# gst: predict the wetting of the wedge; why do the teapots always drip?

<<  The "teapot effect" has been threatening spotless white tablecloths for ages: if a liquid is poured out of a teapot too slowly, then the flow of liquid sometimes does not detach itself from the teapot, finding its way into the cup, but dribbles down at the outside of the teapot. >>

<< This phenomenon has been studied scientifically for decades—now a research team at TU Wien has succeeded in describing the "teapot effect" completely and in detail with an elaborate theoretical analysis and numerous experiments: An interplay of different forces keeps a tiny amount of liquid directly at the edge, and this is sufficient to redirect the flow of liquid under certain conditions. >>

<< Although this is a very common and seemingly simple effect, it is remarkably difficult to explain it exactly within the framework of fluid mechanics,  (..) We have now succeeded for the first time in providing a complete theoretical explanation of why this drop forms and why the underside of the edge always remains wetted, >>  Bernhard Scheichl.

<< The sharp edge on the underside of the teapot beak plays the most important role: a drop forms, the area directly below the edge always remains wet. The size of this drop depends on the speed at which the liquid flows out of the teapot. If the speed is lower than a critical threshold, this drop can direct the entire flow around the edge and dribbles down on the outside wall of the teapot. >>

<< The mathematics behind it is complicated—it is an interplay of inertia, viscous and capillary forces. The inertial force ensures that the fluid tends to maintain its original direction, while the capillary forces slow the fluid down right at the beak. The interaction of these forces is the basis of the teapot effect. However, the capillary forces ensure that the effect only starts at a very specific contact angle between the wall and the liquid surface. The smaller this angle is or the more hydrophilic (i.e. wettable) the material of the teapot is, the more the detachment of the liquid from the teapot is slowed down. >>

<< Interestingly, the strength of gravity in relation to the other forces that occur does not play a decisive role. Gravity merely determines the direction in which the jet is directed, but its strength is not decisive for the teapot effect. The teapot effect would therefore also be observed when drinking tea on a moon base, but not on a space station with no gravity at all. >>️

Why teapots always drip. Vienna University of Technology. Nov 08, 2021

https://phys.org/news/2021-11-teapots.html

Scheichl, B., Bowles, R., & Pasias, G. (2021). Developed liquid film passing a smoothed and wedge-shaped trailing edge: Small-scale analysis and the ‘teapot effect’ at large Reynolds numbers. Journal of Fluid Mechanics, 926, A25. doi: 10.1017/jfm.2021.612. Sep 8, 2021. 

http://dx.doi.org/10.1017/jfm.2021.612

keywords: gst, teapot effect, interfacial flows, thin films, boundary layers, Reynolds number, viscosity, viscous–inviscid interaction 

# gst: apropos of oscillations, viscous streaming around an immersed microfeature (e.g. a bubble)

<< Viscous streaming refers to the rectified, steady flows that emerge when a liquid oscillates around an immersed microfeature, typically a solid body or a bubble. The ability of such features to locally concentrate stresses produces strong inertial effects to which both fluid and immersed particles respond within short length (O(100) microns) and time (milliseconds) scales, rendering viscous streaming arguably the most efficient mechanism to exploit inertia at the microscale. >>️

(AA) << demonstrate that a multi-curvature approach in viscous streaming dramatically extends the range of accessible flow topologies. (They) show that numerically predicted, but never experimentally observed, streaming flows can be physically reproduced, computationally engineered, and in turn used to enhance particle manipulation, filtering and separation in compact, robust, tunable and inexpensive devices. >>️

Yashraj Bhosale, Giridar Vishwanathan, et al. Multi-curvature viscous streaming: flow topology and particle manipulation. arXiv: 2111.07184v1 [physics.flu-dyn]. Nov 13, 2021.

https://arxiv.org/abs/2111.07184

keywords: gst, viscosity, viscous streaming, bubble, oscillations, liquid oscillations, flanking vortex, particle manipulation 

# gst: apropos of Cake-cutting, the Art of dividing a cake by countably many cuts

<< Cake-cutting is a playful name for the fair division of a heterogeneous, divisible good among agents, a well-studied problem at the intersection of mathematics, economics, and artificial intelligence. The cake-cutting literature is rich and edifying. However, different model assumptions are made in its many papers, in particular regarding the set of allowed pieces of cake that are to be distributed among the agents and regarding the agents' valuation functions by which they measure these pieces. >>️

A simple example proposed by AA  <<  shows that a formal mathematical approach to cake-cutting needs to address questions like:

(o) Are (open, closed, half-open) intervals the only possible pieces of cake? 

(o) Do we allow for finitely many or infinitely many cuts (a “cut” being the split of any subset of [0,1] at a single point)? 

(o) Which properties should a valuation function have, and how does it interact with the family of admissible pieces of cake?  >>

<< Among the questions (AA) have tried to answer are: 

(i) Which subsets of [0,1] should be considered as pieces of cake? Only finite unions of intervals or more general sets? 

(ii) If valuation functions are considered as set-functions as studied in measure theory, should they be σ-additive or only finitely additive? 

(iii) more ...

>>️

️

AA << have surveyed the existing rich literature on cake-cutting algorithms and have identified the most commonly used choices of sets consisting of what is allowed as pieces of cake. After showing that these five most commonly used sets are distinct from each other, (they) have discussed them in comparison. >>️

Peter Kern, Daniel Neugebauer, et al. Cutting a Cake Is Not Always a "Piece of Cake": A Closer Look at the Foundations of Cake-Cutting Through the Lens of Measure Theory. arXiv: 2111.05402v1 [cs.GT]. Nov 9, 2021. 

https://arxiv.org/abs/2111.05402

keywords: gst, cake, cake-cutting, math.

# gst: a screw mechanism to separate realistic racemic mixtures by local vorticity

AA developed << an explanatory "screw"  model for predicting the shear-flow separation of enantiomers >>

<< Enantiomers of chiral molecules are non-superposable mirror images with the same structural formula. In achiral environments, enantiomers have identical physical and chemical properties, and this prevents separation by classical methods. >>

<< A screw is a simple chiral object that couples rotation around one axis with displacement along that axis. This displacement is perpendicular to the plane of rotation and is characterized by the screw’s pitch (or lead). Here (it is defined) pitch (P) as the perpendicular distance advanced by a screw in a 2π-revolution. In a lab-fixed frame, left-and right-handed screws have pitches with the same magnitude, but with flipped signs, rotating in opposite directions to do the same task. This concept can be easily extended to chiral molecules by considering the translation-rotation coupling tensor (..). In a medium which induces rotation of molecules (as in a vortex flow), chiral molecules will translate in opposite directions. As a consequence, this asymmetry may enable the resolution of the enantiomers. >>

Thus  a << competition model and continuum drift diffusion equations are developed to predict separation of realistic racemic mixtures. (..) Additionally, (AA) find that certain achiral objects can also exhibit a non-zero molecular pitch. >>

<< Although it has been used << shear flow as the source to rotate the chiral molecules and achieve separation, it may be possible to use external forces to rotate the enantiomers >>️

️

Duraes A, Gezelter JD. Separation of Enantiomers through Local Vorticity: A Screw Model Mechanism. ChemRxiv. Cambridge: Cambridge Open Engage; Vers 1. doi: 10.33774/ chemrxiv-2021-196zw. Oct 04, 2021. 

https://chemrxiv.org/engage/chemrxiv/article-details/61575a0d46030a1245c52107  

keywords: gst, vortices, separation, enantiomeric separation, racemic mixture, screw mechanism, translation-rotation coupling, transitions.

# geo: apropos of oscillations, a 'true polar wander' (TPW); Earth tip on its side 84 Ma ago.

<< It has been debated for the past few decades whether the outer, solid shell of the Earth can wobble about, or even tip over relative to the spin axis. Such a shift of Earth is called "true polar wander," (TPW) but the evidence for this process has been contentious. New research (..) provides some of the most convincing evidence to date that such planetary tipping has indeed occurred in Earth's past. >>️

<< The Earth is a stratified ball, with a solid metal inner core, a liquid metal outer core, and a solid mantle and overriding crust at the surface which we live on. All of this is spinning like a top, once per day. Because the Earth's outer core is liquid, the solid mantle and crust are able to slide around on top of it.  >>

️

Did the Earth tip on its side 84 million years ago? Tokyo Institute of Technology. Oct 18, 2021. 

https://phys.org/news/2021-10-earth-side-million-years.html

<< a new high-resolution palaeomagnetic record from two overlapping stratigraphic sections in Italy (..) provides evidence for a ~12° TPW oscillation from 86 to 78 Ma. This observation represents the most recent large-scale TPW documented and challenges the notion that the spin axis has been largely stable over the past 100 million years. >>️

Mitchell, R.N., Thissen, C.J.,  et al. A Late Cretaceous true polar wander oscillation. Nat Commun 12, 3629. doi: 10.1038/ s41467-021-23803-8. June 15, 2021. 

https://www.nature.com/articles/s41467-021-23803-8

keywords: gst, geo, geodynamics, geophysics, palaeomagnetism, oscillations, wobble, true polar wander, tpw

# gst: apropos of transitions, perspectives on viscoelastic flow instabilities; the 'porous individualism'

<< given the observation that disorder can suppress the transition to elastic turbulence in 2D porous media (..), it has been unclear whether and how this transition manifests in disordered 3D media — though elastic turbulence has been speculated to underlie the long-standing observation that the macroscopic flow resistance of an injected polymer solution can abruptly increase above a threshold flow rate in a porous medium, but not in bulk solution >>️

AA << found that the transition to unstable flow in each pore is continuous, arising due to the increased persistence of discrete bursts of instability above a critical value of the characteristic (Weissenberg no.) Wi; however, the onset value varies from pore to pore. This observation that single pores exposed to the same macroscopic flow rate become unstable in different ways provides a fascinating pore-scale analog of “molecular individualism” [P.  De Gennes, Molecular individualism. Science 276, 1999–2000 (1997)], in which single polymers exposed to the same extensional flow elongate in different ways; the authors therefore termed it “porous individualism”, although it is important to note that here, this effect is still at the continuum (not molecular) scale. Thus, unstable flow is spatially heterogeneous across the different pores of the medium, with unstable and laminar regions coexisting >>

AA << quantitatively established that the energy dissipated by unstable pore-scale fluctuations generates an anomalous increase in flow resistance through the entire medium that agrees well with macroscopic pressure drop measurements. >>

Sujit S. Datta, Arezoo M. Ardekani, et al. Perspectives on viscoelastic flow instabilities and elastic turbulence. arXiv: 2108.09841v1 [physics.flu-dyn]. Aug 22, 2021. 

https://arxiv.org/abs/2108.09841

Also

keyword 'transition' | 'transitional' in FonT

https://flashontrack.blogspot.com/search?q=transition

https://flashontrack.blogspot.com/search?q=transitional

keyword 'transition' | 'transizion*' in Notes (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=transition

https://inkpi.blogspot.com/search?q=transizione

https://inkpi.blogspot.com/search?q=transizioni

keywords: gst, droplet, fluctuations, disorder, instability, viscoelastic flow instability, turbulence, elastic turbulence, individualism, porous individualism, transition

# gst: the effect of noise on the dynamics of microswimmers in externally-driven fluid flows.

AA << have quantified the effect of noise on swimmer dynamics in a steady, two-dimensional hyperbolic fluid flow. In such a flow, swimmers are ultimately forced to escape to the left or the right, with their transient dynamics near the passive unstable fixed point determining which way they go. >>

<< Without noise, a swimmer’s fate is sealed based on its position relative to the SwIM (swimming invariant manifolds) in the xθ phase space. With noise, the swimmer’s motion is a stochastic process. >>

AA << calculated the steady-state orientation distributions of diffusive, run-and-tumble, or mixed swimmers in the hyperbolic flow. The fluctuations give some swimmers greater opportunity to cross the SwIM and exit on the opposite side than they would have without noise. There is however a maximal distance that swimmers can get on either side of the passive fixed point and still be able to swim back to the other side—this is where the stable BIMs (burning invariant manifolds) block inward swimming particles. >>

<< Fluctuations make it increasingly likely that a swimmer close to one of these BIMs does indeed end up crossing it, causing irreversible changes to the fluctuating swimmers’ trajectories (assuming negligible translational diffusion).  >>️

Simon A. Berman, Kevin A. Mitchell. Swimmer dynamics in externally-driven fluid flows: The role of noise. arXiv: 2108.10488v1 [physics.flu-dyn]. Aug 24, 2021.

https://arxiv.org/abs/2108.10488

keywords: gst, swimmer, swimming particle, fluid dynamics, chaotic dynamics, rotational diffusion, random fluctuation, tumbling, noise