F Behroozi

The calming effect of oil on water

The calming effect of oil on water has been known since ancient times. Benjamin Franklin was the first to investigate the effect, but the underlying mechanism for this striking phenomenon remains elusive. We used a miniature laser interferometer to measure the amplitude of surface waves to a resolution of ±5nm, making it possible to determine the effect of an oil monolayer on the attenuation of capillary waves and the surface dilational modulus of the monolayer. We present attenuation data on pure water, water covered by olive oil, water covered by a fatty acid, and a water-acetone mixture for comparison. From the attenuation data at frequencies between 251 and 551Hz, we conclude that the calming effect of oil on surface waves is principally due to the dissipation of wave energy caused by the Gibbs surface elasticity of the monolayer, with only a secondary contribution from the reduction in surface tension. Our data also indicate that the surface-dilational viscosity of the oil monolayer is negligible and...

Direct measurement of the dispersion relation of capillary waves by laser interferometry

Surface waves on fluids with wavelengths in the millimeter range are known as capillary waves. Surface tension determines the propagation and dispersion of capillary waves while gravity plays a minor role. We describe a simple method for generating standing capillary waves of known frequency on water and introduce a novel noncontact technique based on laser interferometry to measure the wavelength of capillary waves with great precision. The data gives the dispersion relation of capillary waves and provides an accurate method for determining the surface tension of fluids.

Fluid viscosity and the attenuation of surface waves: a derivation based on conservation of energy

More than a century ago, Stokes (1819–1903) pointed out that the attenuation of surface waves could be exploited to measure viscosity. This paper provides the link between fluid viscosity and the attenuation of surface waves by invoking the conservation of energy. First we calculate the power loss per unit area due to viscous dissipation. Next we calculate the power loss per unit area as manifested in the decay of the wave amplitude. By equating these two quantities, we derive the relationship between the fluid viscosity and the decay coefficient of the surface waves in a transparent way.

Dispersion of capillary-gravity waves: a derivation based on conservation of energy

Waves on fluids provide an excellent context for introducing some important topics in fluid dynamics. In this paper we first discuss the behaviour of standing surface waves and present their special properties. Next the dispersion relation of surface waves is derived in a novel way by applying the conservation of energy to the case of standing waves.

Efficient deconvolution of noisy periodic interference signals

The interference signal formed by combining two coherent light beams carries information on the path difference between the beams. When the path difference is a periodic function of time, as, for example, when one beam is reflected from a vibrating surface and the other from a fixed surface, the interference signal is periodic with the same period as the vibrating surface. Bessel functions provide an elegant and efficient means for deconvoluting such periodic interference signals, thus making it possible to obtain the displacement of the moving surface with nanometer resolution. Here we describe the mathematical basis for the signal deconvolution and employ this technique to obtain the amplitude of miniature capillary waves on water as a test case.

Capillary-gravity waves and the Navier-Stokes equation

Water waves are a source of great fascination for undergraduates and thus provide an excellent context for introducing some important topics in fluid dynamics. In this paper we introduce the potential theory for incompressible and inviscid flow and derive the differential equation that governs the behaviour of the velocity potential. Next we obtain the harmonic solutions of the velocity potential by a very general argument. These solutions in turn yield the equations for the velocity and displacement of a water element under the action of a harmonic wave. Finally we obtain the dispersion relation for surface waves by requiring that the harmonic solutions satisfy the Navier-Stokes equation.

Thermal expansion of solids: a simple classical model

The usual textbook derivation of the thermal expansion of solids based on the Taylor expansion of the interatomic potential is re-examined. It is shown that the simple theory presented in textbooks not only fails at low temperatures, but that the seemingly reasonable high-temperature result is fortuitous. An alternative classical model is presented, which is based on calculating the time-averaged interatomic distance as a function of temperature. The model is applied to the case of solid argon, as an example, to show the excellent agreement with experiment. Since simple numerical computations form an integral part of the undergraduate physics curriculum, this model presents an attractive alternative to the current treatments in the elementary textbooks. Abstrakt. Vi har undersokt den i larobockerna vanliga derivationen av termisk expansion av amnen i fast form som ar grundad pa Taylors serieexpansion av den interatomiska potensen. Vi vill visa att denna enkla teori inte bara ar felaktig vid laga temperatur men dessutom att resultatet vid hoga temperaturer har framkommit genom en slump. Har presenteras alltsa en ny klassisk modell vilken grundats pa berakningen av medelvardet av den interatomiska distansen over tid som en funktion av temperatur. Modellen anvander argon i fast form som ett exempel for att pavisa den tydliga overensstammelsen i experimenten. Eftersom enkla numeriska berakningar ar en vasentlig dal av studieplanen sa innebar den nya modellen en klar forbattring av textboksinnehallet.

The effect of a soap film on a catenary: measurement of surface tension from the triangular configuration

A chain assumes the well-known shape known as a catenary when it hangs loosely from two points in a gravitational field. The correct solution of the catenary was one of the early triumphs of the newly invented calculus of variations at the end of the 17th century. Here we revisit the catenary and show that, for a chain hanging from a horizontal rod, three new and distinct configurations are possible if a soap film covers the area bounded by the chain and the rod. We first review the general problem and discuss the conditions under which the chain assumes a concave, triangular or convex configuration. The deciding factor is the strength of surface tension relative to the gravitational force per unit length of the chain. The conditions under which the chain assumes the shape of a perfect triangle are discussed in greater detail and analysed to obtain the tension along the chain. The triangular configuration is especially intriguing to undergraduates and may be used as a simple experiment to obtain the surface tension of the soap solution by measuring just one angle of the triangle.

On the equilibrium of coplanar forces

Most current texts on intermediate mechanics do not give a general method for finding the point of application of the equilibriant force needed to balance a set of coplanar forces. In this short paper we give a simple analytical method for finding the line of action which forms the locus of all points at which the equilibriant may be applied to attain balance.