Size Dependence Of Surface Tension Research Articles

Contact Angles of a Sessile Drop and a Captive Bubble Taking into Consideration the Size Dependence of Surface Tension

Contact Angles of a Sessile Drop and a Captive Bubble Taking into Consideration the Size Dependence of Surface Tension

Study of homogeneous bubble nucleation in liquid carbon dioxide by a hybrid approach combining molecular dynamics simulation and density gradient theory.

A new method for predicting homogeneous bubble nucleation rates of pure compounds from vapor-liquid equilibrium (VLE) data is presented. It combines molecular dynamics simulation on the one side with density gradient theory using an equation of state (EOS) on the other. The new method is applied here to predict bubble nucleation rates in metastable liquid carbon dioxide (CO2). The molecular model of CO2 is taken from previous work of our group. PC-SAFT is used as an EOS. The consistency between the molecular model and the EOS is achieved by adjusting the PC-SAFT parameters to VLE data obtained from the molecular model. The influence parameter of density gradient theory is fitted to the surface tension of the molecular model. Massively parallel molecular dynamics simulations are performed close to the spinodal to compute bubble nucleation rates. From these simulations, the kinetic prefactor of the hybrid nucleation theory is estimated, whereas the nucleation barrier is calculated from density gradient theory. This enables the extrapolation of molecular simulation data to the whole metastable range including technically relevant densities. The results are tested against available experimental data and found to be in good agreement. The new method does not suffer from typical deficiencies of classical nucleation theory concerning the thermodynamic barrier at the spinodal and the bubble size dependence of surface tension, which is typically neglected in classical nucleation theory. In addition, the density in the center of critical bubbles and their surface tension is determined as a function of their radius. The usual linear Tolman correction to the capillarity approximation is found to be invalid.

Influence of the size dependence of surface tension on the dynamics of a bubble in a liquid

The Gibbs dividing surface method is used to derive the differential equation defining the dependence of the surface tension of a bubble in a nonpolar single-component liquid on its radius. Exact and asymptotic solutions of this equation have been obtained. It follows from the calculations that the bubble surface tension increases with decreasing radius. The Rayleigh-Plesset equation describing the bubble collapse dynamics is solved numerically by taking into account the size dependence of surface tension. The size dependence of surface tension is shown to affect significantly the final bubble collapse stage and, on the whole, accelerates this process.

Solid-state foaming of Ti–6Al–4V by creep or superplastic expansion of argon-filled pores

Ti–6Al–4V foams are produced by the expansion of pressurized argon pores trapped in billets created by powder metallurgy. Pore expansion during thermal cycling (840–1030 °C, which induces transformation superplasticity in Ti–6Al–4V) improves both the foaming rate (by reducing the flow stress) and the final porosity (by delaying fracture of the pores and subsequent escape of the gas), as compared to isothermal pore expansion at 1030 °C, where Ti–6Al–4V creep is the controlling mechanism. Raising the argon content in the billet increases the foaming rates for both creep and superplastic conditions, in general agreement with an analytical model taking into account the non-ideal behavior of high-pressure Ar and the pore size dependence of surface tension. Superplastically foamed Ti–6Al–4V with 52% open porosity exhibits a combination of high strength (170 MPa) and low stiffness (18 GPa), which is useful for bone implant applications.

Interface tension in a binary system with curved boundary

The equation of interface tension isotherm for a curved boundary in a binary system composed a dispersed particle (α phase) with a curvature radius r and a dispersing medium (β phase) has been obtained from the thermodynamic equilibrium conditions. In going to one-component systems, the well-known expressions for the size dependence of surface tension, previously obtained by other researchers (in particular, the well-known Tolman formula), follow from the equation derived.

On the size dependence of surface tension in the temperature range from melting point to critical point

AbstractThe problem of size dependence of surface tension was investigated in view of a more general problem of the applicability of Gibbs’ thermodynamics to nanosized objects. For the first time, the effective surface tension (coinciding with the specific excess free energy for an equimolecular dividing surface) was calculated within a wide temperature range, from the melting temperature to the critical point, using the thermodynamic perturbation theory. Calculations were carried out for Lennard-Jones and metallic nanosized droplets. It was found that the effective surface tension decreases both, with temperature and particle size.

Molecular dynamics of homogeneous nucleation in the vapor phase. II. Water

Homogeneous nucleation process in the vapor phase of water is investigated with a molecular dynamics computer simulation at 350 K under supersaturation ratio 7.3. Using a method similar to Lennard-Jones fluid (Part I), the nucleation rate is three orders of magnitude smaller than prediction of a classical nucleation theory. The kinetically defined critical nucleus size is 30–45, much larger than the thermodynamically defined value of 1.0 estimated with the classical theory. Free energy of cluster formation is estimated from the cluster size distribution in steady state time region. The predicted nucleation rate with this free energy agrees with the simulation result. It is concluded that considering the cluster size dependence of surface tension is very important.

Some problems concerning the definition of a dividing surface and its influence on the calculation of thermodynamical parameters of small clusters

We discuss the influence of several definitions of the dividing surface on the size dependence of surface tension and surface stress. Among others we apply the original definition of Gibbs for the “surface of tension” (SOT) and the “equimolecular dividing surface” (EMDS). We show that from physical reasons the surface tension must only include curvature terms up to the quadratic term. The considerations are illustrated for microclusters of simple geometric configurations.