic energy $U$ following from the free energy $F$, or the electromagnetic energy $W$, when the last-mentioned quantities are calculated without such dispersive derivatives. To arrive at this conclusion, we adopt a model in which the system is a capacitor, linked to an external self-inductance $L$ such that stationary oscillations become possible. Therewith the model system becomes a non-closed one. As an introductory step, we review the meaning of the nondispersive energies, $F, U,$ and $W$. As a final topic, we consider an anomaly connected with local surface divergences encountered in Casimir energy calculations for higher spacetime dimensions, $D>4$, and discuss briefly its dispersive generalization. This kind of application is essentially a generalization of the treatment of Alnes {\it et al.} [J. Phys. A: Math. Theor. {\bf 40}, F315 (2007)] to the case of a medium-filled cavity between two hyperplanes.Comment: 15 pages, no figures; slight revision of discussio

Direct test of defect mediated laser induced melting theory for two dimensional solids

We investigate by direct numerical solution of appropriate renormalization flow equations, the validity of a recent dislocation unbinding theory for laser induced freezing/melting in two dimensions. The bare elastic moduli and dislocation fugacities which are inputs to the flow equations are obtained for three different 2-d systems (hard disk, inverse $12^{th}$ power and the Derjaguin-Landau-Verwey-Overbeek potentials) from a restricted Monte Carlo simulation sampling only configurations {\em without} dislocations. We conclude that (a) the flow equations need to be correct at least up to third order in defect fugacity to reproduce meaningful results, (b) there is excellent quantitative agreement between our results and earlier conventional Monte Carlo simulations for the hard disk system and (c) while the qualitative form of the phase diagram is reproduced for systems with soft potentials there is some quantitative discrepancy which we explain.Comment: 11 pages, 14 figures, submitted to Phys. Rev.

Thermophoresis of charged colloidal particles

Thermally induced particle flow in a charged colloidal suspension is studied in a fluid-mechanical approach. The force density acting on the charged boundary layer is derived in detail. From Stokes' equation with no-slip boundary conditions at the particle surface, we obtain the particle drift velocity and the thermophoretic transport coefficients. The results are discussed in view of previous work and available experimental data.Comment: 9 pages, 2 figure

Correction to the Casimir force due to the anomalous skin effect

The surface impedance approach is discussed in connection with the precise calculation of the Casimir force between metallic plates. It allows to take into account the nonlocal connection between the current density and electric field inside of metals. In general, a material has to be described by two impedances $Z_{s}(\omega,q)$ and $Z_{p}(\omega,q)$ corresponding to two different polarization states. In contrast with the approximate Leontovich impedance they depend not only on frequency $\omega$ but also on the wave vector along the plate $q$. In this paper only the nonlocal effects happening at frequencies $\omega<\omega_{p}$ (plasma frequency) are analyzed. We refer to all of them as the anomalous skin effect. The impedances are calculated for the propagating and evanescent fields in the Boltzmann approximation. It is found that $Z_p$ significantly deviates from the local impedance as a result of the Thomas-Fermi screening. The nonlocal correction to the Casimir force is calculated at zero temperature. This correction is small but observable at small separations between bodies. The same theory can be used to find more significant nonlocal contribution at $\omega\sim\omega_p$ due to the plasmon excitation.Comment: 29 pages. To appear in Phys. Rev.

Hydration interactions: aqueous solvent effects in electric double layers

A model for ionic solutions with an attractive short-range pair interaction between the ions is presented. The short-range interaction is accounted for by adding a quadratic non-local term to the Poisson-Boltzmann free energy. The model is used to study solvent effects in a planar electric double layer. The counter-ion density is found to increase near the charged surface, as compared with the Poisson-Boltzmann theory, and to decrease at larger distances. The ion density profile is studied analytically in the case where the ion distribution near the plate is dominated only by counter-ions. Further away from the plate the density distribution can be described using a Poisson-Boltzmann theory with an effective surface charge that is smaller than the actual one.Comment: 11 Figures in 13 files + LaTex file. 20 pages. Accepted to Phys. Rev. E. Corrected typos and reference