Viscous Liquid Layer Research Articles

Numerical simulation of the mechanical initiation of liquid explosive systems

The minimum initiation energy is studied numerically as a function of the thickness of a layer of viscous explosive liquid placed in a narrow gap between the plane-parallel surfaces of a striker and an anvil. The statement of the problem simulates the conditions for actual tests of explosives for impact sensitivity. For a given impact force, a layer of liquid with a “soft” type of mechanical behavior is found to exist, which most rapidly acquires energy from a striker and is heated through viscous dissipation of the mechanical energy. It also forms a layer of critical thickness that is characterized by an absolute minimum in the initiation energy. The existence of a layer with a “hard” type of mechanical behavior in the test samples explains the intrinsically nonmonotonic dependence.

Stability of a growing end rim in a liquid sheet of uniform thickness

We study the stability of a viscous liquid layer of uniform thickness subject only to viscous stresses and surface tension. We show that the growing cylindrical end rim does not typically break into droplets for moderate wavelengths. Thus, other mechanisms are needed to cause the instabilities, which, for instance, lead to the famous milk crown. The problem remains open for very large wavelengths.

Possible effect of variation in the internal energy of the free surface of a thin liquid layer on its wavy flow

A formally possible mechanism is considered for the development of longwave perturbations of flow of a thin layer of a heat-conducting viscous liquid with a free boundary, whose characteristic feature is that the Marangoni stresses occurring at the boundary are induced by variations in the internal energy of the interface. The effect of surface internal energy fluctuations on the layer flow in the approximation considered is of a dispersive character, and, in particular, it can facilitate regularization of wave regimes.

Noncircular converging flows in viscous gravity currents

We study the filling of a dry region (cavity) within a viscous liquid layer on a horizontal plane. In our experiments the cavities are created by removable dams of various shapes surrounded by a silicon oil, and we measure the evolution of the cavity's boundaries after removal of the dams. Experimental runs with circular, equilateral triangular, and square dams result in circular collapse of the cavities. However, dams whose shapes lack these discrete rotational symmetries, for example, ellipses, rectangles, or isosceles triangles, do not lead to circular collapses. Instead, we find that near collapse the cavities have elongated oval shapes. The axes of these ovals shrink according to different power laws, so that while the cavity collapses to a point, the aspect ratio is increasing. The experimental setup is modeled within the lubrication approximation. As long as capillarity is negligible, the evolution of the fluid height is governed by a nonlinear diffusion equation. Numerical simulations of the experiments in this approximation show good agreement up to the time where the cavity is so small that surface tension can no longer be ignored. Nevertheless, the noncircular shape of the collapsing cavity cannot be due to surface tension which would tend to round the contours. These results are supplemented by numerical simulations of the evolution of contours which are initially circles distorted by small sinusoidal perturbations with wave numbers $k>~2.$ These nonlinear stability calculations show that the circle is unstable in the presence of the mode $k=2$ and stable in its absence. The same conclusion is obtained from the linearized stability analysis of the front for the known self-similar solution for a circular cavity.

Two-fluid boundary layer stability

The stability of a two-fluid boundary layer is investigated. A boundary layer shears a second fluid that is bounded by the wall and the shearing fluid. The eigenvalue problem governing the linear stability of the configuration is solved using an efficient shooting-search method. Besides the Tollmien-Schlichting mode (hard mode) found in the classical hydrodynamical stability theory an additional Yih-mode (interfacial mode) exists due to the two-fluid interface. Effects of viscosity and density stratifications, thickness of the bounded fluid, gravity, surface tension as well as the non-Newtonian character of the lower fluid on the stability characteristics are determined. The interfacial mode is found to be very sensitive against viscosity stratification. However, with a highly viscous liquid layer, the system approaches a single-layer behavior. The shear-thinning non-Newtonian liquid layer is observed to have a stabilizing effect for both of the modes. Surface tension is stabilizing for short waves for the interfacial mode but a more complex effect was observed for the hard mode. Gravity is stabilizing with a favorable density stratification. Density stratification alone is destabilizing for low and moderate values of this parameter but becomes stabilizing for higher values. When the external boundary layer profile is turbulent, the interfacial mode is more likely to be observed in an experiment. Agreement of the obtained results with experimental, theoretical and numerical results reported in the literature is good. This is encouraging as the study is intended for solving the stability characteristics of de/anti-icing fluid-air systems and comparing the results with the experimental data when they become available.

Theory on mass transport generated by ultrasonic Lamb waves

It was reported that acoustic streaming generated by a Lamb-wave sensor (LWS) can be used to pump fluids and transport solids in a small-scale system [Appl. Phys. Lett. 59 (1991)]. The speed, observed by attracting small polystyrene spheres suspended in water, is proportional to the square of the wave amplitude and is about 100 μm/s for 6.5-nm surface displacement of the plate. In this paper, a fairly practical model, i.e., a thin isotropic plate in contact with a viscous liquid layer on its side, is presented. Based on the rigorous propagation theory of Lamb waves and Nyborg’s [Phys. Acoust. B 2, 265–295] and Bradley’s [J. Acoust. Soc. Am. 100, 1399–1408 (1996)] theories of acoustic streaming, the first-order ultrasonic field in the viscous liquid layer and the second-order mass-transport velocity distribution of the liquid are calculated. Comparison between our theoretical values of the Ao-mode Lamb wave and Moroney et al.’s experimental result is given. It shows good agreement. [Work supported by NSF of China.]

VIBRATION OF A HYDROELASTIC SYSTEM CONSISTING OF A SECTOR SHELL AND VISCOUS LIQUID IN ZERO GRAVITY

For a circular sector system consisting of an elastic shell to which an incompressible and viscous liquid layer is attached, the coupled liquid-structure frequencies are determined under zero gravity conditions. The influence of the viscosity of the liquid, the flexibility of the shell, the thickness of the liquid layer and the Ohnesorge number have been determined for freely slipping and anchored contact lines. With increasing shell flexibility the oscillation frequencies decrease and exhibit a smaller magnitude for a viscous liquid than for a frictionless liquid. In addition, we observe a phenomenon not present in a system with frictionless liquid, involving regions of only aperiodic motion. In these regions, depending mainly on viscosity (Ohnesorge number) and liquid layer thickness, the hydroelastic system cannot perform any oscillatory motion. A motion identification chart is presented showing that for large Ohnesorge number Oh≡(ρν2/σa)1/2only very thick liquid layers are able to perform oscillatory motions. Increasing the flexibility of the shell results in an increased region of aperiodic motion.

Unsteady spreading of a thin layer of viscous liquid over a curved surface

The unsteady spreading of a thin layer of an incompressible viscous liquid over an impermeable curved surface, which occurs under the action of the gravity force, is considered. The solution of the boundary-value problem which arises reduces to solving a Cauchy problem for equations with a small number of independent variables.

Long-wave instabilities of film flow under an electrostatic field

The free-surface behavior of a viscous liquid layer flowing down an inclined plane by gravity and interacting with an overlying uniform electrostatic field is examined in the limit of long-wave approximation. Both linear and nonlinear stability analyses are performed to address two-dimensional surface-wave evolution initiating from a flat interface. The growth of a periodic disturbance is first investigated for a linear analysis, and then to examine the nonlinear surface-wave instabilities the evolution equation for film height is solved numerically by a Fourier-spectral method. For small evolution time the calculated nonlinear modes of instability are consistent with the results obtained from the linear theory. The effect of an electrostatic field increases the wavenumbers showing a maximum linear growth rate as well as a cutoff. A significant phenomenon as Reynolds number is increasing is the appearance of the catastrophic surface waves in the long run whenever any initial wavenumber making a traveling wave linearly unstable is employed into the initial simple-harmonic disturbance.

Thermocapillary instability of a liquid layer in the presence of a soluble surfactant

The effect of capillarity on the stability of a plane layer of viscous heat-conducting liquid in the presence of a soluble surfactant is investigated. It is found that an increase in surfactant solubility has a stabilizing effect on equilibrium. Monotonic instability is the most dangerous mode in the case of long-wave perturbations, whereas in the short-wave region loss of stability is induced by oscillatory perturbations.

Long-wavelength instability in surface-tension-driven Bénard convection.

Laboratory studies reveal a deformational instability that leads to a drained region (dry spot) in an initially flat liquid layer (with a free upper surface) heated uniformly from below. This long-wavelength instability supplants hexagonal convection cells as the primary instability in viscous liquid layers that are sufficiently thin or are in microgravity. The instability occurs at a temperature gradient 34% smaller than predicted by linear stability theory. Numerical simulations show a drained region qualitatively similar to that seen in the experiment.

On the slow motion of an interfacial viscous droplet in a thin liquid layer

In order to investigate the influence of the surface viscosity on the type of the flow inside and outside a droplet moving in a thin liquid layer, it is essential to compute all hydrodynamical parameters which are important for a better understanding of the hydrodynamical interaction of the thin liquid film and the droplet in it. In the present paper, the problem of a translational slow motion of a droplet with a viscous interface in a liquid layer bounded by viscous liquid-gas interfaces is considered. For low Reynolds and capillary numbers, different values of droplet and film bulk viscosity ratios and surface dilatational and shear viscosities are used in the frame of Newtonian surface rheology. The problem reduces to two dimensions when using the “two vorticities-one velocity” formulation of basic flow equations. The model equations and boundary conditions, which contain second-order derivatives of the velocity and the vorticity, are solved numerically to provide information on type of flow, pressure distribution and drag coefficient. The numerical results reveal the strong influence of the surface viscosity on the motion of the droplet in the viscous liquid layer when the radius of the droplet is of the same order of magnitude as the thickness of the liquid film. The presence of the viscous liquid-gas interface close to the droplet changes the flow pattern inside the droplet considerably when the droplet bulk viscosity is sufficiently higher than the viscosity of the film.

Instability of liquid coatings on cylindrical surfaces

Capillary instability of long annular viscous liquid layers coating the surface of a cylindrical wire is studied. Effects of Reynolds number, Re, initial disturbance wave numbers, k, and wire radii, s on the growth rate of the instability are considered. The initial disturbance amplitude is chosen as 5% of the initial unperturbed liquid thickness. It is found that the growth rate of the disturbance amplitude is composed of a linear portion, which is well predicted by the linear theory, and a relatively flat portion, which is not predicted by the linear theory and is strongly dependent on the Re, k, and s. A unique feature of this instability is a double pinch-off process (in certain parameter range) which results in the formation of secondary satellite drops.

The propagation of Lamb waves in a plate bordered with a viscous liquid

The dispersion equations of Lamb waves of a plate bordered with a viscous liquid layer or half-space viscous liquid on both sides have been derived. Numerical solutions of the dispersion equations related to sensing applications are presented.

On the theory of ion current onset delay in liquid metal ion sources

The phenomenon of delayed onset of ion emission is studied in relation to the value of the applied voltage. On the basis of an analysis of the stability of a thin spherical layer of viscous conductive liquid covering the apex of a needle in a strong electric field, the character of the spatial structure reorganisation of spherical harmonics is described and the change of the volume of the liquid cone is calculated as a function of the value of the voltage. Taking this change and also liquid viscosity into account allows us to explain the main features of the observed dependences between the delay time before the ion current onset and the value of the voltage.

Modeling of coating flows on curved surfaces

The equations describing the temporal evolution of a thin, Newtonian, viscous liquid layer are extended to include the effect of substrate curvature. It is demonstrated that, subject to the standard assumptions required for the validity of lubrication theory, the surface curvature is equivalent to an applied time-independent overpressure distribution. Within the mathematical model, a variety of substrate shapes, possessing both ‘inside’ and ‘outside’ corners, are shown to be equivalent. Starting with an initially uniform coating layer, the evolving coating profile is calculated for substrates with piecewise constant curvature. Ultimately, surface tension forces drive the solutions to stable minimum-energy configurations. For small time, the surface profile history, for a substrate with a single curvature discontinuity, is given as the self-similar solution to a linear fourth-order diffusive equation. Using a Fourier transform, the solution to the linear problem is found as a convergent infinite series. This Green's function generates the general solution to the linearized problem for arbitrary substrate shapes. Calculated solutions to the non-linear problem are suggestive of coating defects observed in industrial applications.

Influence of the surface viscosity on the drag and torque coefficients of a solid particle in a thin liquid layer

The present paper provides a short literature survey of the treatment of particle motion in fluids as a basis of the author's own work in this field. The work relates to the motion of a small solid particle inside a thin liquid film. The particle motion is treated numerically to provide information of interest to thin film liquid coating. The numerical computations yield information on the local velocity and pressure distributions, but also integral information expressed in drag and torque coefficients. The computations are carried out for stationary flows of low Reynolds and capillary numbers and results are presented for different values of surface dilatation and shear viscosities. Translational and rotational motions of the particle are considered by integrating the resultant second-order partial differential equation with an alternating direct implicit method. The numerical results reveal in all cases the strong influence of the surface viscosity on the motion of the solid particle in the viscous liquid layer when the radius of the particle is of the same order of magnitude as the thickness of the liquid film or when the particle is close to the liquid-gas interface.

Production of instant foods by jet agglomeration

In the food Industry, jet agglomeration plants have been widely used for several years now, to produce agglomerates with favourable instant properties from fine powders. The process is suitable for all foodstuffs containing water-soluble substances when wetted, as well as for mixtures of other powders containing such soluble substances. Short average residence time and narrow residence time-distribution allow processing of materials containing volatile components. In a jet agglomeration plant, freely falling particles are wetted by turbulent-free jets of steam. Colliding wetted particles form agglomerates, provided their relative kinetic energy can be dissipated by the viscous liquid layers on the particles' surface. This article gives a short overview of the basic principles of agglomeration and deals with the mechanisms underlying the jet agglomeration process. The process is described as conducted in the author's pilot plant. Based on experimental results and calculations some general information for plant design is provided.

Spreading of a drop of viscous liquid over a surface under the action of capillary forces

The capillary dynamics of a thin layer of viscous liquid which wets a smooth solid surface is considered. To formulate the problems of wetting dynamics the method of matched asymptotic expansions is used. A general method of dosing the asymptotic theory of the dynamic wetting angle which was previously known in the first approximation of a small capillary number is described [1]. For the arbitrary external problem of thin-layer hydrodynamics, which describes the flow outside a small neighbourhood of a moving wetting line, asymptotic boundary conditions are formulated on the wetting line in the third approximation. The transient problem of the spontaneous spreading of a drop of viscous liquid over a solid surface, for which the first-approximation theory is known [2], is solved. The dynamics of the drop is determined for long times. The shape of the drop is obtained in three approximations in the capillary number. The effect of the gravity force on the shape of the spreading drop is determined. The limits of applicability of the model of the quasi-uniform shape of a drop with a dynamic wetting angle which depends on the velocity of the edge of the drop are found.

Jet agglomeration and dynamic adhesion forces

Jet agglomeration has been used in the food industry for several years to produce agglomerates with favourable instant properties from fine powders. In a jet agglomeration plant, freely moving, wetted particles are made to collide with each other to form agglomerates. Agglomeration occurs if the relative kinetic energy of the particles can be dissipated by the viscous liquid layers on their surfaces. This size enlargement process can only be understood if the forces between the colliding particles, called dynamic adhesion forces, can be described. Following a description of the jet agglomeration process, an indirect approach to this problem is presented which uses an experimental set-up allowing determination of the adherence probability of spheres colliding with wetted surfaces.