Particle column formation in a stationary ultrasonic field

Abstract

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.

Contactless Acoustic Manipulation and Sorting of Particles by Dynamic Acoustic Fields

“…It is also assumed that the particle is rigid, which is a good assumption for particles immersed in an air medium. The dimensionless form of U is considered, which is calculated by [15] 2 0…”

“…These dynamic field technologies can be implemented by several methods. It has been previously demonstrated that one emitter and a reflector can be used to create a standing wave that traps particles in fixed positions in space [15]- [17]. With this technology, it is possible to trap particles and transport them by changing the driving frequency [18], [19].…”

Effective mixing of laminar flows at a density interface by an integrated ultrasonic transducer

“…In a standing wave, quartz wind is not observed. 17 Instead, Rayleigh streaming may occur 11 and the driving force is also in this case proportional to a spatial gradient in the (time-averaged) energy density. The mechanism is dissipation of acoustic energy adjacent to a solid wall within a resulting boundary layer.…”

Spatial patterning of endothelial cells and vascular network formation using ultrasound standing wave fields

“…to defined locations in suspending media (Dyson et al, 1974;Whitworth and Coakley, 1992;Coakley et al, 1994;Saito et al, 1998;Bazou et al, 2005;Gherardini et al, 2005;Bazou et al, 2006;Garvin et al, 2011). The primary acoustic radiation force generated along the direction of sound propagation is largely responsible for the movement of cells and particles within an ultrasound standing wave field (Gor'kov, 1962;Gol'dberg, 1971;Gould and Coakley, 1974).…”