Alexei Rednikov

Noncontact technique for determining viscosity from the shape relaxation of ultrasonically levitated and initially elongated drops

We present a technique that can determine the viscosity of highly viscous liquids, particularly, undercooled liquids that exist at temperatures below their freezing points. The technique involves levitation of a liquid drop using an ultrasonic standing wave, and elongation of the drop by rotating it beyond the point of bifurcation. The elongated drop is then allowed to be restored to its original shape by surface tension driven relaxation. The time-dependent shape parameters of the relaxing drop are related to the viscosity through a relaxation model. In addition, this technique can also determine the surface tension that has a known relationship with the angular velocity at the bifurcation point. The feasibility of the technique is demonstrated by performing the measurement using sucrose solutions as a model liquid drop. The obtained viscosity values show a good correlation with those determined by a falling ball method.

Steady streaming from an oblate spheroid due to vibrations along its axis

Steady (acoustic) streaming around a rigid oblate spheroid is studied in the incompressible limit when the fluid medium and the particle are in a small-amplitude high-frequency relative oscillatory motion along the symmetry axis of the spheroid. The inner (inside the thin Stokes shear-wave layer) and outer streaming patterns are analysed. A solution for the outer streaming is obtained analytically for small Reynolds numbers. At large Reynolds numbers, a boundary-layer consideration is carried out. Steady streaming in the disk limit, as approached within the family of oblate spheroids, is systematically investigated in the large Reynolds number case, and qualitative implications for shapes other than oblate spheroidal are discussed.

Acoustic/steady streaming from a motionless boundary and related phenomena: generalized treatment of the inner streaming and examples

As originally realized by Nyborg ( J. Acoust. Soc. Am. , vol. 30, 1958, p. 329), the problem of the inner acoustic/steady streaming can be analysed in quite general terms. The inner streaming is the one that develops in the high-frequency limit in a thin Stokes (shear-wave) layer at a boundary, in contrast to the outer streaming in the main bulk of the fluid. The analysis provides relevant inner-streaming characteristics through a given distribution of the acoustic amplitude along the boundary. Here such a generalized treatment is revisited for a motionless boundary. By working in terms of surface vectors, though in elementary notations, new compact and easy-to-use expressions are obtained. The most important ones are those for the effective (apparent) slip velocity at the boundary as seen from a perspective of the main bulk of the fluid, which is often the sole driving factor behind the outer streaming, and for the induced (acoustic) steady tangential stress on the boundary. As another novel development, non-adiabatic effects in the Stokes layer are taken into account, which become apparent through the fluctuating density and viscosity perturbations, and whose contribution into the streaming is often ignored in the literature. Some important particular cases, such as the axisymmetric case and the incompressible case, are emphasized. As far as the application of the derived general inner-streaming expressions is concerned, a few examples provided here involve a plane acoustic standing wave, which either grazes a wall parallel to its direction (convenient for the estimation of the non-adiabatic effects), or into which a small (compared to the acoustic wavelength) rigid sphere is placed. If there are simultaneously two such waves, out-of-phase and, say, in mutually orthogonal directions, a disk placed coplanarly with them will undergo a steady torque, which is calculated here as another example. Two further examples deal with translational high-frequency harmonic vibrations of particles relative to an incompressible fluid medium, viz. of a rigid oblate spheroid (along its axis) and of a sphere (arbitrary three dimensional). The latter can be a fixed rigid sphere, one free to rotate or even a (viscous) spherical drop, for which the outer streaming and the internal circulation are also considered.

Noncontact technique for determining the thermal diffusivity coefficient on acoustically levitated liquid drops

We present a technique that can be used to determine the thermal diffusivity coefficient of undercooled liquids, which exist at temperatures below their freezing points. The technique involves levitation of a small amount of liquid in a flattened drop shape using an acoustic levitator and heating it with a laser beam. The heated drop is then subjected to natural cooling by heat loss from the surface. Due to acoustic streaming, the heat loss mainly occurs through the equator section of the drop. The measured cooling rate in combination with a radial heat conduction model allows us to calculate the thermal diffusivity coefficient of the drop. We demonstrate the feasibility of the technique using glycerin drops as a model liquid. The technique is well suited if the thermal diffusivity coefficient of the liquid in the normal state (i.e., above the freezing point) is known or can be measured by conventional techniques.

The behaviour of a particle in orthogonal acoustic fields

We are concerned with the response of an unconstrained particle, solid or liquid, placed in an acoustic field which consists of two orthogonal sound waves. These have the same amplitude and wavenumber, but differ in phase by π/2. The particle may be either a circular cylinder or a sphere. The effect of the superimposed waves is to create a time-averaged torque on the particle which causes it to rotate with uniform angular velocity. Throughout, a suitably defined Strouhal number is assumed to be large, with the solution developed in appropriate inverse powers of it. The particle size is assumed to be much smaller than the acoustic wavelength. At leading order it is shown that solid and liquid cylinders behave in a similar manner, in the sense that the liquid is in solid-body rotation. For a spherical liquid drop, the dominant time-averaged motion of it is also a solid-body rotation when the drop viscosity is large compared with that of the fluid environment; however, superposed on this is a time-averaged recirculatory flow within the droplet in the form of a pair of toroidal vortices.

Shape relaxation of liquid drops in a microgravity environment

Abstract: We investigated shape relaxation of liquid drops in a microgravity environment that was created by letting the drops fall freely. The drops were initially levitated in air by an acoustic/electrostatic hybrid levitator. The levitated drops were deformed due to the force balance among the levitating force, surface tension, and gravity. During the free fall, the deformed drops underwent shape relaxation driven by the surface tension to restore a spherical shape. The progress of the shape relaxation was characterized by measuring the aspect ratio as a function of time, and was compared to a simple linear relaxation model (in which only the fundamental mode was considered) for perfectly conductive drops. The results show that the model quite adequately describes the shape relaxation of uncharged/charged drops released from an acoustically levitated state. However, the model is less successful in describing the relaxation of drops that were levitated electrostatically before the free fall. This may be due to finite electrical conductivities of liquids, which somehow affects the initial stage of the shape relaxation process.

Noncontact Thermophysical Property Measurement by Levitation of a Thin Liquid Disk

Abstract:  The purpose of the current research program is to develop techniques for noncontact measurement of thermophysical properties of highly viscous liquids. The application would be for undercooled liquids that remain liquid even below the freezing point when suspended without a container. The approach being used here consists of carrying out thermocapillary flow and temperature measurements in a horizontally levitated, laser‐heated thin glycerin disk. In a levitated state, the disk is flattened by an intense acoustic field. Such a disk has the advantage of a relatively low gravitational potential over the thickness, thus mitigating the buoyancy effects, and helping isolate the thermocapillary‐driven flows. For the purpose of predicting the thermal properties from these measurements, it is necessary to develop a theoretical model of the thermal processes. Such a model has been developed, and, on the basis of the observed shape, the thickness is taken to be a minimum at the center with a gentle parabolic profile at both the top and the bottom surfaces. This minimum thickness is much smaller than the radius of disk drop and the ratio of thickness to radius becomes much less than unity. It is heated by laser beam in normal direction to the edge. A general three‐dimensional momentum equation is transformed into a two‐variable vorticity equation. For the highly viscous liquid, a few millimeters in size, Stokes equations adequately describe the flow. Additional approximations are made by considering average flow properties over the disk thickness in a manner similar to lubrication theory. In the same way, the three‐dimensional energy equation is averaged over the disk thickness. With convection boundary condition at the surfaces, we integrate a general three‐dimensional energy equation to get an averaged two‐dimensional energy equation that has convection terms, conduction terms, and additional source terms corresponding to a Biot number. A finite‐difference numerical approach is used to solve these steady‐state governing equations in the cylindrical coordinate system. The calculations yield the temperature distribution and the thermally driven flow field. These results have been used to formulate a model that, in conjunction with experiments, has enabled the development of a method for the noncontact thermophysical property measurement of liquids.

Thermal Diffusivity Coefficient of Glycerin Determined on an Acoustically Levitated Drop

Abstract: We present a technique that can be used to determine the thermal diffusivity coefficient of undercooled liquids that exist at temperatures below their freezing points. The technique involves levitation of a small amount of liquid in the shape of a flattened drop using an acoustic levitator and heating it with a CO2 laser. The heated drop is then allowed to cool naturally by heat loss from the surface. Due to acoustic streaming, heat loss is highly non‐uniform and appears to mainly occur at the drop circumference (equatorial region). This fact allows us to relate the heat loss rate with a heat transfer model to determine the thermal diffusion coefficient. We demonstrate the feasibility of the technique using glycerin drops as a model liquid.

An Analytical Model of External Streaming and Heat Transfer for a Levitated Flattened Liquid Drop

We present here the heat transfer and fluid flow analysis of an acoustically levitated flattened disk-shaped liquid drop. This work arises due to an interest in the non-contact measurement of the thermophysical properties of liquids. Such techniques have application to liquids in the undercooled state, i.e., the situation when a liquid stays in a fluidic state even when the temperature falls below the normal freezing point. This can happen when, for example, a liquid sample is held in a levitated state. Since such states are easily disrupted by measurement probes, non-contact methods are needed. We have employed a technique involving the use of acoustically levitated samples of the liquid. A thermal stimulus in the form of laser-heating causes thermocapillary motion with flow characteristics depending on the thermophysical properties of the liquid. In a gravity field, buoyancy is disruptive to this thermocapillary flow, masking it with the dominant natural convection. As one approach to minimizing the effects of buoyancy, the drop was flattened (by intense acoustic pressure) in the form of a horizontal disk, about 0.5 mm thick. As a result, with very little gravitational potential, with most of the buoyant flow suppressed, thermocapillary flow remained the dominant form of fluid motion within the drop. This flow field is visualizable and subsequent analysis for the inverse problem of the thermal property can be conducted. This calls for numerical calculations involving a heat transfer model for the flattened drop. With the presence of an acoustic field, the heat-transfer analysis requires information about the corresponding Biot number. In the presence of a high-frequency acoustic field, the steady streaming originates in a thin shear-wave layer, known as the Stokes layer, at a surface of the drop. The streaming develops into the main fluid, and is referred to as the outer streaming. Since the Stokes layer is asymptotically thin in comparison to the length scale of the problem, the outer streaming formally appears to be caused by an effective slip velocity at the boundary. The presence of the thin Stokes layer, and the slip condition at the interface, changes the character of the heat transfer mechanism which is inherently different from the traditional boundary layer. The current analysis consists of a detailed semi-analytical calculation of the flow field and the heat transfer characteristics of a levitated drop in the presence of an acoustic field.

Non-Contact Measurement of Thermophysical Properties of Liquids by Acoustic and Electrostatic Levitation

The thermodynamic behavior of liquids in undercooled states is an area that has gained considerable importance in various applications. In nature, as well as with industrial situations such as liquid-metal spray deposition, liquid states are found to exist below the freezing point, especially if a pure liquid remains in a relatively undisturbed state. Since a disturbance can easily disrupt the undercooled state, measurements need to be carried out non-intrusively. Furthermore, the liquid sample has to be held without a container since most solid containers would promote heterogeneous nucleation at the freezing point. Therefore, electrostatic and acoustic levitation techniques are being employed. The measurement of viscosity and surface tension are being conducted by observing the response of initially deformed drops (acoustically and electrostatically) to more spherical shapes upon relaxation of the deforming force fields. The measurement of properties, such as thermal diffusivity, are conducted by the application of a thermal stimulus to a levitated liquid sample and the observation of the response from which such properties can be inferred. The effect of buoyancy-driven convection is suppressed by horizontally flattening the drop with an acoustic field, thus leaving a small gravitational force potential. This approach has been found to effectively reduce the flow to a thermoacapillary dominant type, accompanied by acoustic disturbances. This lends itself to measurements of the thermocapillary flows with minimal buoyancy interference even in a unit-gravity field.Copyright