Flat Fluid Research Articles

Dynamics and rupture of planar electrified liquid sheets

We investigate the stability of a thin two-dimensional liquid film when a uniform electric field is applied in a direction parallel to the initially flat bounding fluid interfaces. We consider the distinct physical effects of surface tension and electrically induced forces for an inviscid, incompressible nonconducting fluid. The film is assumed to be thin enough and the surface forces large enough that gravity can be ignored to leading order. Our aim is to analyze the nonlinear stability of the flow. We achieve this by deriving a set of nonlinear evolution equations for the local film thickness and local horizontal velocity. The equations are valid for waves which are long compared to the average film thickness and for symmetrical interfacial perturbations. The electric field effects enter nonlocally and the resulting system contains a combination of terms which are reminiscent of the Kortweg–de-Vries and the Benjamin–Ono equations. Periodic traveling waves are calculated and their behavior studied as the electric field increases. Classes of multimodal solutions of arbitrarily small period are constructed numerically and it is shown that these are unstable to long wave modulational instabilities. The instabilities are found to lead to film rupture. We present extensive simulations that show that the presence of the electric field causes a nonlinear stabilization of the flow in that it delays singularity (rupture) formation.

Waves in alternating solid and viscous fluid layers

Explicit expressions for the frequency dependence of the velocity and attenuation of shear waves in a periodic system of flat solid and viscous fluid layers have been derived by solving exact Rytov's dispersion equation in the long-wavelength approximation. The dispersion and attenuation are related to the well known mechanisms of dissipation in porous media: viscoelastic mechanism(viscous shear relaxation) and visco-inertial Biot's mechanism. The expressions describing the effects of these two mechanisms in a broad frequency range have been derived from the same standpoint. The asymptotic expressions for various limiting cases coincide with the results of previous studies.

Interface Dynamics of Immiscible Fluids under Circularly Polarized Vibration (Experiment)

This paper is one of a series of experimental studies of immiscible fluid interfaces under vibration of different types. A comparison between the average interface dynamics for high-frequency rotational vibration [1] and translational unidirectional vibration [2, 3] shows that a complication of the oscillation pattern leads to qualitatively novel effects. In this study, the cavity oscillates circularly and translationally in a horizontal plane. Two average vibration effects are discovered: a uniform azimuthal rotation of the fluid relative to the cavity and the excitation of a periodic hexagonal relief on the initially flat fluid interface.

Fun with flat fluids.

Fun with flat fluids.

Symmetries of the Stephani universes

Two classes of solutions for conformally flat perfect fluids exist depending on whether the fluid expansion vanishes or not. The expanding solutions have become known as the Stephani universes and are generalizations of the well known Friedmann-Robertson-Walker solutions; the solutions with zero expansion generalize the interior Schwarzschild solution. The isometry structure of the expansion-free solutions was completely analysed some time ago. For the Stephani universes it is shown that any Killing vector is orthogonal to the fluid flow and so the situation for the expanding case is somewhat simpler than the expansion-free case where `tilted' Killing vectors may exist. The existence of isometries in Stephani universes depends on the dimension r of the linear space spanned by certain functions of time and which appear in the metric. If r is 4 or 5, no Killing vectors exist. If r = 3, the isometry group is one dimensional. If r = 2, the spacetime admits a complete three-dimensional isometry group with two-dimensional orbits. If r = 1, there are six Killing vectors and the spacetime is Friedmann-Robertson-Walker. Not all choices of the metric functions and lead to distinct spacetimes: the ten-dimensional conformal group, which acts on each of the hypersurfaces orthogonal to the fluid flow, preserves the overall form of the metric, but induces a group of transformations on these five metric functions which is locally isomorphic to . A result of the same ilk is derived for the non-expanding solutions.

Covariant cosmological perturbation dynamics in the large-scale limit

Using the existence of a covariant conserved quantity on large perturbation scales in a spatially flat perfect fluid or scalar field universe, we present a general formula for gauge-invariantly defined comoving energy density perturbations which encodes the entire linear perturbation dynamics in a closed time integral. On this basis we discuss perturbation modes in different cosmological epochs.

Curvature instability in fluid membranes with polymer lipids subject to tension

Shape transformations of a flat fluid membrane with polymer lipids subject to lateral tension are studied as an approximation for multimembrane systems. Using Monte Carlo simulations, we find several characteristic structures of membranes, such as thermal fluctuations, large localized deformations, and undulations due to a curvature instability. The effect of thermal fluctuations on the curvature instability is investigated, and the undulations are characterized by a single-mode approximation for unstable modes. It is shown that thermal fluctuations, the curvature instability and vesiculation determine the parameter region in which an undulating membrane is observed. The phase diagram of undulation obtained through simulations closely resembles that measured experimentally for ``biogels.'' This suggests that the undulation corresponds to defects in multimembrane systems and that the curvature instability is the main cause of defect formation in ``biogels.''

Non-static non-conformally flat fluid plates of embedding class one

In the present article four non-static perfect fluid solutions have been derived by considering a plane symmetric metric of embedding class one. Out of the solutions so obtained two solutions possess an acceleration free velocity vector field while the other two have flow with acceleration. As far as the authors are aware the solutions with non-vanishing acceleration are new.

Atomization of a liquid drop by pulsation

By using stability analysis, it is shown that a spherical drop can be resonated parametrically to initiate the formation of droplets of diameters much smaller than that of the original drop. Both the surface tension and the density of the surrounding gas tend to retard this atomization process. The interfacial instability associated with the D'Alembert apparent body force in two superposed flat fluid layers is shown to be closely related to the interfacial instability caused by parametric resonance.

Leaky Rayleigh wave scattering from elastic media with random microstructures

Scattering of leaky Rayleigh waves from a flat fluid–solid interface is studied. The fluid half-space is taken to be ideal and homogeneous while the solid half-space has randomly inhomogeneous anisotropic elastic constants due to the microstructure of the material. For plane waves incident from the fluid onto the interface at the critical Rayleigh angle the singly scattered incoherent field is obtained by utilizing a first Born approximation. When the solid is a crystal aggregate and when the correlation function is of exponential form, the mean-square scattered signal level is found to be inversely proportional to the dimensionless frequency in the geometrical (high-frequency) limit but proportional to the third power of frequency in the Rayleigh (low-frequency) limit. Numerical results are given for water–aluminum (cubic polycrystals) interface scattering.

Low Reynolds number motion of bubbles, drops and rigid spheres through fluid–fluid interfaces

The low Reynolds number buoyancy-driven translation of a deformable drop towards and through a fluid–fluid interface is studied using boundary integral calculations and laboratory experiments. The Bond numbers characteristic of both the drop and the initially flat fluid–fluid interface are sufficiently large that the drop and interface become highly deformed, substantial volumes of fluid may be entrained across the interface, and breakup of both interfaces may occur. Specifically, drops passing from a higher- to lower-viscosity fluid are extended vertically as they pass through the interface. For sufficiently large drop Bond numbers, the drop may deform continuously, developing either an elongating tail or enlarging cavity at the back of the drop, analogous to the deformation characteristic of a single deformable drop in an unbounded fluid. The film of fluid between the drop and interface thins most rapidly for those cases that the drop enters a more viscous fluid or has a viscosity lower than the surrounding fluids. In the laboratory experiments, bubbles entering a less viscous fluid are extended vertically and may break into smaller bubbles. The column of fluid entrained by particles passing through the interface may also break into drops. Further experiments with many rigid particles indicate that the spatial distribution of particles may change as the particles pass through interfaces: particles tend to form clusters.

Leaky Rayleigh wave scattering from elastic media with microstructure

Scattering of leaky Rayleigh wave from a flat fluid–solid interface is studied. The fluid half-space is taken to be ideal and homogeneous while the solid half-space has randomly inhomogeneous anisotropic elastic constants due to the microstructure of the material. For plane waves incident from the fluid onto the interface at the critical Rayleigh angle, the singly scattered incoherent field is obtained by utilizing a first Born approximation. When the solid is a crystal aggregate and when the correlation function is of exponential form, the mean-square scattered signal level is found to be inversely proportional to the dimensionless frequency in the high-frequency limit but proportional to the third power of frequency in the low-frequency limit. Numerical results are given for water–aluminum interface scattering. [Work supported by NSF.]

Direct observation of primary fluid-inclusion formation

Observations of crystal growth in supersaturated KH 2 PO 4 solutions indicate that it duplicates natural crystallization processes and formation of fluid inclusions in free liquids similar to vein formation or igneous systems. Continuous crystal growth by surface nucleation results in elongate fluid inclusions forndng as hollow tubes within kinked growth steps. Large, flat fluid inclusions also form either by sealing of etch pits and other surface irregularities or along cracks propagated by crystal growth. Microscopic observation of real-time crystal growth documents the formation of fluid inclusions along a surface or within a plane, inclusions that would otherwise be identified as secondary. These primary fluid inclusions resemble pseudosecondary inclusions or secondary necked-down inclusions commonly observed in geologic samples. Furthermore, these fluid inclusions, and many or most in natural samples, are not generated by spiral growth processes. This simple analogue experiment serves as a model for crystal growth and fluid-inclusion entrapment in hydrothermal and igneous systems.

Killing vectors in conformally flat perfect fluids via invariant classification

The conditions for conformally flat perfect fluid spacetimes without expansion to admit Killing vectors were recently considered. This work shows the possibility of achieving the same results by a different approach. Considering the invariant classification of gravitational fields, basically the Karlhede classification, the conditions on the metric are determined by imposing functional dependence among the invariants. The continuous symmetries and consequently the number of Killing vectors are obtained naturally from the theory.

Killing vectors in conformally flat perfect fluid spacetimes

The existence of Killing vectors in conformally flat perfect fluid spacetimes in general relativity is considered. In particular Killing vectors which are neither orthogonal nor parallel to the fluid velocity vector are considered and stationary fields in which the fluid velocity vector is not parallel to the timelike Killing vector field are shown to exist. This class of solutions is shown to include several stationary (but non-static) axisymmetric fields, thus providing counter-examples to a theorem of Collinson (1976). In the case when the fluid is non-expanding, the number of spacelike Killing vectors is shown to depend on the rank of four functions of time which appear in the metric. Some examples of stationary but non-static fields are presented in closed form.

Extension of plane rubber films

Extension of thin plane films, uneven in initial thickness and obeying the constitutive equation of rubber‐like elasticity, was analyzed mathematically with the following results. (i) The plane extension of rubber films is governed by two simultaneous partial differential equations whose independent variables are (u,v) and dependent variables are ( f,g) where (u,v) is the position in Cartesian coordinates of a rubber particle constituting the film occupied before the extension and ( f,g) is the position of the same particle after the extension. (ii) The axisymmetrical stretching mode is governed by a single ordinary differential equation which can readily be solved analytically or numerically upon specification of film thickness known at any one radial position. (iii) Uniform thickness extension is possible only when the film is initially uniform in thickness and the mode of extension is uniform biaxial, i.e., the two principal strains in x and y directions, respectively, are independent of position (u,v). This is in marked difference from the case of the extension of flat Newtonian fluid films in which a complex mode of uniform thickness extension obeying the Cauchy–Riemann equations exists. (iv) The governing equations were solved numerically for the general case by means of the Newton iteration scheme used in a finite difference approximation.

Nonlinear waves on the magnetic fluid surface

The magnetic fluid stability in the presence of a tangential magnetic fielf and instability dynamics are studied experimentally. Nonlinear theory of instability and shape of a flat magnetic fluid surface and the theory of solitary and cnoidal waves on the cylindrical surface are developed.

A static conformally flat cosmological model in Lyra's manifold

A static conformally flat spherically-symmetric perfect fluid cosmological model based on Lyra's modified Riemannian geometry is proposed. Some properties of the model are discussed.

Construction and invariant classification of perfect fluids in general relativity

A formalism for classifying and constructing perfect fluids is developed. The Ricci tensor and its first covariant derivatives in a comoving frame are expressed as functions of energy density, pressure, their gradients and the kinematic quantities. All conformally flat perfect fluids are constructed and thus also classified. In general the third covariant derivative is needed for a complete classification of these metrics.

Nozzle design yielding interferometrically flat fluid jets for use in single-mode dye lasers

Fundamentals and design principles are presented for the generation of interferometrically flat jets of viscous fluids. The jet quality is optically analyzed and nozzle performance investigated in cw single-mode dye laser operation. A nozzle providing a dye jet with an optically flat area of 9 mm2 is described. It produces a single-mode bandwidth of ∼5 MHz without any active stabilization.