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Nuclear Magnetic Resonance studies of an ultrasonically vibrated granular bed

Presented by: 
JM Huntley & T Tarvaz & NA Sheikh [Loughborough]
Thursday 8th January 2009 - 14:00 to 14:25
INI Seminar Room 1
A granular bed on a vibrating base (with vibration amplitude A, and angular frequency w) is normally fluidised once the peak base acceleration A0w2 exceeds that due to gravity. Once fluidised, the rate of energy input to the bed is normally controlled by the peak base velocity A0w. In the current paper we test both experimentally and numerically the validity of these assertions at vibration frequencies some 2-3 orders of magnitude higher than normally used. The experiments were performed using a Nuclear Magnetic Resonance spectrometer that provided time-averaged 1-D profiles of packing fraction and granular temperature within a bed of mustard seeds. A high power ultrasonic transducer and waveguide produced peak velocities of order 1ms -1 and peak accelerations of order 105 ms-2. A laser vibrometer was used to maintain a constant peak base velocity at a set of discrete resonant frequencies in the range 10-20 kHz. Despite the constant base velocity, dramatic reductions in granular temperature and mean height of the bed were observed as the frequency increased. The interaction between a grain and the vibrating base was modelled using a Hertzian contact law, with the stiffness coefficient measured experimentally through quasi-static compression tests of the grains. The equation of motion was integrated by a Runge-Kutta scheme, taking proper account of multiple contacts. By averaging over all vibration phases, an efficient coefficient of restitution, e, was obtained as a function of approach velocity and vibration frequency over the range 10-20 kHz, in agreement with the experimentally-observed reduction in granular temperature and mean height of the bed over the same range.The Hertzian mean impact duration of approximately 60 us lies within the 50-100 us range of the vibration period. The transition between "classical" vibrofluidised bed behaviour and the "high-frequency" behaviour studied here can therefore be interpreted as a consequence of a breakdown of the usual assumption of instantaneous collisions. Presentation of the results in non-dimensional form provides a general expression for the energy flux boundary condition, which may prove useful for the development of future applications of ultrasonic excitation.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons