Luis P. Thomas

Laplace pressure driven drop spreading

This work concerns the spreading of viscous droplets on a smooth rigid horizontal surface, under the condition of complete wetting (spreading parameter S≳0) with the Laplace pressure as the dominant force. Owing to the self‐similar character foreseeable for this flow, a self‐similar solution is built up by numerical integration from the center of symmetry to the front position to be determined, defined as the point where the free‐surface slope becomes zero. Mass and energy conservation are invoked as the only further conditions to determine the flow. The resulting fluid thickness at the front is a small but finite (≊10−7) fraction of the height at the center. By comparison with experimental results the regime is determined in which the spreading can be described by this solution with good accuracy. Moreover, even within this regime, small but systematic deviations from the predictions of the theory were observed, showing the need to add terms modifying the Laplace pressure force.

Droplet profiles obtained from the intensity distribution of refraction patterns

A noninterferometric method for obtaining profiles of axially symmetric transparent liquid droplets is described. The drops are illuminated along the symmetry axis by a uniform parallel beam whose intensity distribution is recorded at the focal plane of a lens placed behind the drop. In some conditions and within the geometrical optics approach, it is possible to reconstruct the profile of the drop from this intensity distribution except for the length scale factor, which, if necessary, may be provided by an additional simple measurement. Because of CCD cameras and digital image processing, this method is an interesting alternative technique for measuring drop profile shapes with considerable accuracy when interferometry is unwieldy. We also analyze the diffraction features of the intensity distribution to clarify the extent that they affect the approach that we used and to establish additional information that they may provide.

Instantaneous viscous flow in a corner bounded by free surfaces

We study the instantaneous Stokes flow near the apex of a corner of angle 2α formed by two plane stress free surfaces. The fluid is under the action of gravity with g↘ parallel to the bisecting plane, and surface tension is neglected. For 2α≳126.28°, the dominant term of the solution as the distance r to the apex tends to zero does not depend on gravity and has the character of a self‐similar solution of the second kind; the exponent of r cannot be obtained on dimensional grounds and the scale of the coefficient depends on the far flow field. Within this angular domain, the instantaneous flow is deeply related to the (steady) flow in a rigid corner known since Moffatt [J. Fluid Mech. 18, 1 (1964)] and, as in that case, there may be eddies in the flow. The situation is substantially different for 2α<126.28°, as the dominant term is related to gravity and not to the far flow. It has the character of a self‐similar solution of the first kind, with the exponent of r being given by dimensional analysis. The so...

Lock-Exchange Flows in Non-Rectangular Cross-Section Channels

Lock-exchange flows driven by density differences in non-rectangular cross-section channels are investigated in situations that resemble estuaries, navigation canals and hydraulic engineering structures. A simple analytical model considering stratified flows suggests practical relationships corroborated by results of laboratory experiments carried out in a straight channel of triangular cross-section

A numerical study on the transition to self-similar flow in collapsing cavities

In the collapse of a spherical cavity surrounded by a perfect gas initially at rest, the velocity R of the free gas boundary has an initial valve of −2c0/(γ−1) (c0 is the speed of sound in the undisturbed gas and γ is the adiabatic exponent). Hereafter R remains practically constant until R becomes a certain fraction ξ(γ) of the initial radius R0. Finally, for R<ξR0, R approaches the asymptotic behavior R∼R−τ(γ) predicted by self‐similar solutions. The function ξ(γ), which has been obtained numerically, decreases as γ decreases and vanishes for a certain value of γ near 1.5. This fact, together with the analogous behavior of τ(γ), suggests that there exists a certain value γcr≊1.5 of the adiabatic exponent such that, for 1<γ<γcr the velocity R of the free boundary is strictly a constant during the entire collapse. This behavior seems to be closely related to the results obtained by Lazarus [Phys. Fluids 25, 1146 (1982)] who demonstrates that a degenerate stable, asymptotic solution, with R=const, ex...

Entropy distribution in a slab driven by a two-step pressure pulse

The shocks developed in a plane layer of ideal gas when it is driven by a two-step pressure pulse are studied. An explicit anaiytical expression of the Lagrangian distribution of entropy is found.

Free expansion of a gas against a rigid wall

The flow behind the shock wave produced when a freely expanding gas strikes a rigid wall is studied. The shock speed is known within an early stage after the shock onset, when the flow is self‐similar and, also, as is pointed out, when the shock decays into a sonic disturbance, propagating in an almost uniform gas. On this basis, an approximate differential equation can be written for the shock position, whose solution is analytic, and therefore, the flow magnitudes are given by simple relationships. Comparison with numerical simulations shows that the flow is well described by this approximation. This work also includes a brief review of the equations for the self‐similar regime, because corrections to previously published results were found necessary.

Compression of a gas by a solid slab: Entropy distribution due to a two-step pressure pulse

Studies of waves developed in a solid/gas layer driven by a two-step pressure pulse have been performed. The solid is treated with a realistic equation of state and the gas is considered to be ideal. An explicit analytical expression for the Lagrangian distribution of the entropy function p/ργ is found.

Acceleration of a slab driven by a constant pressure piston

The sequence of shock and rarefaction waves, which occur in a plane layer of ideal gas initially at rest when it is driven toward the vacuum by a very high constant pressure piston, is studied. In the rarefaction flow that relaxes the layer compressed by the first strong shock, a second shock is generated. The time and position of its formation are obtained by an exact analytical expression. The subsequent motion and intensity of the shock wave are approximated by the Chester–Chisnell–Whitham (CCW) method. Then, the Lagrangian distribution of entropy in the layer is analytically derived.