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- Type of Document: Ph.D. Dissertation
- Language: Farsi
- Document No: 46325 (08)
- University: Sharif University of Technology
- Department: Mechanical Engineering
- Advisor(s): Jalali, Mir Abbas
- Abstract:
- Each of us at some point in our life has been astonished by the observation of the collective motion of certain animals such as birds, fishes or insects. These coherent and synchronized structures are apparently produced without the active role of a leader in the grouping and it has been reported even for some microorganisms such as bacteria or red blood cells. In all the mentioned examples agents are surrounding with the moving fluid which can affect the collective behavior of the system. The collaborative flock of birds in windy conditions and the swimming of fishes in rivers or along oceanic currents are some examples. Moreover, micro-organisms produce different collective behavior in the presence of turbulence, vortices, and shear flow.
In this thesis we study the collective dynamic of interacting particles in fluid flow. At the first part of the thesis, we have studied one-dimensional collective dynamics of particles with soft-core interactions in steady and unsteady flow. The kinetic and hydrodynamic models have been obtained based on particle-based model. We have used Morse potential to model the interaction between particles. By solving the kinetic model, we have found the catastrophic and H-stable phases based on Morse potential parameters. We find analytic single-peaked traveling solutions for the spatial density of particles in the catastrophic phase. In steady flow conditions the streaming velocity of particles is identical to their carrier fluid, but we show that particle streaming is asynchronous with an unsteady carrier fluid. Using linear perturbation analysis, the stability of traveling solutions is investigated in unsteady conditions. It is shown that the resulting dispersion relation is an integral equation of the Fredholm type and yields two general families of stable modes: singular modes whose eigenvalues form a continuous spectrum, and a finite number of discrete global modes. Depending on the value of drag coefficient, stable modes can be overdamped, critically damped, or decaying oscillatory waves.
In the second part of the thesis we study the interfacial instabilities in the two-dimensional channel flow of a sediment suspension. The particles interaction is hard-core and they diffuse in the carrier fluid due to shear-induced collisions. We derive partial differential equations that govern the deformations of the interface between the sediment suspension and the clear fluid, and devise a perturbation method that preserves the positivity of the particle volume fraction. We solve perturbed momentum, particle transport, and deforming interface equations to show that a Kelvin-Helmholtz type unstable wave develops at the interface for wavelengths longer than a critical value. Short-wavelength oscillations of the interface are damped due to shear induced diffusion of particles. We also show that the lowest critical Reynolds number, above which the interface is unstable, occurs for intermediate values of the total volume fraction of particles - Keywords:
- Cooperative Movement ; Kinetic Equations ; H-stable Phase ; Interfacial Kelvin-Helmholtz Mode ; Shear Induced Diffusion (SID) ; Catastrophic Phase
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