Acoustic radiation-force theory for noninteracting particles predicts that when a particle suspension is exposed to a stationary ultrasonic field, the particles may become concentrated at half-wavelength intervals. In a plane stationary field, these particle concentrations would have the shape of uniform planar sheets. Gould and Coakley have observed that particles within these sheets often redistribute to form striated columns in the direction of the ultrasonic beam.In this paper, it is shown that particle columns can result from radial nonuniformity of the ultrasonic beam. Theory is presented that describes the equilibrium distribution of particles when subjected to the lowest axially symmetric acoustic mode of a cylindrical waveguide having a pressure-release wall. Particles with higher density and lower compressibility than that of the host medium will form a column along the axis of a wide waveguide but will migrate to the wall of a narrow waveguide. The direction of radial movement for lower density particles is a function of compressibility but not of waveguide diameter. Results of experiments carried out using aqueous polystyrene suspensions in tubes having thin walls and driven at 3 MHz with a transducer designed to excite primarily the lowest axially symmetric mode were consistent with theory. PACS numbers: 43.25.Uv, 43.25.Gf, 43.20.Mv LIST OF SYMBOLS a C S P( r,z,t ) (Po)min u radius of the liquid cylinder radius of a suspended particle constant [ see Eq. (14) ] V characteristic wave speed in the liquid host mediXo,• um characteristic longitudinal-wave speed in the parz ticle (KE) characteristic shear-wave speed in the particle viscous correction factor [see Eqs. (15) ] (PE) gravitational field strength cylindrical Bessel function of order n a Boltzmann constant /• * wave number in the axial direction [see Eq. (2) ]/• integers /lz acoustic pressure •5 spatial-peak acoustic pressure amplitude minimum spatial-peak pressure amplitude re-• quired to levitate an axial particle column p radial distance p* time p temperature (Kelvin) co total potential energy of a suspended particle acoustic potential energy of a suspended particle gravitational potential energy of a suspended particle particle volume characteristic value of the zero-order cylindrical Bessel function axial position relative to the reflector temporal-average kinetic energy density of the acoustic field temporal-average potential energy density of the acoustic field linear absorption coefficient adiabatic compressibility of the particles adiabatic compressibility of the host medium effective wavelength in the z direction dimensionless boundary layer thickness [see Eqs.

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An apparatus was designed to allow a suspension of biological cells to be subjected to a well-defined, 160-kHz standing ultrasonic field while being viewed through a stereo microscope. Cell positions were recorded either photographically or by means of a video camera. The chamber cavity, which has a square cross section and pressure-release walls, acts as a single-mode acoustic waveguide. The well-defined single-mode field is achieved through use of a special design involving air-filled chamber windows. Aqueous metrizamide solution is used to fill the ultrasonic chamber because it has a unique combination of properties, including low viscosity, low osmolarity, and high density. The chamber rotates about its axis (whose inclination can be varied) producing the centripetal force necessary to contain the buoyant cells in the axial region. Observations were made on stroboscopically illuminated suspensions both of latex microspheres and of red blood cells. The particles formed groups at half-wavelength intervals along the rotation axis near positions of acoustic pressure-amplitude minima. The position and shape of these groupings are explained by a scalar-potential theory for noninteracting particles that considers gravitational, rotational, and acoustic radiation forces on the particles.

An apparatus was designed to allow a suspension of biological cells to be subjected to a well-defined, 160-kHz standing ultrasonic field while being viewed through a stereo microscope. The chamber, which has a square cross section and pressure release walls, acts as a single mode acoustic waveguide. Aqueous metrizamide solution is used to fill the ultrasonic chamber because it has a unique combination of properties including low viscosity, low osmolarity, and high density. The chamber rotates about its axis (whose inclination can be varied) producing the centripetal force necessary to contain the buoyant cells in the axial region. Observations were made on stroboscopically illuminated suspensions both of latex microspheres and of red blood cells. The particles arranged themselves at half-wavelength intervals into axially symmetric formations that became complex and flowering when many particles were present. Some aspects of this behavior are explained by preliminary theory that considers gravitational, rotational, and acoustic radiation forces on the particles. [Work supported by NIH grants GM0729409 (University of Virginia) and GM08209 (University of Vermont).]