The Tensile Strength of Liquid Helium Four

Abstract

It is well known that most liquids exhibit a tensile strength which is much smaller in magnitude than the tensile strength predicted by homogeneous nucleation theory. This lack of agreement is usually attributed to the difficulty of preparing liquid samples free from foreign gases which act as heterogeneous nucleation sites.Liq"lid heliurr. occupies a unique place among liquids for tensile strength measurements because all fcreign gases are frozen OLt at liquid helium temperatures. LIST OF FIGURESAt Equilibrium, a van der Waals substance Exhibits a Phase Change . . . . . 2.A Schematic Representation of the Work If instead of expanding the stable liquid slowly at equilibrium, the volume is suddenly increased, the liquid will penetrate into the metastable region along the curve BC. The metastable state is a state in which the Gibbs free energy is at a local rather than a global minimum.After a characteristic mean time, <T>, which is highly dependent on the depth of penetration into the metastable region, the liquid will decompose to a stable equilibrium configuration on the coexistence curve. When T/T c is less than about 0.8, rapid stretching of the liquid into the metastable region can result in negative pressure such as point G in Fig. 1. Point C lies on the liquid spinodal, the curve marking the transition to instability, and represents a true limit to the tensile strength of the liquid. In practice this limit is not reached, rather the tensile strength is determined by kinetic rates of bubble formation in the metastable region. THE WORK REQUIRED TO FORM A BUBBLEThe rate of bubble formation is calculated by considering the minimum work that must be done to form a vapor bubble in the liquid. An amount of work equal to the surface tension times the surface area, aA, must be done to form a cavity. Part of the work is done by the gas vaporized into the cavity so that the total work (W) needed to ·form a bubble iswhere PG is the pressure of the gas in the bubble, PL is the pressure of the surrounding liquid, VG is the volume of the bubble, x is the number of molecules vaporized into the cavity, ~G and ~L are the chemical potentials of the gas and vapor respectively. On the coexistence curve, the pressure of the gas and the pressure of the liquid are equal to the vapor pressure. The chemical potentials are also equal on the coexistence curve, so that the work necessary to form a bubble rises to infinity as the bubble radius is increased (curve a of Fig.2). If the liquid is brought rapidly into the metastable region by means of a pressure excursion .then the following conditions will hold: PL < P G and ~ G < ~ L. Under these conditions, the work necessary to form a bubble increases to a maximum w P-P-=05 -12 r Figure 2. A schematic representatioc of tte work n~eded to form a critical size bubble as a function of bubble radius. On the sa.turated vapor pressure curve, the work ris~s monotonically (curve a). As the liquid is brought into the metastable regio~, the work necessary to form a bubble of radius r first in...

The Tensile Strength of Liquid Nitrogen

“…This kind of signal was also observed by Nissen (1988Nissen ( , 1989 in his study of the tensile strength of liquid helium. He defined the signal as the characteristic signal of the homogeneous nucleation.…”

“…Since a short ultrasonic pulse is focused onto a very small volume of the bulk liquid, the possibility of heterogeneous nucleation caused by the impurities or walls can be greatly reduced. We adopt the method developed by Nissen (1988Nissen ( , 1989) to obtain the measurement of the tensile strength of liquid nitrogen. Although he used a hemispherical transducer, we will use ultrasonic transducers with a small aperture angle since the theories concerning this kind of transducer are well developed.…”

“…Nissen (1988) explained the appearance of this characteristic signal of the homogeneous nucleation from a different approach. His argument is as follows.…”

“…This issue has been discussed for liquid helium by Nissen (1988). We will apply his method to liquid nitrogen.…”

Limiting tensile strength of liquid nitrogen

“…Nevertheless, homogeneous nucleation may be observed even in the presence of heterogeneous cavitation centers if the volume of the liquid being stretched and the time of its transition into a metastable state (the shock phase-transition regime 10 ) are considerably reduced. For this purpose focused acoustic fields may be employed, which make it possible to transfer the cavitation zone from the walls of the piezoelectric transducer by reducing its volume to (λ/2) 3 , where λ is the length of the acoustic wave 11,12 and the wave of reflection from the liquid free surface. 13,14 In the present work the pulse method of superheating a liquid on a thin platinum heater in a tension wave 15,16 has been used to investigate the tensile stress of liquid nitrogen.…”