Viscosity drag force

After solvent removal the aerosols produced from slurries deliver solid particles, the diameters of which are those of the powder particles. In slurry nebulization used for flame work or plasma spectrometry, they are injected with a velocity that is less than or equal to the nebulizer gas atom velocities, as viscosity drag forces are responsible for their entrainment into the ICP. The velocity of the gas atoms (vG) can be calculated from the gas temperature at the location considered (TG), the injection velocity (vi) and the temperature at the point of injection (T), as vG = Vi x TG/Ti and the acceleration of particles (d2z/dt2) as a result of the viscosity drag forces is ... 

Viscous Drag. The velocity, v, with which a particle can move through a Hquid in response to an external force is limited by the viscosity, Tj, of the Hquid. At low velocity or creeping flow (77 < 1), the viscous drag force is /drag — SirTf- Dv. The Reynolds number (R ) is deterrnined from... 

The resistance to liquid flow aroimd particles may be presented by an equation similar to the viscosity equation but with considering the void fraction. Recall that the shear stress is expressed by the ratio of the drag force, R, to the active surface, K27td. The total sphere surface is Ttd and Kj is the coefficient accoimting for that part of the surface responsible for resistance. Considering the influence of void fraction as a function 2( ). we obtain ... 

Consider a spherical particle of diameter dp and density pp falling from rest in a stationary fluid of density p and dynamic viscosity p.. The particle will accelerate until it reaches its terminal velocity a,. At any time t, let a be the particle s velocity. Recalling that the drag force acting on a sphere in the Stokes regime is of magnitude iirdppu, application of Newton s second law of motion can be written as... 

Thus, if the liquid is highly viscous, then the drag force is so predominant that the bubble volume is highly sensitive to viscosity. Again, if the viscosity and the flow rate are both small, then variations in the viscosity do not affect the bubble volume appreciably. 

Because most shear-thinning fluids, particularly polymer solutions and flocculated suspensions, have high apparent viscosities, even relatively coarse particles may have velocities in the creeping-flow of Stokes law regime. Chhabra(35,36) has proposed that both theoretical and experimental results for the drag force F on an isolated spherical particle of diameter d moving at a velocity u may be expressed as a modified form of Stokes law ... 

When solvated ions migrate within the electrolyte, the drag force applied by the surrounding solvent molecules is measured by solvent viscosity rj. Thus, in a solvent of lower viscosity, the solvated ions would move more easily in response to an applied electric field, as expressed by the Einstein—Stokes relation (eq 3). Solvents of low viscosity have always been considered the ideal candidates for electrolyte application however, their actual use was restricted because most of these solvents have low dielectric constants (Tables 1 and 2) and cannot dissociate ions effectively enough to prevent ion pairing. 

The first requirement is obvious and easy to accomplish, but the second is difficult to understand and also to accomplish and needs explanation. For example, if forces that may act on a fluid element in a fermenter during agitation are the viscosity force Fv, drag force on impeller F0, and gravity force FG, each can be expressed with characteristic quantities associated with the agitating system. According to Newton s equation of viscosity, viscosity force is... 

The dynamic response of a particle in gas-solid flows may be characterized by the settling or terminal velocity at which the drag force balances the gravitational force. The dynamic diameter is thus defined as the diameter of a sphere having the same density and the same terminal velocity as the particle in a fluid of the same density and viscosity. This definition leads to a mathematical expression of the dynamic diameter of a particle in a Newtonian fluid as... 

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