David B. Thiessen

Manipulation of fluid objects with acoustic radiation pressure

Abstract: Conditions are summarized for manipulating and stabilizing fluid objects based on the acoustic radiation pressure of standing waves. Examples include (but are not limited to) liquid drops, gas bubbles in liquids, and cylindrical liquid bridges. The emphasis is on situations where the characteristic wavelength of the acoustic field is large in comparison to the relevant dimension of the fluid object. Tables are presented for ease of comparing the signs of qualitatively different radiation force parameters for a variety of fluid objects.

Acoustic radiation force on a compressible cylinder in a standing wave

The radiation force-per-length on an infinitely long circular cylinder in an acoustic plane standing wave is expressed in terms of partial-wave scattering coefficients for the corresponding traveling wave scattering problem. This information allows a dimensionless radiation force function to be expressed using coefficients available from two-dimensional scattering theory. Four examples are given for fluid circular cylinders: A hot gas column (used to approximate a small flame), a compressible liquid bridge in a Plateau tank, a liquid bridge in air, and a cylindrical bubble of air in water. A long-wavelength approximation for the force is also examined which is analogous to one for the radiation force on compressible spheres [K. Yosioka and Y. Kawasima, Acustica 5, 167–173 (1955)]. A long-wavelength approximation is also known for the monopole and dipole scattering coefficients of a compressible elliptical cylinder and the radiation force is also examined for that situation. Some of the results for the rad...

Driven and freely decaying nonlinear shape oscillations of drops and bubbles immersed in a liquid: experimental results

Large-amplitude oscillations of drops and bubbles immersed in an immiscible liquid host have been investigated using ultrasonic radiation pressure techniques. Single levitated or trapped drops and bubbles with effective radius between 0.2 and 0.8 cm have been driven into resonant shape oscillations of the first few orders. The direct coupling of driven drop shape oscillations between the axisymmetric l =6 and l =3 modes has been documented as well as the interaction between axisymmetric and non-axisymmetric l =3 and l =2 modes. Effective resonant energy transfer from higher- to lower-order modes has been observed together with a much less efficient energy transfer in the reverse direction. The first three resonant modes for bubbles trapped in water have also been excited, and mode coupling during driven and free-decaying oscillations has been measured. The evidence gathered thus far indicates that efficient drop resonant coupling between a higher- and a lower-order mode occurs when the characteristic frequency of the latter mode roughly coincides with a harmonic resonance.

Stabilization of a cylindrical capillary bridge far beyond the Rayleigh-Plateau limit using acoustic radiation pressure and active feedback

A novel method of suppressing the Rayleigh–Plateau capillary instability of a cylindrical liquid bridge is demonstrated which uses the radiation pressure of an ultrasonic wave to control the shape of the bridge. The shape of the bridge is optically sensed and the information used to control the spatial distribution of the radiation stress on the surface of the bridge. The feedback is phased so as to suppress the growth of the axisymmetric mode which normally becomes unstable when the slenderness, given by the length to diameter ratio, exceeds π. Stabilization is achieved out to a slenderness of 4.3 for a bridge density matched to the surrounding water bath in a Plateau tank. Breakup of such long bridges was found to produce a satellite drop from the receding thread of liquid. The active stabilization mechanism used may have application to other capillary systems.

CAPILLARY BRIDGE MODES DRIVEN WITH MODULATED ULTRASONIC RADIATION PRESSURE

The method of modulated ultrasonic radiation pressure, previously used to drive the capillary modes of drops and bubbles, is used to excite the capillary modes of a cylindrical oil bridge in a Plateau tank. Specific modes may be selected by adjusting the modulation frequency and the location or orientation of the bridge in the ultrasonic field. Mode frequencies were measured as a function of the slenderness for the lowest two axisymmetric modes and two nonaxisymmetric modes. The frequencies of the lowest modes agree with an approximate theory which neglects viscous corrections where the interfacial tension is a fitted parameter.

Stabilization of electrically conducting capillary bridges using feedback control of radial electrostatic stresses and the shapes of extended bridges

Electrically conducting, cylindrical liquid bridges in a density-matched, electrically insulating bath were stabilized beyond the Rayleigh–Plateau (RP) limit using electrostatic stresses applied by concentric ring electrodes. A circular liquid cylinder of length L and radius R in real or simulated zero gravity becomes unstable when the slenderness S=L/2R exceeds π. The initial instability involves the growth of the so-called (2, 0) mode of the bridge in which one side becomes thin and the other side rotund. A mode-sensing optical system detects the growth of the (2, 0) mode and an analog feedback system applies the appropriate voltages to a pair of concentric ring electrodes positioned near the ends of the bridge in order to counter the growth of the (2, 0) mode and prevent breakup of the bridge. The conducting bridge is formed between metal disks which are grounded. Three feedback algorithms were tested and each found capable of stabilizing a bridge well beyond the RP limit. All three algorithms stabiliz...

Active electrostatic stabilization of liquid bridges in low gravity

In experiments performed aboard NASAs low-gravity KC-135 aircraft, it was found that rapid active control of radial electrostatic stresses can be used to suppress the growth of the (2,0) mode on capillary bridges in air. This mode naturally becomes unstable on a cylindrical bridge when the length exceeds the Rayleigh–Plateau (RP) limit. Capillary bridges having a small amount of electrical conductivity were deployed with a ring electrode concentric with each end of the bridge. A signal produced by optically sensing the shape of the bridge was used to control the electrode potentials so as to counteract the growth of the (2,0) mode. Occasionally the uncontrolled growth of the (3,0) mode was observed when the length far exceeded the RP limit. Rapid breakup from the growth of the (2,0) mode on long bridges was confirmed following deactivation of the control.

Scattering observations for tilted transparent fibers: evolution of Airy caustics with cylinder tilt and the caustic merging transition

When a dielectric circular cylinder is obliquely illuminated, the scattering angle associated with the Airy caustics of the cylinders primary rainbow depends on the tilt of the cylinder. We display records of the scattering pattern for a transparent poly(methyl methacrylate) fiber ranging from small values of tilt through values of tilt that are sufficiently large for the Airy caustics from both sides of the fiber to merge in a meridional plane containing the incident wave vector and the fibers axis. The records are compared directly with the evolution of the caustic projected onto the observation plane, and certain qualitative features of the global evolution of the caustics are confirmed. Although the observations used laser illumination, they are relevant to anticipating the scattering by sunlit transparent tilted cylinders.

Fixed contact line helical interfaces in zero gravity

Fluid interfaces supported in microgravity by a helical structure are shown to have a more robust stability than more common structures such as liquid bridges. In particular, helical interfaces can take the form of infinite right circular cylinders over a broad range of configurations. In the case of a single fixed contact line support, the infinite cylinder is stable for all cases in which the pitch to diameter ratio is less than π∕3 (more tightly coiled interfaces). When there are two or more equally spaced fixed contact line supports, the infinite cylinder is stable for all configurations. Furthermore, in the two support case (the double helix), stability persists for all volumes from the cylinder to zero volume, when the pitch to diameter ratio is greater than 2.082 (more loosely coiled interfaces). The equivalent to the axisymmetric Young-Laplace equation is derived for helical interfaces. Interfacial stability is determined from equilibrium branch structure following the application of Maddocks’ met...

Liquid jet response to internal modulated ultrasonic radiation pressure and stimulated drop production.

Experimental evidence shows that a liquid jet in air is an acoustic waveguide having a cutoff frequency inversely proportional to the jet diameter. Ultrasound applied to the jet supply liquid can propagate within the jet when the acoustic frequency is near to or above the cutoff frequency. Modulated radiation pressure is used to stimulate large amplitude deformations and the breakup of the jet into drops. The jet response to the modulated internal ultrasonic radiation pressure was monitored along the jet using (a) an optical extinction method and (b) images captured by a video camera. The jet profile oscillates at the frequency of the radiation pressure modulation and where the response is small, the amplitude was found to increase in proportion to the square of the acoustic pressure amplitude as previously demonstrated for oscillating drops [P.L. Marston and R.E. Apfel, J. Acoust. Soc. Am. 67, 27-37 (1980)]. Small amplitude deformations initially grow approximately exponentially with axial distance along the jet. Though aspects of the perturbation growth can be approximated from Rayleighs analysis of the capillary instability, some detailed features of the observed jet response to modulated ultrasound are unexplained neglecting the effects of gravity.