Decay length viscous

Like the viscous entrainment of liquid by the surface, the electrical entrainment of ions decays exponentially with distance from the solid/liquid interface. Since the electric field has a decay length of A/2ir, however, ion coupling extends several micrometers into the liquid. Ion, dipole, and induced-dipole motion resulting from this acoustoelectric coupling lead to a perturbation in plate mode velocity and attenuation. 

Example 3.15 Calculate the viscous decay length and the value of M, for a 100-micron-wavelength, 5 MHz FPW device of Example 3.50 that contacts water on one side (the viscosity of water, if, is one centipoise = 10 Pa-s). 

Solution The viscous decay length is 250 nm, which is much smaller than the evanescent decay length 16 microns, from Example 3.55). The value of is 1.3 x 10 kg/m ... 

As mentioned in Sect. 2.2 the decay length of the shear wave into a viscous medium in contact wiht the resonator can be estimated from Eq. 1. If a 5 MHz resonator, as used in our studies, is loaded with pure water at room temperature, the characteristic axial decay length of the shear displacement amoimts... 

This equation shows that vorticity is a maximum at the moving wall (which acts a source of vorticity) and decays exponentially on a length scale 0(l/Re) by the action of viscous forces. Thus for Rey 1 the flow is effectively irrotational. In this respect the problem is atypical as we normally expect vorticity to decay on a diffusive length scale of 0( / J Re) (cf. oscillatory Couette flow). The reason for this difference is that in the present probiem we have a balance between convective inertia and viscous forces as opposed to a balance between transient inertia and viscous forces. 

The distribution of a decaying scalar field advected by a turbulent flow was studied by Corrsin (1961) who generalized the Obukhov-Corrsin theory of passive scalar turbulence for the linear decay problem F(C) = S(x) — bC. As in the case of the passive non-decaying scalar field, depending on the length scales considered, one can identify inertial-convective and viscous-convective regimes with qualitatively different characteristics. 

It is known that a viscoelastic fluid, e.g., a solution with a trace amount of highly deformable polymers, can lead to elastic flow instability at Reynolds number well below the transition number (Re 2,000) for turbulence flow. Such chaotic flow behavior has been referred to as elastic turbulence by Tordella [2]. Indeed, the proper characterization of viscoelastic flows requires an additional nondimensional parameter, namely, the Deborah number, De, which is the ratio of elastic to viscous forces. Viscoelastic fluids, which are non-Newtonian fluids, have a complex internal microstructure which can lead to counterintuitive flow and stress responses. The properties of these complex fluids can be varied through the length scales and timescales of the associated flows [3]. Typically the elastic stress, by shear and/or elongational strains, experienced by these fluids will not immediately become zero with the cessation of fluid motion and driving forces, but will decay with a characteristic time due to its elasticity. 

Fig. 22.5 Dimensionless breakup lengths of liquid threads plotted against the gas-Weber number for two dimensionless flow rates and viscosities. With increasing gas relative velocity, the breakup length decreases. Higher viscous threads show minor decay of breakup length compared to threads with lower viscosity. Increasing flow rate expressed by F leads to longer threads. Test liquids are glycerol water mixtures [33]...

If the liquid substrate is thick, the only characteristic length in the substrate is the drop radius R and the velocity decays over a length R. The viscous stress is of the order of... 

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