Erratum: Marangoni Shocks in Unobstructed Soap-Film Flows [Phys. Rev. Lett.103, 104501 (2009)]

Abstract

In the Letter we refer to the point x ? , where the derivative of the velocity of the flow becomes singular, as the ''theoretical position of the shock.'' Note, however, that for consistency with our simple model of the flow [Eq.(2)] the theoretical position of the shock should be computed using the Rayleigh jump condition, which can be found in note 13 of the Letter. (We thank François Blanchette and Morris R. Flynn for bringing this point to our attention.) Although the Rayleigh jump condition places the shock slightly downstream of x ? , the interpretation of the experiments does not depend on the exact position of the shock, and remains valid as it appears in the Letter.

Marangoni elasticity of flowing soap films

“…The valve opening is calibrated to F by directly collecting the solution per unit time and weighing them, and it gives the measurement of F up to 5% of uncertainty. We work in a section of the soap film where the thickness does not vary with downstream distance, far from any "hydraulic jump" that can form near the end of the channel [24]. The flow speed u of the channel is determined by particle tracking using high speed imaging (Photron SA4).…”

“…4 shows the estimated range of Ma for these studies, which indicates that for the vast majority of the cases the flow is clearly of a compressible nature. One study [24] recognized the compressible nature of the flow and used the Marangoni shock to estimate the compressibility, while the others do not attempt to measure the compressible character of the flow. Our method presents a non-intrusive and low cost method for estimating the Marangoni Mach number in situ for a complete characterization of flowing soap films in future investigations.…”

“…It is desirable to monitor v M given that it may change with the operational parameters of the soap film and that it could be comparable to the typical velocity scale of the simulated 2D flows. Indeed, based on separate measurements of v M (246 to 362 cm/s [23]) and the typical flow speeds (150 to 250 cm/s [10], 100 to 400 cm/s [24] or 270 to 600 cm/s [25]), the soap film flows may not be assumed to be incompressible.…”

Scaling of Near-Wall Flows in Quasi-Two-Dimensional Turbulent Channels

“…This approach neglects two factors: the frictional drag between the falling film and surrounding air, and the Marangoni stresses due to soap molecules [27][28][29]. How these factors affect the near-wall MVPs in soap-film channels remains an open question.…”

Janus Spectra in Two-Dimensional Flows

“…To interrogate the turbulent flow we turn to Laser Doppler Velocimetry (LDV). We use LDV to measure the time-series of u and v along the centerline of the channel, downstream of the rods and well upstream (> 15w) of the Marangoni shock [16]. Using Taylor's hypothesis [17] we transform this time-series data to spatial data in the streamwise direction, from which we compute E uu (k x ) and E vv (k x ).…”