Skip to main content

John Bush

Massachusetts Institute of Technology (MIT), Mathematics, Faculty Member

Followers

122

Following

10

Co-authors

10

Public Views

Interests

Uploads

Papers by John Bush

The hydraulic bump: The surface signature of a plunging jet

Physics of Fluids, Sep 1, 2013

When a falling jet of fluid strikes a horizontal fluid layer, a hydraulic jump arises downstream ... more When a falling jet of fluid strikes a horizontal fluid layer, a hydraulic jump arises downstream of the point of impact, provided a critical flow rate is exceeded. We here examine a phenomenon that arises below this jump threshold, a circular deflection of relatively small amplitude on the free surface that we call the hydraulic bump. The form of the circular bump can be simply understood in terms of the underlying vortex structure and its height simply deduced with Bernoulli arguments. As the incoming flux increases, a breaking of axial symmetry leads to polygonal hydraulic bumps. The relation between this polygonal instability and that arising in the hydraulic jump is discussed. The coexistence of hydraulic jumps and bumps can give rise to striking nested structures with polygonal jumps bound within polygonal bumps. The absence of a pronounced surface signature on the hydraulic bump indicates the dominant influence of the subsurface vorticity on its instability.

format_quoteIntroduced Reynolds and Weber numbers to characterize the flow of a plunging jet, enhancing the understanding of fluid dynamics under varied conditions.format_quote

Stability Limit of Electrified Droplets

Physical Review Letters, Jun 17, 2019

In many physical processes, including cloud electrification, electrospray and demulsification, dr... more In many physical processes, including cloud electrification, electrospray and demulsification, droplets and bubbles are exposed to electric fields and may either remain whole or burst in response to electrical stresses. Determining the stability limit of a droplet exposed to an external electric field has been a longstanding mathematical challenge, and the only analytical treatment to date is an approximate calculation for the particular case of a free floating droplet. Here we demonstrate, experimentally and theoretically, that the stability limit of a conducting droplet or bubble exposed to an external electric field is described by a power law with broad generality, that, in practice, applies to the cases in which the droplet or bubble is pinned or sliding on a conducting surface, or free floating. This power law can facilitate the design of devices for liquid manipulation via a simple formula that captures the parameter range of bubbles and droplets that can be supported on electrified surfaces.

Sub-regional Dynamic Topography and Deformation of the Lower Crust by Decoupled Channel Flow in Tibet

AGUFM, Dec 1, 2001

ABSTRACT Deformation of a weak, lower continental crust by decoupled channel flow, in response to... more ABSTRACT Deformation of a weak, lower continental crust by decoupled channel flow, in response to lateral pressure gradients, has been proposed as a mechanism to explain the low-relief but topographically high Tibetan Plateau. By contrast, much of the region surrounding the plateau (the Indian craton and the Tarim and Sichuan Basins) is interpreted as having a much stronger lower crust, where channel flow is essentially absent. The plateau margins adjacent to these strong crustal regions are steep and concave in plan view, as lower crustal material appears to have flowed around these foreland areas of strong crust and into foreland areas of weaker crust. In these places we also observe belts of anomalously high topography relative to the surrounding plateau regions, young and rapid exhumation, and in some localities, extensional geologic structures. Geodynamic models of viscous flow around rigid obstacles in a Hele-Shaw cell simulate high strength heterogenieties within or adjacent to flowing, weak lower continental crust. Results suggest that flow induces differential pressure gradients in the lower crust, which are in turn expressed as dynamic topography at the surface. We suggest that the geologic and geomorphic observations of high topography, rapid exhumation and extensional faulting adjacent to strong foreland regions around the Tibetan Plateau are consistent with dynamic topography produced by lower crustal flow.

Impact and bouncing of a liquid onto an inclined wet surface

Bulletin of the American Physical Society, Nov 22, 2010

Impact and bouncing of a liquid onto an inclined wet surface TRISTAN GILET, JOHN BUSH, MIT -We re... more Impact and bouncing of a liquid onto an inclined wet surface TRISTAN GILET, JOHN BUSH, MIT -We report the results of an experimental investigation of the impact of droplets onto a solid planar surface coated with a thin layer of high viscosity silicon oil. Particular attention is given to deducing criteria for bouncing, and elucidating the energetics of impact. The viscosity, size and impact velocity of the droplet are varied, as well as the inclination of the surface. The motion is recorded with a high speed camera and the energy transfers are measured by image processing. The principle dissipation mechanisms are discussed, and scaling laws proposed for the parameters characterizing the impact (e.g. coefficient of restitution, contact time, slip length). Our results are compared to those reported in previous studies of bouncing.

Beyond Six Feet: A Guideline to Limit Indoor Airborne Transmission of COVID-19

medRxiv (Cold Spring Harbor Laboratory), Sep 1, 2020

The current revival of the world's economy is being predicated on social distancing, specifically... more The current revival of the world's economy is being predicated on social distancing, specifically the Six-Foot Rule, a guideline that offers little protection from pathogen-bearing aerosol droplets sufficiently small to be continuously mixed through an indoor space. The importance of airborne transmission of COVID-19 is now widely recognized. While tools for risk assessment have recently been developed, no safety guideline has been proposed to protect against it. We here build upon models of airborne disease transmission in order to derive an indoor safety guideline that would impose an upper bound on the "cumulative exposure time", the product of the number of occupants and their time in an enclosed space. We demonstrate how this bound depends on the rates of ventilation and air filtration, dimensions of the room, breathing rate, respiratory activity and face-mask use of its occupants, and infectiousness of the respiratory aerosols. By synthesizing available data from the best characterized indoor spreading events with respiratory drop-size distributions, we estimate an infectious dose on the order of ten aerosol-borne virions. The new virus is thus inferred to be an order of magnitude more infectious than its forerunner (SARS-CoV), consistent with the pandemic status achieved by COVID-19. Case studies are presented for classrooms and nursing homes, and a spreadsheet and online app are provided to facilitate use of our guideline. Implications for contact tracing and quarantining are considered, appropriate caveats enumerated. Particular consideration is given to respiratory jets, which may substantially elevate risk when face masks are not worn. C oronavirus disease 2019 (COVID-19) is an infectious pneumonia that appeared in Wuhan, Hubei Province, China in December 2019 and has since caused a global pandemic (1, 2). The pathogen responsible for COVID-19, severeacute-respiratory-syndrome coronavirus 2 (SARS-CoV-2), is known to be transported by respiratory droplets exhaled by an infected person (3-7). There are thought to be three primary routes of human-to-human transmission of COVID-19, large drop transmission from the mouth of an infected person to the mouth, nose or eyes of the recipient, physical contact with droplets deposited on surfaces (fomites) and subsequent transfer to the recipient's respiratory mucosae, and inhalation of the microdroplets ejected by an infected person and held aloft by ambient air currents (6, 8). We subsequently refer to these three modes of transmission as, respectively, 'large-drop', 'contact' and 'airborne' transmission, while noting that the distinction between large-drop and airborne transmission is somewhat nebulous given the continuum of sizes of emitted droplets (9). We here build upon the existing theoretical framework for describing airborne disease transmission in order to characterize the evolution of the concentration of pathogen-laden droplets in a well-mixed room, and the The possibility of pathogen resuspension from contaminated surfaces has also recently been explored (10, 11).

Violent expiratory events: on coughing and sneezing

Journal of Fluid Mechanics, Mar 24, 2014

Violent respiratory events such as coughs and sneezes play a key role in transferring respiratory... more Violent respiratory events such as coughs and sneezes play a key role in transferring respiratory diseases between infectious and susceptible individuals. We present the results of a combined experimental and theoretical investigation of the fluid dynamics of such violent expiratory events. Direct observation of sneezing and coughing events reveals that such flows are multiphase turbulent buoyant clouds with suspended droplets of various sizes. Our observations guide the development of an accompanying theoretical model of pathogen-bearing droplets interacting with a turbulent buoyant momentum puff. We develop in turn discrete and continuous models of droplet fallout from the cloud in order to predict the range of pathogens. According to the discrete fallout model droplets remain suspended in the cloud until their settling speed matches that of the decelerating cloud. A continuous fallout model is developed by adapting models of sedimentation from turbulent fluids. The predictions of our theoretical models are tested against data gathered from a series of analogue experiments in which a particle-laden cloud is ejected into a relatively dense ambient. Our study highlights the importance of the multiphase nature of respiratory clouds, specifically the suspension of the smallest drops by circulation within the cloud, in extending the range of respiratory pathogens.

Non-local features of a hydrodynamic pilot-wave system

Bulletin of the American Physical Society, Nov 21, 2016

Non-local features of a hydrodynamic pilot-wave system ANDRE NACHBIN, IMPA/Brazil, MILES COUCHMAN... more Non-local features of a hydrodynamic pilot-wave system ANDRE NACHBIN, IMPA/Brazil, MILES COUCHMAN, JOHN BUSH, Math. Dept./MIT -A droplet walking on the surface of a vibrating fluid bath constitutes a pilot-wave system of the form envisaged for quantum dynamics by Louis de Broglie: a particle moves in resonance with its guiding wave field. We here present an examination of pilot-wave hydrodynamics in a confined domain. Specifically, we present a onedimensional water wave model that describes droplets walking in single and multiple cavities. The cavities are separated by a submerged barrier, and so allow for the study of tunneling. They also highlight the non-local dynamical features arising due to the spatially-extended wave field. Results from computational simulations are complemented by laboratory experiments.

$Research paper thumbnail of Diffraction and interference of walking drops$

Diffraction and interference of walking drops

Bulletin of the American Physical Society, Nov 21, 2016

MIT, JOHN W. M. BUSH, Department of Mathematics, MIT -A decade ago, Yves Couder and Emmanuel Fort... more MIT, JOHN W. M. BUSH, Department of Mathematics, MIT -A decade ago, Yves Couder and Emmanuel Fort discovered a wave-particle association on the macroscopic scale: a drop can bounce indefinitely on a vibrating bath of the same liquid and can be piloted by the waves that it generates. These walking droplets have been shown to exhibit several quantum-like features, including single-particle diffraction and interference. Recently, the original diffraction and interference experiments of Couder and Fort (Couder, Y. & Fort, E. Phys. Rev. Lett. 97, 154101 (2006)) have been revisited and contested (Andersen, A. et al. Phys. Rev. E 92(1) 013006 ( )). We have revisited this system using an improved experimental set-up, and observed a strong dependence of the behavior on system parameters, including drop size and vibrational forcing. In both the single-and the double-slit geometries, the diffraction pattern is dominated by the interaction of the walking droplet with a planar boundary. Critically, in the double-slit geometry, the walking droplet is influenced by both slits by virtue of its spatially extended wave field.

Drop impact and capture on a thin flexible fiber

Soft Matter, 2016

Viscous sheet retraction

Journal of Fluid Mechanics, May 10, 2009

We present the results of a combined theoretical and numerical investigation of the rim-driven re... more We present the results of a combined theoretical and numerical investigation of the rim-driven retraction of flat fluid sheets in both planar and circular geometries. Particular attention is given to the influence of the fluid viscosity on the evolution of the sheet and its bounding rim. In both geometries, after a transient that depends on the sheet viscosity and geometry, the film edge eventually attains the Taylor-Culick speed predicted on the basis of inviscid theory. The emergence of this result in the viscous limit is rationalized by consideration of both momentum and energy arguments. We first consider the planar geometry considered by Brenner & Gueyffier (Phys. Fluids, vol. 11, 1999, p. 737) and deduce new analytical expressions for the speed of the film edge at the onset of rupture and the evolution of the maximum film thickness for viscous films. In order to consider the expansion of a circular hole, we develop an appropriate lubrication model that predicts the form of the early stage dynamics of film rupture. Simulations of a broad range of flow parameters confirm the importance of geometry on the dynamics, verifying the exponential hole growth reported in early experimental studies. We demonstrate the sensitivity of the initial retraction speed on the film profile, and so suggest that the anomalous rate of retraction reported in these experiments may be attributed in part to geometric details of the puncture process.

format_quoteNovel results show PDMS films with viscosity 1 million times that of water can exhibit significant differences in retraction dynamics.format_quote

Visualization of sneeze ejecta: steps of fluid fragmentation leading to respiratory droplets

Experiments in Fluids, Jan 20, 2016

Natural drinking strategies

Journal of Fluid Mechanics, Apr 17, 2012

We examine the fluid mechanics of drinking in nature. We classify the drinking strategies of a br... more We examine the fluid mechanics of drinking in nature. We classify the drinking strategies of a broad range of creatures according to the principal forces involved, and present physical pictures for each style. Simple scaling arguments are developed and tested against existing data. While suction is the most common drinking strategy, various alternative styles have evolved among creatures whose morphological, physiological and environmental constraints preclude it. Particular attention is given to creatures small relative to the capillary length, whose drinking styles rely on relatively subtle interfacial effects. We also discuss attempts to rationalize various drinking strategies through consideration of constrained optimization problems. Some biomimetic applications are discussed.

The water entry of decelerating spheres

Physics of Fluids, Mar 1, 2010

We present the results of a combined experimental and theoretical investigation of the vertical i... more We present the results of a combined experimental and theoretical investigation of the vertical impact of low-density spheres on a water surface. Particular attention is given to characterizing the sphere dynamics and the influence of its deceleration on the shape of the resulting air cavity. A theoretical model is developed which yields simple expressions for the pinch-off time and depth, as well as the volume of air entrained by the sphere. Theoretical predictions compare favorably with our experimental observations, and allow us to rationalize the form of water-entry cavities resulting from the impact of buoyant and nearly buoyant spheres.

format_quoteSpheres of various densities were used to study impact dynamics; coatings enhanced cavity formation efficiency.format_quote

Polygonal instabilities on interfacial vorticities

European Physical Journal E, Oct 1, 2015

We report the results of a theoretical investigation of the stability of a toroidal vortex bound ... more We report the results of a theoretical investigation of the stability of a toroidal vortex bound by an interface. Two distinct instability mechanisms are identified that rely on, respectively, surface tension and fluid inertia, either of which may prompt the transformation from a circular to a polygonal torus. Our results are discussed in the context of three experiments, a toroidal vortex ring, the hydraulic jump, and the hydraulic bump.

format_quotePolygonal instabilities arise in hydraulic jumps due to parameter dependence; critical radius impacts the number of polygonal sides formed.format_quote

The Tibetan Singing Bowl

arXiv (Cornell University), Oct 15, 2010

The Tibetan singing bowl is a type of standing bell. Originating from Himalayan fire cults as ear... more The Tibetan singing bowl is a type of standing bell. Originating from Himalayan fire cults as early as the 5th century BC, they have since been used in religious ceremonies, for shamanic journeying, exorcism, meditation and shakra adjustment. A singing bowl is played by striking or rubbing its rim with a wooden or leather-wrapped mallet. The sides and rim of the bowl then vibrate to produce a rich sound. When the bowl is filled with water, this excitation can cause crispation of the water surface that can be followed by more complicated surface wave patterns and ultimately the creation of droplets. We here demonstrate the means by which the Tibetan singing bowl can levitate droplets. This is a sample arXiv article illustrating the use of fluid dynamics videos.

Hydrodynamic quantum analogues: droplets walking on the impossible pilot wave

Bulletin of the American Physical Society, Nov 19, 2012

Hydrodynamic quantum analogues: droplets walking on the impossible pilot wave 1 JOHN BUSH, Depart... more Hydrodynamic quantum analogues: droplets walking on the impossible pilot wave 1 JOHN BUSH, Department of Mathematics, MIT -Yves Couder and coworkers have demonstrated that droplets walking on a vibrating fluid bath exhibit several features previously thought to be peculiar to the microscopic quantum realm. We explore the connection between this hydrodynamic system and the pilot-wave theory of quantum mechanics proposed by de Broglie and extended by workers in the field of stochastic electrodynamics. Critical common features of these ostensibly disparate systems are identified, and quantitative differences noted. 1 The author thanks the NSF.

Pilot-wave dynamics in a harmonic potential: Quantization and stability of circular orbits

Physical review, Mar 23, 2016

format_quoteOrbital radius increases with memory parameter, transitioning to quantized orbits as memory effects dominate in harmonic potentials.format_quote

The pilot-wave dynamics of walking droplets

Physics of Fluids, Sep 1, 2013

Bell test in a classical pilot-wave system

arXiv (Cornell University), Aug 18, 2022

Since its discovery in 2005, the hydrodynamic pilot-wave system has provided a concrete macroscop... more Since its discovery in 2005, the hydrodynamic pilot-wave system has provided a concrete macroscopic realization of wave-particle duality and concomitant classical analogs of a growing list of quantum effects. The question naturally arises as to whether this system might support statistical states that violate Bell's inequality, and so yield a classical analog of quantum entanglement. We here introduce a new platform for addressing this question, a numerical model of coupled bipartite tunneling in the hydrodynamic pilot-wave system. We demonstrate that, under certain conditions, the Bell inequality is violated in a static Bell test owing to correlations induced by the wave-mediated coupling between the two subsystems. The establishment of non-factorizable states with two spatially separated classical particles introduces the possibility of novel forms of quantum-inspired classical computing. Significance Millimeter-scale droplets self-propelling along the surface of a vibrating liquid bath represent a macroscopic realization of wave-particle duality, an oddity once thought to be exclusive to the microscopic realm. This classical pilot-wave system bears a strong resemblance to an early model of quantum dynamics proposed by Louis de Broglie, and has provided the basis for a surprising number of hydrodynamic quantum analogs. We here take the first step towards assessing the plausibility of achieving entanglement with this hydrodynamic system. Our numerical investigation of the dynamics of two distant droplets reveals violations of Bell's inequality that may be rationalized in terms of the wave-induced coupling between them. The resulting non-factorizable, spatially separated classical states may find application in quantum-inspired classical computing.

Regulating flow with substrate shape in capillary micropumps

Bulletin of the American Physical Society, Nov 22, 2010

Regulating flow with substrate shape in capillary micropumps MATTHEW HANCOCK, Brigham & Women's H... more Regulating flow with substrate shape in capillary micropumps MATTHEW HANCOCK, Brigham & Women's Hospital, JOHN BUSH, MIT -Capillarity offers a passive mechanism to pump fluid through portable lab-on-a-chip systems, making them ideal for rapid in situ analysis of medical samples in the developing world. A common capillary micropump design is powered by the difference in curvature pressures between drops at the inlet and outlet of a microchannel. The resulting flow rate is transient, depending on the geometry of the inlet cavity and the instantaneous droplet volumes. We here present a class of microcavity shapes that maintain constant pressure within droplets regardless of their volumes. This special class of microcavities may prove useful for regulating pressure in microfluidic devices. We suggest the design of a passive capillary micropump fitted with a special pressure regulating inlet cavity that forces a constant flux through a microchannel. The influence of gravity on this class of microcavities is considered.