Trajectory analysis, hydrodynamic

LaFrance and Grasso [29] report an application of MD methods (again, termed trajectory analysis ) to the dissolved air flotation of nitrocellulose particles of 2.3 fim diameter. This work also neglected Brownian motion considerations, but included electrostatic, van der Waals, the Lewis acid-base interaction forces, and hydrodynamic forces. Lafrance and Grasso found limiting trajectories by successions of forward integrations, and from this calculated the capture efficiency per air bubble as a function of solution chemistry. 

A simplified particle-trajectory analysis has been used to explain the essential features of US-assisted filtration. Acoustic forces can cause particle trajectories to deviate from hydrodynamic pathlines towards particle collectors, thereby enhancing their collection efficiency in comparison to pure hydrodynamic interception. 

Our analysis describes virus adsorption from the standpoint of chemical equilibrium. Since adsorption equilibrium appears to be approached closely in our systems in less than or equal to 2 hr, and since the residence time of viruses in natural water systems is greater than 2 hr for many cases (for example, lakes, groundwaters, rivers, etc.), equilibrium considerations are entirely appropriate. In other situations, where residence times of the virus in the system are small compared to expected times required for adsorption to approach equilibrium (for example, sand filters in water treatment, water distribution systems, etc.), the DLVO-Lifshitz theory may still be applied directly. The work of Fitzpatrick and Spielman (57) concerning filtration and that of Zeichner and Schowalter (58) concerning colloid stability in fiow fields demonstrate this clearly. Their developments of hydrodynamic trajectory analysis coupled to DLVO-Lifshitz considerations can be extended... 

In general, the approaches of the trajectory analysis and the build-up models are based on the force-balance equation. Among the forces (external and interparticle) involved in the system, magnetic and hydrodynamic forces, the most significant ones, also compete with one another. The performance of magnetic separation is, therefore, examined in terms of magnetic velocity (Vjj ) and superficial velocity ( Vq) (Watson, 1973),... 

Another class of practically important situations arises when the particle is driven toward the interface by the macroscopic flows discussed earlier. Due to the presence of the wall, the hydrodynamic driving forces are modified, which causes the deviation of particle trajectory fi-om liquid streamlines. Hydrodynamic torques on particles and the coupling between the translational and rotational motion also appear, which make the theoretical analysis of this problem rather involved. The problem of a particle moving in a simple shear flow given by Eq. (108) was solved by Goren and O Neill [99]. It was shown that the particle velocity can be expressed as... 

The analysis of this trajectory requires the resolution of the dynamics equations that needs the evaluation of the hydrodynamic effect in the film. The main difficulty comes from the dependence of the hydrodynamic force on both the position of the shaft within the housing and the velocity of the shaft centre. In most industrial applications, the external force is the weight of the shaft, with or without superimposed dynamic forces from mass unbalance for example. 

Ovod, V. L, Hydrodynamic Focusing of Particle Trajectories in Light-Scattering Counters and Phase-Doppler Analysis, Parr. Part Syst Charact, 1995, 12,207-211. 

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