Teapot effect

The teapot effect, also known as dribbling, is a fluid dynamics phenomenon that occurs when a liquid being poured from a container runs down the spout or the body of the vessel instead of flowing out in an arc.^[1]

Diagram of tea running down the spout of a teapot

Markus Reiner coined the term "teapot effect" in 1956 to describe the tendency of liquid to dribble down the side of a vessel while pouring.^[2][3] Reiner received his PhD at TU Wien in 1913 and made significant contributions to the development of the study of flow behavior known as rheology.^[1] Reiner believed the teapot effect could be explained by Bernoulli's principle, which states that an increase in the speed of a fluid is always accompanied by a decrease in its pressure. When tea is poured from a teapot, the liquid's speed increases as it flows through the narrowing spout. This decrease in pressure was what Reiner thought to cause the liquid to dribble down the side of the pot.^[4][3] However, a 2021 study found the primary cause of the phenomenon to be an interaction of inertia and capillary forces.^[3] The study found that the smaller the angle between the container wall and the liquid surface, the more the teapot effect is slowed down.^[5]

Research

Around 1950, researchers from the Technion Institute in Haifa (Israel) and from New York University tried to explain this effect scientifically.^[6] In fact, there are two phenomena that contribute to this effect: on the one hand, the Bernoulli equation is used to explain it, on the other hand, the adhesion between the liquid and the spout material is also important.

According to the Bernoulli explanation, the liquid is pressed against the inner edge of the spout when pouring out, because the pressure conditions at the end, the edge, change significantly; the surrounding air pressure pushes the liquid towards the spout. With the help of a suitable pot geometry (or a sufficiently high pouring speed) it can be avoided that the liquid reaches the spout and thus triggers the teapot effect. Laws of hydrodynamics (flow theory) describe this situation, the relevant ones are explained in the following sections.

Since adhesion also plays a role, the material of the spout or the type of liquid (water, alcohol or oil, for example) is also relevant for the occurrence of the teapot effect.

The Coandă effect is sometimes mentioned in this context,^{[7][8][9][10]} but it is rarely cited in the scientific literature^[8] and is therefore not precisely defined. Often several different phenomena seem to be mixed up in this one.

Continuity equation

In hydrodynamics, the behavior of flowing liquids is illustrated by flow lines. They run in the same direction as the flow itself. If the outflowing liquid hits an edge, the flow is compressed into a smaller cross-section. It only does not break off if the flow rate of liquid particles remains constant, regardless of where an imaginary cross section (perpendicular to the flow) is located. So the same amount of mass must flow in through one cross-sectional area as flows out of another. One can now conclude from this, but also observe in reality, that the flow accelerates at bottlenecks and the streamlines are bundled. This situation describes the continuity equation for non-turbulent flows.

Bernoulli equation

But what happens to the pressure conditions in the flow if you change the flow speed? The scientist Daniel Bernoulli dealt with this question as early as the beginning of the 18th century. Based on the considerations of continuity mentioned above, and incorporating the conservation of energy, he linked the two quantities of pressure and speed. The core statement of the Bernoulli equation is that the pressure in a liquid falls where the velocity increases (and vice versa): Flow according to Bernoulli and Venturi.

Impact

The pressure in the flow is reduced at the edge of the can spout. However, since the air pressure on the outside of the flow is the same everywhere, there is a pressure difference that pushes the liquid to the edge. Depending on the materials used, the outside of the spout is now wetted during the flow process. At this point, additional interfacial forces occur : the liquid runs as a narrow trickle along the spout and can until it detaches from the underside.

The unwanted teapot effect only occurs when pouring slowly and carefully.^[6] In fast pouring, the liquid flows out of the spout in an arc without dripping, so it is given a relatively high velocity with which the liquid moves away from the edge (see Torricelli outflow velocity). The pressure difference resulting from the Bernoulli equation is then not sufficient to influence the flow to such an extent that the liquid is pushed around the edge of the spout.

Since the flow conditions can be described mathematically, a critical outflow velocity is also defined. If it falls below when pouring, the liquid flows down the pot; it drips. Theoretically, this speed could be precisely calculated for a specific can geometry, the current air pressure and the fill level of the can, the spout material, the viscosity of the liquid and the pouring angle. Since, apart from the fill level, most of the influencing variables cannot be changed (at least not sufficiently precisely in practice), the only way to avoid the teapot effect is usually to choose a suitable geometry for the pot.

Another phenomenon is the reduction in air pressure between the spout and the jet of liquid due to the entrainment of gas molecules (one-sided water jet pumping effect), so that the air pressure on the opposite side would push the jet of liquid to the spout side. However, under the conditions usually prevailing when pouring tea, this effect will hardly appear.

Consequence

 

Pot examples

A good jug should, regardless of fashion, have a spout with a tear-off edge (i.e. no rounded edge) to make it more difficult to run around the edge. And – even more important - after the edge, the spout should first lead upwards (regardless of the position in which the jug is held). As a result, the liquid would be forced to flow upwards after going around the edge of the spout when pouring, but this is prevented by gravity. The flow can thus resist wetting even when pouring slowly and the liquid does not reach the downwardly inclined part of the spout and the body of the jug.

The image on the right^{[clarification needed]} shows three vessels with poor pouring behavior. Even in a horizontal position, that is standing on the table, the bottom edges of the spouts do not point upwards.^[6] Behind are four vessels with good flow characteristics resulting from well formed tips. Here, the liquid rises at the lower edge of the spout at an angle of less than 45°.^[6] In part, this only becomes apparent when one considers the normal maximum fill level: the glass carafe on the far right, for example, appears at first glance to be a poor pourer because of its slender neck. However, since such vessels are generally filled at most up to the edge of the round part of the flask, an advantageous rise at the neck is then obtained when pouring horizontally.Upward angle for the liquid when pouring. With the two lower jugs on the right, the high position of the spout (above the maximum filling level) means that the vessel has to be tilted quite a bit before pouring, so that the spout can also be pushed up directly after the edge (against gravity). indicates.

To avoid the teapot effect, the pot can be filled less, so that a larger tilting angle is necessary from the start. However, the effect or the ideal filling level again depends on the can geometry.

The teapot effect does not occur with bottles because the slender neck of the bottle always points upwards when pouring; the current would therefore have to "flow uphill" a long way.^[6] Bottle-like containers are therefore often used for liquid chemicals in the laboratory. Certain materials are also used there to prevent dripping, for example glass, which can be easily shaped or even ground to create the sharpest possible edges, or Teflon, for example, which reduces the adhesion effect described above.

Drip catcher

See also

• Adhesion
• Coandă effect
• Stall (fluid dynamics)
• Spout (teapot) [de]

References

1. "Why Teapots Always Drip – Scientists Finally Explain the "Teapot Effect"". SciTechDaily. Vienna University of Technology. 2022-01-09. from the original on 2023-01-28. Retrieved 2022-07-02.
2. Reiner, Markus (September 1956). "The teapot effect...a problem". Physics Today. 9 (9). American Institute of Physics: 16. doi:10.1063/1.3060089. Retrieved 2023-01-28. (1 page)
3. Ouellette, Jennifer (2021-11-10). "Dribble, dribble, dribble — Physicists say they've finally solved the teapot effect—for real this time - Is due to interplay of inertial viscous capillary forces—but gravity's less relevant". Ars Technica. from the original on 2023-01-28. Retrieved 2022-07-02.
4. Keller, Joseph Bishop (1957). "Teapot Effect" (PDF). Journal of Applied Physics. 28 (8): 859–864. Bibcode:1957JAP....28..859K. doi:10.1063/1.1722875. (PDF) from the original on 2022-03-13. Retrieved 2023-01-28. (6 pages)
5. Scheichl, Bernhard; Bowles, Robert I.; Pasias, Georgios (2021-11-10) [2021-09-08, 2021-07-01, 2021-05-17, 2020-11-09]. "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. Cambridge University Press: A25-1–A25-40, S1–S12. arXiv:2011.12168. Bibcode:2021JFM...926A..25S. doi:10.1017/jfm.2021.612. ISSN 0022-1120. S2CID 235444365. from the original on 2023-01-28. Retrieved 2023-01-28. (40+12 pages)
6. Dittmar-Ilgen, Hannelore (2007) [2006, 2004]. "Immer Ärger mit tröpfelnden Kannen". Wie der Kork-Krümel ans Weinglas kommt - Physik für Genießer und Entdecker (in German) (1 ed.). Stuttgart, Germany: S. Hirzel Verlag [de]. pp. 21–25. ISBN 978-3-7776-1440-3. ISBN 978-3-7776-1440-3. (172+4 pages)
7. Reba, Imants (June 1966). "Applications of the Coanda Effect". Scientific American. Vol. 214, no. 6. pp. 84–92. Bibcode:1966SciAm.214f..84R. doi:10.1038/scientificamerican0666-84. JSTOR 24930967. Retrieved 2023-01-28. (9 pages)
8. Reiner, Markus (May 1967). "Teapot means Coanda". Letters. Physics Today. 20 (5). American Institute of Physics: 15. Bibcode:1967PhT....20e..15R. doi:10.1063/1.3034300. Retrieved 2023-01-28. (1 page)
9. Reiner, Markus (1969). Deformation, Strain and Flow - An Elementary Introduction To Rheology (3 ed.). H. K. Lewis & Co. Ltd. ISBN 0-71860162-9. (347 pages)
10. Ziegler, Alfred; Wodzinski, Ruth (2001) [2000, 1999]. "Die Physik des Fliegens als Bestandteil eines Unterrichts zur Strömungslehre: Zielsetzungen und Begründungen". Vorträge / Physikertagung, Deutsche Physikalische Gesellschaft, Fachausschuss Didaktik der Physik (Book, CD) (in German). Arbeitsgruppe Didaktik der Physik, Universität Kassel. pp. 549–552. from the original on 2023-01-29. Retrieved 2023-01-29. Coanda-Effekt (bzw. "Kaffeekanneneffekt"-ein Tropfen folgt der Oberfläche) (NB. Calls the effect "coffeepot effect" rather than "teapot effect".)

Further reading

• "Tropfenfangrinne an der Innenseite der Ausgussschnauze von Gefaessen, insbesondere Kannen fuer Kaffee, Tee usw." (in German). 1928. German patent DE457585C. from the original on 2023-01-29. Retrieved 2023-01-29.
• "Non-drip spouts for coffee and like pots with a spout opening directed downwardly". 1938 [1936]. GB patent 477613. from the original on 2023-01-29. Retrieved 2023-01-29., Alcock, Lindley & Bloore Ltd, ,
• Sakowski, Christian (2023). "Melitta Kaffeekannen No. 301 u. 304, D.R.P. für 1 1/2 und 4 Tassen". Mein Sammlerportal & sampor.de (in German). Berlin, Germany. from the original on 2023-01-29. Retrieved 2023-01-29. (NB. Picture shows the anti-drip groove and pinhole underneath the spout of Melitta coffee pots (protected by D.R.P. [de] patents) model No. 301 for 1½ cups and model No. 304 for 4 cups, presumably manufactured in the 1920s or 1930s.)
• Walker, Jearl Dalton (1984-10-01). "The troublesome teapot effect, or why a poured liquid clings to the container". Scientific American. Vol. 251, no. 10. pp. 144–152. (9 pages)
• Vanden-Broeck, Jean-Marc; Keller, Joseph Bishop (1986-05-19) [1986-09-12]. "Pouring Flows". Physics of Fluids. 29 (12): 3958–3961. Bibcode:1986PhFl...29.3958V. doi:10.1063/1.865735. (4 pages)
• Vanden-Broeck, Jean-Marc; Keller, Joseph Bishop (1989) [1988-06-27, 1988-09-19]. "Pouring flows with separation". Physics of Fluids A: Fluid Dynamics. 1 (1): 156–158. Bibcode:1989PhFlA...1..156V. doi:10.1063/1.857542. (3 pages)
• Kistler, Stephan F.; Scriven, Laurence Edward (1994-04-26) [1990-02-05, 1991-04-03]. "The teapot effect: sheet-forming flows with deflection, wetting and hysteresis". Journal of Fluid Mechanics. 263. Cambridge University Press: 19–62. Bibcode:1994JFM...263...19K. doi:10.1017/S0022112094004027. S2CID 123277240. (44 pages)
• Träger, Susanne (1996). "Die nichttropfende Schnaupe". In Siemen, Wilhelm [in German] (ed.). In 80 Tassen um die Welt: Gastlichkeit und Porzellan - Ein Beitrag zur Geschichte des Porzellans für die Gastronomie vom Ende des 19. Jahrhunderts bis in Gegenwart. Schriften und Kataloge des Deutschen Porzellanmuseums (DPM) (in German). Vol. 46 (1 ed.). Hohenberg an der Eger, Germany: Deutsches Porzellanmuseum / Druckhaus Münch GmbH, Selb, Germany. p. 27. ISBN 3-927793-45-0. p. 27: Eine tropfende Schnaupe ist nicht nur bei den Kannen, die in der Gastronomie eingesetzt werden, ein Ärgernis. Was an funktionalen Mängeln im Haushaltsgebrauch noch toleriert werden kann, ist in der Gastronomie ein ernsthaftes Problem. Verschmutzte Tischtücher und vertropfte Untertassen sind kein Aushängeschild für ein gut geführtes Café. Nach dem Ausgiessen sollte keine Flüssigkeit mehr an der Außenwand der Kanne entlanglaufen und kein Tropfen an der Tülle hängen bleiben. Es gab einige absonderlich wirkende Versuche, Flüssigkeit am Ablaufen zu hindern. So sollten beispielsweise ablaufende Tropfen durch Rillen in der Kannenwandung aufgehalten werden. Bereits 1929 führte die Porzellanfabrik Weiden [de] Gebr. Bauscher [de] Kannen mit einer nichttropfenden Schnaupe ein. Infolge einer Bohrung durch den Ausguß und einer dünnen Rille auf der Innenseite der Tülle strömt die Flüssigkeit nach dem Aufrichten der Kanne durch Kapillarkraft zurück. Die Herstellung eines Tropfenfangs mit einer Bohrung ist heute produktionstechnisch zu aufwendig. Viele Versuche und Testreihen waren und sind nötig, um den idealen Neigungswinkel von Ausgüssen zu finden, damit die Flüssigkeit beim Aufrichten des Gefäßes ohne zu tropfen in die Schnaupe zurückläuft. (1+2+186+2 pages) (NB. The print run of this publication is limited to 1000 pieces.)
• Hesselberth, John (January–February 1997). "How to Make Drip-Free Spouts". Clay Times. from the original on 2023-01-28. Retrieved 2023-01-29.
• "A groovy kind of pot". Sci/Tech. BBC News. 1998-12-08. from the original on 2023-01-29. Retrieved 2023-01-29.
• Seißer, Peter [in German]; Zehentmeier, Sabine; Meyer, Rudolf; Siemen, Wilhelm [in German]; Symossek, Ronja (1999). "Sortimentumstellung". In Siemen, Wilhelm [in German] (ed.). "Mit der Zeit gehen" - 100 Jahre Porzellanfabrik Walküre (1899–1999) - Ein mittelständiges Industrieunternehmen im Wandel ["Going with the times" - 100th anniversary of porcelain manufacturer Walküre (1899–1999) - A medium-sized industrial company in transition]. Schriften und Kataloge des Deutschen Porzellanmuseums (DPM) (in German). Vol. 58 (1 ed.). Hohenberg an der Eger, Germany: Deutsches Porzellanmuseum. pp. 101–105 [105]. ISBN 3-927793-57-4. p. 105: […] Das Interesse der "Porzellanfabrik Walküre" richtete sich dabei weniger auf das schmucklose Erscheinungsbild eines Porzellangegenstandes, sondern vielmehr auf den wortwörtlich verstandenen funktionalen Nutzen. Ausdruck dieses Bestrebens ist neben der bereits zum Standard gewordenen Deckelhalterung nun auch die nichttropfende Schnaupe. Das Problem des Tropfens ist für den Gastronomiesektor aufgrund verschmutzter Tischdecken natürlich ein besonderes Ärgernis. Unzählige Testreihen bringen verschiedene Lösungen^[A] hervor, von denen die Rille in der Kannenwandung, wie sie das Geschirr der Porzellanfabrik Walküre aufweist, sich als zuverlässig erweist und dementsprechend patentiert wird. Der Stolz dieser Erfindung wird auch nach außen hin sichtbar, indem man den speziell damit versehenen Servicen ein P, wie Patent, hinzufügte. […] Werbeblatt, Gastronomiegeschirr, Kannenmodell 604P. "P" kennzeichnet die Patentierung für die nichttropfende Schnaupe. […] (1+195+1 pages) (NB. The print run of this publication is limited to 1000 pieces. The corresponding patent is D.R.P. [de] 476417.)
• "Ig Nobel Prize Winners". Improbable Research. 2023 [2012, 1999]. from the original on 2023-01-28. SPECIAL ANNOUNCEMENT: We are now, in 2012, correcting an error we made in the year 1999, when we failed to include one winner's name. We now correct that, awarding a share of the 1999 physics prize to Joseph Keller. Professor Keller is also a co-winner of the 2012 Ig Nobel physics prize, making him a two-time Ig Nobel winner. […] The corrected citation is:1999 PHYSICS PRIZE: Len Fisher [UK and Australia] for calculating the optimal way to dunk a biscuit, and Jean-Marc Vanden-Broeck [UK and Belgium] and Joseph Keller [USA], for calculating how to make a teapot spout that does not drip.
• Bolton, David (Fall 2007). "Functional Teapot Options & Rules of Thumb" (PDF). CLC Ceramics. (PDF) from the original on 2023-01-28. Retrieved 2023-01-29. (2 pages)
• Dillon, Frank (2009-05-11). "The pot of gold - Design & Invention: It is a problem that has confounded scientists for generations". Department. Irish Times. from the original on 2023-01-29. Retrieved 2023-01-29.
• "How to stop a teapot dribbling". Physics Today. American Institute of Physics. 2009-10-28. doi:10.1063/PT.5.023796. from the original on 2023-01-29. Retrieved 2023-01-28 – via The Daily Telegraph.
• Duez, Cyril; Ybert, Christophe [at Wikidata]; Clanet, Christophe; Bocquet, Lydéric [in French] (2010-02-26) [2009-10-17]. "Wetting controls separation of inertial flows from solid surfaces". Physical Review Letters. 104 (8). American Physical Society: 084503. arXiv:0910.3306v1. Bibcode:2010PhRvL.104h4503D. doi:10.1103/PhysRevLett.104.084503. PMID 20366936. S2CID 118601911. 084503. Retrieved 2023-01-29.
• Mugele, Frieder G. (2010). "Was tun wenn die Teekanne tropft? Benetzungseigenschaften auf mikroskopischer Skala bestimmen das makroskopische Strömungsverhalten". Brennpunkt. Physik Journal (in German). 9 (6). Weinheim, Germany: Wiley-VCH Verlag GmbH & Co. KGaA: 18–19. from the original on 2023-01-28. Retrieved 2023-01-28. (2 pages)
• Lossau, Norbert (2010-06-22). "Wie man tropfende Teekannen in den Griff bekommt". Wissenschaft. Die Welt (in German). from the original on 2023-01-28. Retrieved 2023-01-28.
• "Ever Wonder About the Teapot Effect?". Science World. ASTC Science World Society. 2015-10-18. from the original on 2023-01-28. Retrieved 2023-01-28.
• Robert (2017-02-03). "Why Do Teapots Dribble?". Trivia. guernseyDonkey.com. from the original on 2022-09-25. Retrieved 2023-01-28.
• Ouellette, Jennifer (2019-05-17). "I'm a little teapot — Dribble no more: Physics can help combat that pesky "teapot effect" - Dutch scientists devised a model to predict flow rate when dribbling will occur". Ars Technica. from the original on 2023-01-29. Retrieved 2022-07-02.
• Gagné, Jonathan [at Wikidata] (2020). "6. Kettles and Agitation - 6.1. The Teapot Effect". In Zimmer, Jean (ed.). The Physics of Filter Coffee (1 ed.). Scott Rao. pp. 127–144 [127–128]. ISBN 978-0-578-24608-6. (xvi+249+3 pages)
• "Flüssigkeitenmechanik - Wiener Forscher erklärt, warum Tee aus der Kanne danebengeht - Wenn ein Flüssigkeitsstrahl nicht trifft, sondern am Behälter entlangfließt, heißt das Teekanneneffekt. Nun gibt es eine detaillierte Erklärung dafür". Der Standard (in Austrian German). Vienna, Austria: STANDARD Verlagsgesellschaft m.b.H. 2021-11-08. Retrieved 2023-01-28 – via Austria Presse Agentur.
• Mihai, Andrei (2021-12-01). "The maths behind the annoying teapot effect — and how to prevent it". SciLogs - Heidelberg Laureate Forum. Heidelberg, Germany: Spektrum der Wissenschaft Verlagsgesellschaft mbH. from the original on 2023-01-28. Retrieved 2023-01-28.
• Jones, David (2022). "Pours for thought? [The teapot effect: theory and practice]". Jones the Pots. from the original on 2023-01-28. Retrieved 2023-01-28.
• Hinze, Betsy (2023). "Teapot Cheat Sheet". from the original on 2024-01-29. Retrieved 2024-01-29.
• https://feldlilie.wordpress.com/2012/01/19/physikfrage-12485521/
• https://www.stevenabbott.co.uk/practical-coatings/Teapot.php
• https://thiru.de/pages/teekanne-tropft
• https://www.kalkspatzforum.de/viewtopic.php?t=2417
• https://teehaus-bachfischer.de/tropfenfaenger-fuer-teekannen, https://sterntee.de/navi.php?a=15902 drop catcher