Viscous drag force

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... 

Based on such analyses, the Reynolds and Weber numbers are considered the most important dimensionless groups describing the spray characteristics. The Reynolds number. Re, represents the ratio of inertial forces to viscous drag forces. 

Surface area of torpedo = nDL Viscous drag force = nDLx... 

The Reynolds number for mixing ReM represents the ratio of the applied to the opposing viscous drag forces. 

When a low frequency AC electric field is imposed, the particle oscillates around its mean position and platy particles may become optimally aligned with the field. At high frequencies, neither particle shift nor alignment takes place. However, translational movement of dispersed particles can be attained in an asymmetric AC field (without a DC component). The observed drift is attributed to the velocity-dependent viscous drag force in relation to double layer polarization as sketched in Figure 2 for reference, bacteria swim at 0.02-1 mm/s. For more details see Palomino [2], The field frequency co must be low enough such that ionic concentrations and hydrodynamic fields may adjust to... 

In principle, one can write down all of these forces and formulate the Newtonian equations of motion for the fluid this yields a complicated differential equation known as the Navier-Stokes equation [1-3]. A complete solution of the Navier-Stokes equation gives the exact trajectory and velocity of each fluid element. In practice, the calculations are often difficult because one must simultaneously account for all fluid elements and the interactions between these elements caused by the viscous drag forces. (The simultaneous motion of many interacting fluid elements is analogous to the simultaneous motion of many interacting mechanical objects, the latter being so complicated that it is described as the many body problem. ) However, in certain cases, the Navier-Stokes equation is reduced to a tractable form by the existence of steady low-velocity flow and high symmetry in the flow conduit (e.g., capillary tubes of circular cross section). We will examine such simple cases shortly. 

Flow in a capillary can be maintained by a steady pressure difference Ap applied between inlet and outlet ends. We assume gravitational (and other external) forces to be negligible (true for a horizontal tube or for any tube with a large Ap). With the application of Ap, the fluid in the tube accelerates to a flowrate at which the viscous drag forces balance the applied pressure forces. For thin tubes the Newtonian acceleration forces are significant for only a brief moment before steady flow is achieved. 

Particle inertia has been assumed to be substantially smaller than the viscous drag force. This assumption will be valid provided the Reynolds number ppOp/iU/it is sufficiently small, which is more likely to he the case with liq-... 

The diffusion coefficient Di characterizes the mobility of species i in solution, determined by the thermal energy that promotes translational motion and the viscous drag force that opposes that motion. Substituting the expression above into the conservation... 

When there is an energy barrier to aggregation, only a fraction 1/W of encounters lead to attachment. The variable W is the stability ratio, W = k2 /k2- Using W gives slow coagulation (hindered) times. In this case, the interaction energy and hydrodynamic viscous drag forces must be considered (J6). 

Since the constant force acting on the particle results in a constant velocity, there must be an equal and opposite viscous drag force of the liquid acting on the particle with magnitude Cv. The diffusion coefficient D and the friction coefficient C are related through the Einstein relation ... 

Pneumatic nebulization of liquids is based on the viscous drag forces of a gas flow passing over a liquid surface and entraining parts of the liquid, by which small independent droplets are produced. This may occur when the liquid is forced through a capillary tube and at the exit the gas then flows concentrically around the tube or perpendicularly with respect to the liquid stream. A frit can also be used, which is continuously wetted and through which the gas passes. 

Langlois [83], White [169], Clift et al [22] and Zapryanov and Tabakova [174] give further details on the derivation of the viscous drag force on a small spherical droplet. 

Viscous drag force, dyne Hamaker constant, erg Integrals... 

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