ICA Madrid September 2-7 th 2007 Movement of airborne particles in tubular metal resonators Jeremy J. Hawkes Rito Mijarez-Castro 2, Peter R. Fielden 1, Bernard Treves Brown 1 and Pramukh N Jayasekera 3 Frederic Cegla, Mike Lowe and Jon Allin 1 School of Chemical Engineering and Analytical Science, The University of Manchester, PO Box 88, Sackville Street, Manchester, M60 1 QD, UK 2 Gerencia de Control e Instrumentación, Instituto de Investigaciones Eléctricas, CP Cuernavaca, Morelos, México. 3 dstl Porton Down, Salisbury, Wiltshire, SP4 OJQ, UK

Laser beam used to observe structure in an aerosol emerging from a tube containing a standing wave Camera Click pictures to see sound on

Laser beam used to observe structure in an aerosol emerging from a tube containing a standing wave Click pictures to see sound on

Liquids and solids move to different locations Aerosol of 5  m water droplets ~1  m smoke particles stress Mixture of 10  m polystyrene and 5  m water droplets Click pictures to see sound on

Mixture of 10  m polystyrene and 5  m water droplets H. Zhao, SS. Sadhal and EH. Trinh, Internal circulation in a drop in an acoustic field JASA (1999) TJ. Matula, SM. Cordry, RA. Roy, and LA. Crum The Bjerknes force and bubble levitation under single- bubble sonoluminescence conditions, JASA (1997) 102, Liquids and solids move to different locations Aerosol of 5  m water droplets ~1  m smoke particles

Most cavity modes can be found Click pictures to see sound on

Modes in two directions should form clumps?

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Lattice Boltzmann simulations of acoustic streaming and the radiation force on objects in a sound field David Haydock PhD Thesis 2004 (Oxford) Modes in two directions produce Rayleigh streaming

Mixture of 10  m polystyrene and 5  m water droplets Liquids and solids also separate in rectangular ducts

Circumferential tube vibration modes 0 to 4 Mode 0 Mode 1 Mode 2 Mode 3 Mode 4 Click pictures to see sound on

Predictions of vibration frequency from Disperse

The prediction can be applied to any wall material or tube cavity diameter by combining with the analytical equation for vibrations of a cylindrical shell (thin walled tube surrounded by vacuum inside and outside, Blevins p298). Tube design Modes for the wall of infinite length tubes Disperse predicts a relationship between frequency and all thickness for each mode The scaling factors obtained are: where E= Young’s Modulus; R= mid-wall tube radius; ν= Poisson’s ratio;  = density of shell material; λi = (1+i2)1/2 for mode number i= 0,1,2,…

Aluminium tube 200 kHz transducer glued to the aluminium Aerosol flow direction Piezoelectric driving ring glued to one end of an aluminium tube Driving to produce mixed modes gives good agreement with predictions for infinite length tubes Driving to produce pure modes requires full 3D FE modelling to obtain near agreement between experiments and models. Tube design, advantages and disadvantages of modelling

Pressure and displacement curves predicted by Disperse Click pictures to see sound on

Concentration of particles on axis Click pictures to see sound on

There are many other modes Click pictures to see sound on

Mike Lowe Frederic Cegla Jon AllinImperial College Pramukh Jayaskera dstl Click pictures to see sound on