A well producing primarily gas with a small amount of liquid, which could be oil, water or sometimes a mixture of both, is likely to have an annular flow regime, with the liquid phase forming a thin annulus on the inside wall of the pipe and the gas flowing in the form of a central core.
Truth be told, along most of the track, the eclipse appears as a total, with a very thin annulus (or ring) of sunlight visible near the very beginning of the track.
By successive applications of this transformation, the root is isolated to lie within a thin concentric annulus of width η ⪡ 1 centered at the origin.
Bird et al. [4] presented an asymptotic solution and arbitrary values of the flow behavior index for the power-law fluid in a very thin annulus.
Of course the correlation spectra measured in real V1 maps are not concentrated on an infinitely thin annulus (for precise measurements, see Schnabel [31], p. 103).
Of course this is very close to (varLambda_{mathrm{mean}}) when the support of the power spectrum is contained in a thin enough annulus (if the width of such an annulus is less than a fifth of its radius, (varLambda _{mathrm{mean}}) and (varLambda_{mathrm{sq}}) are within 3%% of each other).
To explore this, we used a model based on the wrinkling of a thin circular annulus (represented by the hierarchical mineralized structure) supported by elastic foundations (represented by the underlying ELR matrix 56.
In this figure, a fouling oil layer is shown to surround a thin water annulus that lubricates the oil-rich core.
Since it is also difficult to observe the stress distribution inside the thin-walled annulus of the casing or the cement sheath, the annuluses are extended as a rectangle in accordance with radius and azimuth angle, as shown in Fig. 15.
When a thin film of titanium oxide was located on the outer surface of a quartz glass tube, which was set to protect the germicidal lamp from direct contact with an aqueous solution flowing through the annulus, i.e., when the photocatalyst was located at the inner surface of the annulus, the sterilization and decomposition slowed down.
