Dynamics of a helium-4 meniscus on a strongly disordered cesium substrate

Abstract

We have studied the dynamics of the contact line of a helium-4 meniscus on a strongly disordered cesium substrate. We have used photolithographic techniques to obtain a controlled disorder with a correlation length $\ensuremath{\xi}=9 \ensuremath{\mu}\mathrm{m}.$ We observe a strong pinning of the contact line on the defects. We have measured the roughness W of the contact line as a function of its length L at the depinning threshold; we find that W scales as ${L}^{\ensuremath{\zeta}},$ and is almost independent of the contact angle $\ensuremath{\theta}$ of the meniscus for values between $4\ifmmode^\circ\else\textdegree\fi{}$ and $12\ifmmode^\circ\else\textdegree\fi{}.$ The roughness exponent is found to be $\ensuremath{\zeta}=0.56\ifmmode\pm\else\textpm\fi{}0.03,$ which is higher than the value of 1/3 predicted at equilibrium. We have analyzed the avalanchelike motion of the contact line, and confirmed the above value of \ensuremath{\zeta} by measuring the ratio of the size of the step forward to the length of the line involved in a jump. Most theoretical and numerical calculations assume that the motion of the contact line is quasistatic. We show that this assumption is false for our system, which is weakly dissipative. This probably explains why the dynamical behavior of the contact line depends on the contact angle, while the roughness does not. Whether the underdamped motion of the contact line can account for the value of \ensuremath{\zeta} is still an open question.