The spreading of liquids on low energy surfaces. I. polytetrafluoroethylene

Macleod’s (1923) empirical formula for the surface tension σ of a liquid in equilibrium with its own vapour, namely σ = const. ( ρ liq. ─ ρ vap)4, (1) where the ρ ’s are densities in g./c. c., must impress everyone with the feeling that such a simple and successful relation must have some equally simple foundation in thermodynamic or statistical theory. This feeling is only intensified when one realizes the wide use to which this formula has been put by Sugden and his followers. Sugden (1930) writes M *σ¼/ ρ liq. ─ ρ vap. = P , (2) where M * is the (chemical) molecular weight of the substance, and calls P the parachor . The comparative study of the parachors for various liquids seems to have proved fruitful. This study is described by Sugden as the comparative study of molecular volumes at equal surface tensions, and therefore, to the best of our opportunities, at equal “internal pressures”. We need not here enquire into the precise significance (if any) of the phrase ‘‘internal pressure”. It is sufficient to recognize that the quantity P defined by (2) is in fact a constant (very nearly) for any given substance, independent of the temperature over a wide range, from the critical temperature Tc downwards—and having recognized this important empirical fact, to attempt to derive it as a theorem in statistical mechanics applied to a reasonable model, and to give a formula for P in terms of molecular diameters and (or) intermolecular forces.

A Tentative Statistical Theory of Macleod's Equation for Surface Tension, and the Parachor

A study of the recently obtained data on the velocity of sound and density in liquids reveals a simple relation between these quantities namely the law, v⅓M/ρ = R where v is the velocity of sound in the liquid, M the molecular weight, ρ the density and R a constant independent of temperature. It is shown that the velocity of sound cannot be a proper basis of comparison in any homologous series. The result of plotting the constant R against the molecular weight of members of homologous series leads to the equation R = αM + β where α is a general constant and β a characteristic constant for any one homologous series. The difference in R for successive members of homologous series is a constant independent of the series and R is an additive function of the chemical structure. Values of R for hydrogen, carbon, oxygen, bromine, and chlorine are tabulated.

Velocity of Sound in Liquids and Chemical Constitution

The combination of short-range repulsive and long-range attractive forces in many-body dissipative particle dynamics (MDPD) is examined at a vapor/liquid and liquid/solid interface. Based on the radial distribution of the virial pressure in a drop at equilibrium, a systematic study is carried out to characterize the sensitivity of the surface tension coefficient with respect to the inter-particle interaction parameters. For the first time, the approximately cubic dependence of the surface tension coefficient on the bulk density of the fluid is evidenced. In capillary flow, MDPD solutions are shown to satisfy the condition on the wavelength of an axial disturbance leading to the pinch-off of a cylindrical liquid thread; correctly, no pinch-off occurs below the cutoff wavelength. Moreover, in an example that illustrates the cascade of fluid dynamics behaviors from potential to inertial-viscous to stochastic flow, the dynamics of the jet radius is consistent with the power law predictions of asymptotic analysis. To model interaction with a solid wall, MDPD is augmented by a set of bell-shaped weight functions; hydrophilic and hydrophobic behaviors, including the occurrence of slip in the latter, are reproduced using a modification in the weight function that avoids particle clustering. The dynamics of droplets entering an inverted Y-shaped fracture junction is shown to be correctly captured in simulations parametrized by the Bond number, confirming the flexibility of MDPD in modeling interface-dominated flows.

Many-body dissipative particle dynamics simulation of liquid/vapor and liquid/solid interactions.

The surface tension between silicate liquid and gas has been measured for four lava compositions (limburgite to andesite) from 1,200° to 1,500° C. The magnitude of surface tension (γ) is in the range 350–370 dynes/cm. Variations found in γ as a function of liquid composition were small and had no obvious relation to liquid composition. γ was also found to vary little with furnace atmosphere — air, Ar, CO2, H2, CO and their mixtures. A relaxation time of hours to days, depending on temperature, is required before reproducible results can be obtained from originally crystalline starting material.

Surface tension of natural silicate melts from 1,200°–1,500° C and implications for melt structure

The parachor and valency

The determination of surface tension from the rise in capillary tubes

THIS book gives a clear and straightforward account of the principal parts of elementary physical chemistry. It contains instructions for carrying out illustrative experiments, and is provided with questions at the ends of the chapters.A Class Book of Physical Chemistry.By Prof. T. Martin Lowry Dr. Samuel Sugden. Pp. vii + 436. (London: Macmillan and Co., Ltd., 1929.) 6s. 6d.

Samuel Sugden

Papers

The parachor and valency

The determination of surface tension from the rise in capillary tubes

A class book of physical chemistry