On the response of neutrally stable flows to oscillatory forcing with application to liquid sheets

Industrial coating processes create thin liquid films with tight thickness tolerances, and thus models that predict the response to inevitable disturbances are essential. The mathematical modeling complexities are reduced through linearization as even small thickness variations in films can render a product unsalable. The signaling problem, considered in this paper, is perhaps the simplest model that incorporates the effects of repetitive (oscillatory) disturbances that are initiated, for example, by room vibrations and pump drives. In prior work, Gordillo and P\'erez (Phys. Fluids 14, 2002) examined the structure of the signaling response for linear operators that admit exponentially growing or damped solutions, i.e., the medium is classified as unstable or stable via classical stability analysis. The signaling problem admits two portions of the solution, the transient behavior due to the start-up of the disturbance and the long-time behavior that is continually forced; the superposition reveals how the forced solution evolves through the passage of a transient. In this paper, we examine signaling for the linear operator examined by King et al. (King et al. 2016, Phys. Rev. Fluids 1(7)) that governs varicose waves in a thin liquid sheet and that can admit solutions having algebraic growth although the underlying medium is classified as being neutrally stable. Long-time asymptotic methods are used to extract critical velocities that partition the response into distinct regions having markedly different location-dependent responses, and the amplitudes of oscillatory responses in these regions are determined. Together, these characterize the magnitude and breadth of the solution response. Results indicate that the signaling response in neutrally stable flows (that admit algebraic growth) is significantly different from that in exponentially unstable systems

The Effect of Pressure Fluctuations on the Shapes of Thinning Liquid Curtains

We consider the time-dependent response of a gravitationally thinning inviscid liquid sheet (a coating curtain) leaving a vertical slot to sinusoidal ambient pressure disturbances. The theoretical investigation employs the hyperbolic partial differential equation developed by Weinstein et al. (Phys. Fluids, vol. 9, issue 12, 1997, pp. 3625–3636). The response of the curtain is characterized by the slot Weber number, We0=ρqV/2σ role= presentation style= box-sizing: border-box; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline-table; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative; \u3eWe0=ρqV/2σWe0=ρqV/2σ, where V role= presentation style= box-sizing: border-box; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline-table; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative; \u3eVV is the speed of the curtain at the slot, q role= presentation style= box-sizing: border-box; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline-table; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative; \u3eqq is the volumetric flow rate per unit width, σ role= presentation style= box-sizing: border-box; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline-table; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative; \u3eσσ is the surface tension and ρ role= presentation style= box-sizing: border-box; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline-table; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative; \u3eρρ is the fluid density. Flow disturbances travel along characteristics with speeds relative to the curtain of ±uV/We0 role= presentation style= box-sizing: border-box; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline-table; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative; \u3e±uV/We0−−−−−−−√±uV/We0, where u=V2+2gx role= presentation style= box-sizing: border-box; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline-table; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative; \u3eu=V2+2gx−−−−−−−−√u=V2+2gx is the curtain speed at a distance x role= presentation style= box-sizing: border-box; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline-table; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative; \u3exx downstream from the slot. Here g is the acceleration of gravity. When the flow is subcritical (We0We0\u3c1We0We0We0. In contrast, all disturbances travel downstream in supercritical curtains (We0\u3e1 role= presentation style= box-sizing: border-box; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline-table; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative; \u3eWe0\u3e1We0\u3e1) and the slope of the curtain at the slot is vertical. Here, we specifically examine the curtain response under supercritical and subcritical flow conditions near We0=1 role= presentation style= box-sizing: border-box; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline-table; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative; \u3eWe0=1We0=1 to deduce whether there is a substantial change in the overall shape and magnitude of the curtain responses. Despite the local differences in the curtain solution near the slot, we find that subcritical and supercritical curtains have similar responses for all imposed sinusoidal frequencies

Communications Biophysics

Contains research objectives, summary of six research projects and reports on three research projects.National Institutes of Health (Grant 2 P01 MH-04737-06)Joint Services Electronics Programs (U. S. Army, U.S. Navy, and U.S. Air Force) under Contract DA 36-039-AMC-03200(E)National Science Foundation (Grant GK-835)National Aeronautics and Space Administration (Grant NsG-496)National Institutes of Health (Grant 5 ROI NB-05462-03

Communication: Analytic continuation of the virial series through the critical point using parametric approximants

The mathematical structure imposed by the thermodynamic critical point motivates an approximant that synthesizes two theoretically sound equations of state: the parametric and the virial. The former is constructed to describe the critical region, incorporating all scaling laws; the latter is an expansion about zero density, developed from molecular considerations. The approximant is shown to yield an equation of state capable of accurately describing properties over a large portion of the thermodynamic parameter space, far greater than that covered by each treatment alone

Improved Standardization of Type II-P Supernovae: Application to an Expanded Sample

In the epoch of precise and accurate cosmology, cross-confirmation using a variety of cosmographic methods is paramount to circumvent systematic uncertainties. Owing to progenitor histories and explosion physics differing from those of Type Ia SNe (SNe Ia), Type II-plateau supernovae (SNe II-P) are unlikely to be affected by evolution in the same way. Based on a new analysis of 17 SNe II-P, and on an improved methodology, we find that SNe II-P are good standardizable candles, almost comparable to SNe Ia. We derive a tight Hubble diagram with a dispersion of 10% in distance, using the simple correlation between luminosity and photospheric velocity introduced by Hamuy & Pinto 2002. We show that the descendent method of Nugent et al. 2006 can be further simplified and that the correction for dust extinction has low statistical impact. We find that our SN sample favors, on average, a very steep dust law with total to selective extinction R_V<2. Such an extinction law has been recently inferred for many SNe Ia. Our results indicate that a distance measurement can be obtained with a single spectrum of a SN II-P during the plateau phase combined with sparse photometric measurements.Comment: ApJ accepted version. Minor change

Communication Biophysics

Contains reports on five research projects.National Institutes of Health (Grant 5 RO1 NB-05462-02)National Aeronautics and Space Administration (Grant NsG-496)National Science Foundation (Grant GP-2495)National Institutes of Health (Grant MH-04737-05