transport of particles
V.O. Afenchenko, S.V. Kiyashko, A.V. Nazarovsky
In work dynamics of a spot of heavy particles at the bottom of a thin layer of a viscous liquid under the influence of a field parametrically raised standing waves is experimentally investigated. Experiment was spent as follows. In a cavity from aluminum with a diameter 140mm the layer of a liquid with depth of 0,71,5mm was located. Then at the bottom of cavity the round spot from microparticles of copper of thickness 0,050,5 mm was created. For creation of two-dimensional structure of parametrically raised standing waves a ditch with a liquid was located on a vibrotable «TIRA VIB». After inclusion of the vibrоtable at increase in amplitude of external force above some critical value on a surface of a liquid there was a square structure from two pairs of mutually orthogonal standing waves. At small supercriticality structures of standing waves were regular, and at greater supercriticality there were defects and further chaos of defects. Thus at occurrence of defects regular structure of a standing field it was broken, defects arose casually in time and in space. Further to growth of number of defects there was a transition to spatiotemporal chaos.
At the certain depth of a layer of a liquid series of experiments were spent at the fixed parameters of a liquid for the various sizes and thickness of a spot of heavy particles. In each series of experiments at the fixed frequency and amplitude of external force videorecordings dynamics of a spot by duration about ten minutes were done. Then they were processed on a computer and graphs of dependence of the sizes of a spot and density of particles in a spot for the various moments of time were under construction. Similar series of experiments were spent for the various sizes and thickness of a layer of particles.
It has been experimentally established, that in an investigated range of frequencies key parameters which influence qualitatively various behavior of dynamics of a spot of an impurity are amplitude of fluctuations of standing waves in the location of particles of an impurity (which depends from supercriticality and depths of a layer of a liquid) and initial thickness of a layer of particles. It was found out, that process of formation of structure from a spot of an impurity of heavy particles has threshold value and at small supercriticalities it does not occur, and process begins at supercriticality excess some threshold value. In the measured range of frequencies of external force (34-121Гц) this value was ~0,25. At excess of amplitude of external force critical in all frequency range process of carry of an impurity was observed. As a result there was a formation of spatially periodic structure of distribution of density of particles from homogeneous distribution of particles in an initial spot. The initial size of a spot of particles thus practically did not change. After an establishment of stationary distribution of density of particles in space process of formation of structure stopped. With growth of supercriticality speed of process also increased.
At increase in initial thickness of a layer process remained is similar only up to some thickness of an initial layer. Experiments have shown, that there is a limiting value of thickness after which process qualitatively varies and begins process of increase of the spot’s area because of diffusion. Characteristic time of an establishment of stationary distribution thus increases for the order. Thus simultaneously occurred, as well as earlier, process of formation of structure on all area of an initial spot and simultaneously diffusion of excessive volume of particles on edges of a spot. Process of diffusion stopped after on all area of an initial spot the distribution close to stationary was established.
As already it was specified earlier, at increase in external force at a background of regular periodic structure of a standing field there can be infringements of the order in the form of separate defects. Further at increase in their number the field becomes chaotic in space and time. It is revealed that thus the behavior in system qualitatively changes in steps and speeds of diffusive processes increase several times.
The modeling equations describing diffusion of an initial spot of an impurity and an establishment of stationary structure of distribution of an impurity are offered. The explanation of existence of threshold thickness of a layer on which character of carry of an impurity qualitatively depends is offered