Stokes quasi-steady

Fig. 8. The ratio of the drag force to the weight of an a-pinene droplet with initial diameter 29.8 /tm evaporating in nitrogen at 293 K. The solid line is the prediction based on Stokes law for the drag force on a sphere, assuming a quasi-steady process.

Our next approximation considers the transport process as quasi-steady state. This implies that the characteristic diffusion and conduction times, P/D and Pcc /K (in which I is a characteristic length), are much smaller than the characteristic time appropriate for relative fall. A very conservative characteristic time would be that required for a drop to fall a distance of one diameter, i.e., by using Stoke s law ... 

These also result even if the motion is unsteady, providing that ajxV and the other dimensionless terms remain finite in the limit R = 0 Equations (7) and (8) are then referred to as the quasi-static or quasi-steady Stokes equations. In this case the time variable enters the equations of motion only in an implicit form. The precise relationship between the solutions of Eqs. (7) and (8) and the asymptotic solutions of the Navier-Stokes equations at small Reynolds numbers is discussed in Section III. 

In this section we treat the steady and quasi-steady motions of rigid, three-dimensional particles in a fluid at rest at infinity on the basis of Stokes... 

Complete characterization of the hydrodynamic resistance of a solid particle in quasi-steady Stokes motion generally requires knowledge of 21... 

The dyadic resistance coefficients derive from the quasi-steady Stokes equations as follows Let be the intrinsic solutions of the dyadic... 

Following the approach of Chouly and co-workers (1), a simplified three-dimensional flow configuration representing the pharyngeal airway is illustrated in Fig. 1 with the tongue idealised as a pressurised shell. With Strouhal Numbers in the order of 10 (5), the flow is considered quasi-steady and is characterised by the standard continuity and Navier-Stokes equation. For laminar conditions, these reads ... 

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