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Crookes radiometer

The Crookes radiometer, also known as a light mill, is a scientific device consisting of an airtight glass bulb partially evacuated to a low pressure of approximately 1 Pa, containing a low-friction spindle supporting a lightweight rotor with four to eight thin vanes, each coated black on one side (typically with soot) and reflective or white on the other.^[1]^[2] When exposed to light, the rotor spins continuously, with the black sides trailing and moving away from the light source, converting radiant energy into mechanical rotation at speeds proportional to light intensity.^[3]^[1] Invented by British chemist and physicist Sir William Crookes in 1873 during his investigations into the effects of light on precise chemical measurements involving thallium, the radiometer was first publicly described in his 1874 paper "On Attraction and Repulsion Resulting from Radiation," published in the Philosophical Transactions of the Royal Society.^[1]^[2] Crookes initially attributed the motion to radiation pressure from photons, a hypothesis that sparked intense scientific debate in the late 19th century, as it seemed to challenge prevailing views on the nature of light and heat.^[2] However, subsequent analyses, including those by Osborne Reynolds in 1879, established that the phenomenon arises not from direct photon momentum but from thermal effects in the residual gas: the black surface absorbs light and heats up more than the reflective side, creating a temperature gradient that drives gas molecules to rebound with higher velocity from the hotter surface, imparting greater momentum and causing the vane to move.^[3]^[1] This radiometric force, or thermal transpiration, is most pronounced at low pressures where the mean free path of gas molecules approaches the vane dimensions, and it diminishes in high vacuum or atmospheric pressure.^[2]^[3] The device's historical significance lies in its role as an early tool for studying radiation and vacuum phenomena, influencing developments in vacuum technology and inspiring later inventions like the Crookes tube for cathode ray experiments.^[2] Patented by Crookes in 1876, it became a popular demonstration apparatus in physics education and museums, exemplifying principles of thermodynamics and gas kinetics while highlighting the interplay between light, heat, and molecular motion.^[1] Modern variants continue to illustrate these concepts, though the core design remains unchanged since the 19th century.^[3]

Description

Components and Assembly

The Crookes radiometer is constructed with an airtight glass bulb that houses a partial vacuum, typically maintained at a pressure of approximately 1 Pa (about 0.01 torr or 0.0075 mmHg), achieved through evacuation using a pump such as the Sprengel pump in historical designs.^[4]^[5] The bulb, often spherical or pear-shaped with a diameter of around 70-100 mm and height up to 210 mm, is sealed after assembly to preserve the low-pressure environment essential for the device's function.^[6] In original constructions by William Crookes, the glass was selected from types like soft German glass or uranium glass for optical clarity and vacuum integrity.^[7] At the center of the bulb is a low-friction pivot or spindle, typically a thin glass rod or wire supporting a rotating assembly, with the pivot point formed by a needle resting in a hard steel cup to minimize friction.^[7] Mounted radially on this spindle are 4 to 8 lightweight vanes, usually square or diamond-shaped and measuring about 1-2 cm on each side, made from thin sheets of mica or aluminum leaf for their low mass and rigidity.^[2]^[5] One surface of each vane is blackened with an absorbent material such as lampblack, soot, or India ink to maximize light absorption, while the opposite surface is left polished, silvered, or naturally reflective to enhance light reflection.^[7]^[4] Assembly involves attaching the vanes to radial arms—often of aluminum—forming a winged cross or fly that is balanced on the central pivot and connected via sealed wires (platinum or aluminum) to external terminals if needed for experimentation.^[7] The entire rotating system is then placed inside the glass bulb, which is evacuated to the desired pressure and hermetically sealed, often using sealing wax or fusion techniques to ensure airtightness and allow free rotation with minimal resistance.^[6] Historical versions by Crookes incorporated materials like ivory or bone for supportive elements, emphasizing durability under vacuum conditions.^[8]

Observed Rotation Effect

When illuminated by light, the vanes of a Crookes radiometer rotate such that the black, absorbing surfaces trail behind the reflective surfaces, moving away from the light source.^[9]^[10] This directional motion is consistent across typical setups with asymmetrically coated vanes, one side blackened for absorption and the other polished for reflection.^[9] The rotation activates under exposure to electromagnetic radiation in the visible or infrared spectrum, requiring a minimum light intensity on the order of 1 mW/cm² for observable motion, though brighter sources accelerate the effect.^[11] The device responds proportionally to light intensity, with rotation ceasing below threshold levels or in darkness, but resuming promptly upon re-illumination.^[10] Under standard sunlight conditions, the radiometer achieves rotational speeds of 1-10 revolutions per second, varying with vane dimensions, ambient temperature, and incident light strength—for instance, a focused flashlight yields about 2 revolutions per second, while intense sources can exceed 20 revolutions per second.^[10] Optimal performance occurs in a partial vacuum at pressures around 1-10 Pa, where rotation is brisk; at higher atmospheric pressures, motion slows due to viscous drag, and in complete high vacuum below 10^{-3} Pa, no rotation occurs as residual gas is insufficient.^[12] Uniformly colored vanes produce no net rotation, emphasizing the role of surface asymmetry.^[9] The effect is readily demonstrated qualitatively using sunlight or a strong incandescent lamp, where the contactless spinning surprised early observers like William Crookes, who noted the vanes' indefinite motion under illumination without mechanical input.^[10]

History

Invention by William Crookes

William Crookes (1832–1919), an English chemist and physicist renowned for his spectroscopic discoveries, invented the Crookes radiometer in 1873 as a byproduct of precise quantitative experiments on the element thallium, which he had identified in 1861.^[2] While determining the atomic weight of thallium using a highly sensitive vacuum balance in his laboratory, Crookes observed that radiant heat from an incandescent lamp caused the balance arm to deflect upward, making the heated body appear lighter than its cold counterpart even in a near-perfect vacuum.^[13] This unexpected repulsion effect, noted initially in his June 1872 paper to the Royal Society on thallium's atomic weight, motivated him to develop a device capable of detecting and quantifying such interactions between radiant energy and matter in low-pressure environments.^[13] In his private laboratory at his home on Mornington Road in London, Crookes constructed initial prototypes by suspending lightweight vanes—typically made of mica with one side blackened and the other polished—on a fine pivot within a partially evacuated glass bulb, refining the design through iterative testing to amplify the rotational response to radiation.^[14] These experiments built directly on his 1873 investigations, culminating in a detailed description of the device's construction and behavior in his paper "On Attraction and Repulsion Resulting from Radiation," received by the Royal Society on August 12, 1873, and read on December 11, 1873.^[13] Crookes first publicly demonstrated the radiometer at the Royal Society's soirée on April 22, 1874, where the device's vanes rotated visibly under lamplight, captivating attendees and marking a pivotal moment in his research trajectory. The invention occurred amid Crookes' pioneering work on high-vacuum technology and "radiant matter," where he adapted and improved upon Geissler tubes—sealed glass discharge tubes developed in the 1850s that enabled visualization of electrical phenomena in rarefied gases—to achieve pressures as low as 10^{-6} atmospheres for studying cathode rays and molecular trajectories.^[15] Inspired by these tools, Crookes aimed to create an instrument sensitive enough to measure subtle forces from radiant energy, bridging his chemical analyses with emerging insights into gaseous dynamics and light propagation in vacua.^[14] Crookes' personal interests further shaped his pursuits in light-matter interactions; his early studies on phosphorescence, beginning in the 1850s with selenium compounds, had already drawn him to luminescence and energy absorption, while his growing fascination with spiritualism—sparked in the late 1860s after his brother's death and intensified through investigations of mediums like Florence Cook from 1871 to 1874—fueled a broader curiosity about invisible forces and ethereal phenomena that paralleled his radiometer research.^[16]

Early Recognition and Naming

Following its invention, the Crookes radiometer garnered significant scientific and public interest through demonstrations by William Crookes. He first publicly demonstrated the device at the Royal Society's soirée on April 22, 1874. A further presentation occurred at a meeting of the Royal Society on April 7, 1875, where its novel rotation under light exposure astonished attendees and prompted widespread discussion.^[17] The instrument was subsequently exhibited at the Special Loan Collection of Scientific Apparatus in South Kensington in 1876, further amplifying its visibility to both experts and the general public.^[18] The device was patented by Crookes in 1876. Crookes coined the term "radiometer" for the device in his 1874 paper, deriving it from the Latin radius to denote its perceived function in detecting and quantifying radiant energy, particularly from light and heat sources.^[13] This nomenclature reflected his initial belief that the motion resulted from radiation pressure, a concept inspired by Maxwell's electromagnetic theory. Over time, the full name "Crookes radiometer" became standard in scientific literature, while the colloquial term "light mill" emerged to describe its spinning vanes.^[19] The radiometer received early acclaim from leading figures in physics, including Lord Kelvin, who hailed it as a "grand discovery" in his popular lectures, emphasizing its potential to illuminate fundamental interactions between light and matter. It featured prominently in contemporary journals, such as Nature, with articles in 1874 and 1875 detailing Crookes' experiments and their implications for radiant phenomena. However, the device also ignited controversies, as scientists debated whether its rotation truly demonstrated radiation pressure or involved other mechanisms, such as residual gas effects in the partial vacuum—disputes that persisted through the late 1870s and challenged Crookes' interpretation.^[19] By the 1880s, commercial production of radiometers proliferated, with versions manufactured in England and Germany for educational use in schools and laboratories to illustrate principles of light and vacuum dynamics.^[20] Crookes' meticulous work on achieving high vacuums for the device—employing improved mercury pumps and exhaustion techniques—additionally advanced 19th-century vacuum technology, influencing applications in spectroscopy and early electric lighting.^[21]

Theoretical Developments

Initial Incorrect Theories

In 1874, William Crookes proposed that the rotation of the radiometer resulted from direct radiation pressure exerted by light photons, with the reflective surfaces of the vanes experiencing greater repulsion than the light-absorbing black surfaces due to the doubled momentum transfer upon reflection.^[22] This hypothesis drew support from observations of natural phenomena, such as the orientation of comet tails pointing away from the Sun and the apparent repulsion in stellar atmospheres, both attributed to solar radiation pressure.^[23] Furthermore, Crookes' idea aligned with James Clerk Maxwell's electromagnetic theory of light from 1873, which theoretically predicted the existence of such pressure from light's momentum.^[24] Early evidence against pure radiation pressure emerged from the observed direction of rotation, which was opposite to expectations: the vanes spin with the black sides trailing and moving away from the light source, rather than the black sides leading the motion as predicted by greater push on the reflective side.^[9] Additional disproof came from the device's performance in partial vacuums around 1 Pa, where rotation is maximal but the mean free path of residual gas molecules exceeds the vane spacing, rendering direct photon momentum transfer insufficient to overcome mechanical friction—yet the device fails entirely in higher vacuums where gas effects are minimized.^[24] Other initial suggestions, including electrostatic attractions between charged vanes or magnetic influences from light, were quickly ruled out through experiments substituting various non-conductive and non-magnetic materials, which produced no change in rotational behavior.^[25] These erroneous theories lingered into the 1880s, largely because contemporary vacuum technology could not achieve the high vacuums needed to isolate light pressure effects from residual gas interactions.^[26]

Partially Correct Explanations

In the late 19th century, intermediate theories began to recognize the thermal nature of the radiometer's motion while still falling short of a complete description. James Clerk Maxwell proposed in 1879 that the absorption of light by the black surfaces of the vanes generates heat, leading to convection currents in the residual gas within the bulb that propel the vanes. This idea marked a shift from purely mechanical explanations to ones involving gas dynamics driven by temperature gradients. Building on this, Osborne Reynolds introduced the concept of "radiometric streaming" in 1879, positing that gas molecules in contact with the hotter black side of a vane acquire higher thermal velocities upon rebounding, creating a net streaming force away from the heated surface and causing rotation. Reynolds' model emphasized the role of molecular interactions in rarefied gases under temperature differences.^[25] These explanations were partially accurate in identifying the essential temperature disparities across the vanes, where the black side becomes approximately 10–20 °C hotter than the reflective side due to differential light absorption.^[27] They also correctly highlighted the necessity of residual gas, as experiments varying the internal pressure demonstrated optimal rotation speeds around 1 Pa, with negligible motion at higher pressures (where viscous drag dominates) or in high vacuum (where insufficient molecules are present).^[12] Supporting evidence included tests with uniform heating applied to both sides of the vanes, which significantly reduced or halted rotation, confirming that localized temperature gradients are crucial for the effect. Nevertheless, these models had key limitations: they inadequately accounted for edge effects along the vane boundaries, where much of the force actually originates, and struggled to explain sustained motion in pressure regimes too low for significant bulk convection. Such gaps prompted refinements in 20th-century investigations that integrated molecular kinetic theory more fully.

Currently Accepted Theory

The currently accepted theory explains the rotation of the Crookes radiometer through the radiometric force generated by thermal transpiration, or thermal creep, resulting from the temperature gradient across the vanes within the rarefied gas.^[28] This effect occurs because the partial vacuum inside the device creates conditions where gas molecules interact asymmetrically with the heated black surfaces and cooler reflective surfaces of the vanes.^[29] In this environment, the mean free path of gas molecules is approximately 5 mm, comparable to the vane dimensions, enabling molecules rebounding from the hot black side to carry higher average kinetic energy and velocity than those from the cool side.^[29] The net force arises primarily at the vane edges, where the thermal gradient drives a tangential flow of gas from the cold to the hot side, imparting momentum that propels the black (hot) side backward, consistent with the observed rotation direction.^[28] This edge-dominated mechanism was rigorously formalized by Albert Einstein in 1924, who derived the force in terms of molecular agitation analogous to Brownian motion, emphasizing the role of pressure differences over narrow boundary layers near the edges.^[30] Radiation pressure, involving photon momentum transfer, contributes negligibly to the motion, as the momentum per photon is on the order of $10^{-27} N s and the total radiation force is orders of magnitude smaller than the thermal radiometric forces, which can reach micro-Newton scales under typical operating conditions.^[31] Experimental validations, including pressure-dependent torque measurements and simulations, confirm that thermal effects dominate, with the approximate force scaling as F \approx \frac{P}{2} \left( \frac{\Delta T}{T} \right) A, where P is gas pressure, \Delta T the temperature difference, T the ambient temperature, and A the effective vane area.^[32]

Thermodynamic Principles

Temperature Gradients and Gas Interactions

The black side of each vane in a Crookes radiometer absorbs nearly all of the incident radiation due to its dark coating, while the reflective side rejects most of it, establishing a pronounced temperature gradient across the vane.^[33] Under illumination from a bright source such as sunlight, the black side heats to approximately 30°C, whereas the reflective side remains close to ambient conditions around 20°C, resulting in a differential of about 9–10 K.^[33] This asymmetry arises from the radiative heating process, where absorbed photons convert to thermal energy primarily on the blackened surface. The partial vacuum inside the bulb, maintained at pressures around 1–10 Pa, places the system in the Knudsen regime of rarefied gas dynamics. In this regime, the mean free path of air molecules λ is approximately 0.7–7 mm, exceeding the vane thickness or inter-vane gap of about 0.01–0.1 mm, such that molecules undergo ballistic trajectories with few collisions among themselves and primarily interact with the vane surfaces. The velocity distribution of these molecules follows the Maxwell-Boltzmann distribution, given by f(v) \propto v^2 \exp\left(-\frac{m v^2}{2 k T}\right), where m is the molecular mass, k is Boltzmann's constant, and T is the local temperature. Molecules desorbing from the hot black side acquire higher thermal velocities, with the most probable speed v_\text{hot} \approx \sqrt{\frac{2 k T_\text{hot}}{m}}, compared to those from the cooler reflective side. Conversely, the cool side receives these faster-moving molecules from the hot side, leading to asymmetric momentum exchanges during collisions. This disparity drives the thermal creep effect, wherein a net mass flux of gas occurs from the cold side to the hot side along the vane edges, induced by the tangential temperature gradient parallel to the surfaces. The resulting pressure imbalance, higher on the hot side, stems from this directed flow in the rarefied environment. The total radiometric force includes contributions from thermal creep at the edges and the Einstein radiometric effect on the vane faces.^[34] The average difference in momentum transfer per collision, Δp, can be approximated as \Delta p \approx \frac{1}{2} \rho v_\text{th} \frac{\Delta T}{T}, where ρ is the gas density, v_\text{th} is the thermal velocity, and ΔT/T quantifies the relative temperature difference. This formulation captures the kinetic imbalance without requiring detailed collision integrals, highlighting how the temperature gradient modulates the net force through altered molecular kinetics.

Radiometric Force on Vanes

The radiometric force arises primarily from interactions at the edges of the vanes, where a temperature gradient established across each vane leads to asymmetric gas flow. The uniform pressure exerted by gas molecules on the opposing faces of a vane cancels out, resulting in no net translational force from the central regions. Instead, the net force and resulting torque stem from thermal transpiration effects at the edges, where gas molecules exhibit a preferential flow from the cooler to the hotter side, generating a reaction force on the vane directed from hot to cold.^[34]^[35] The magnitude of this edge-dominated force can be approximated using kinetic theory as F = \frac{\eta}{2} \left( \frac{\Delta T}{T} \right) \nabla T \times perimeter, where \eta is the gas viscosity, \Delta T is the temperature difference across the vane, T is the average temperature, and \nabla T is the temperature gradient. This expression derives from the thermal creep velocity in rarefied gases, scaled by the momentum transfer along the vane perimeter. For the narrow gaps typical in Crookes radiometers (on the order of 0.5 mm between vanes), a simplified form accounts for the aspect ratio: F \approx \frac{P \Delta T}{2T} \times \frac{l}{h}, where P is the gas pressure, l is the vane length, and h is the inter-vane gap width; this highlights how the force increases with pressure and the geometric ratio l/h.^[34]^[36]^[35] The torque \tau on each vane is then given by \tau = \mathbf{r} \times \mathbf{F}, where \mathbf{r} is the position vector from the rotation axis to the vane center (typically the rotor radius, around 1–2 cm). At steady state, this torque balances the viscous drag on the rotating assembly, yielding an angular speed \omega \approx \frac{\tau}{ \frac{8\pi \eta r^3}{3} }, where the denominator represents the rotational drag torque in the rarefied gas regime, analogous to Stokes' law for a low-Reynolds-number rotor.^[35]^[37] The direction of the force confirms the observed rotation: on the black (hotter) side of a vane, gas molecules depart with higher thermal velocity and thus impart greater backward momentum to the surface compared to the cooler white side, propelling the black face away from the light source. This asymmetry drives clockwise rotation when viewed from above for standard designs.^[34]^[36] Experimental verification of the force has employed torsion balances, such as delicate pendulums or thrust stands, to measure deflections proportional to F under controlled illumination and pressure. These studies show the force scaling linearly with pressure at low values (below ~1 Pa), peaking around 1–10 Pa (where the mean free path matches vane dimensions), and then declining at higher pressures due to collisional damping of the edge effects.^[34]^[36]

Variants and Extensions

All-Black Radiometer

The all-black radiometer is a variant of the Crookes radiometer in which both sides of the vanes are coated with a highly absorbing material, such as lampblack or, in modern implementations, carbon nanotubes, to ensure uniform light absorption across the surfaces. This design was developed in the 20th century to test thermal theories of radiometer motion by eliminating the absorption asymmetry present in the standard model. When exposed to light, the all-black radiometer still rotates, but at a reduced speed compared to the standard version, with the direction of rotation determined by differences in heating at the vane edges rather than face-to-face contrasts. The mechanism differs from the standard radiometer in that there is no temperature difference between the two faces of the vane; instead, motion arises purely from thermal gradients at the edges, leading to asymmetric gas flow around the heated perimeter through a process known as thermal creep. This demonstrates that thermal creep can drive rotation without absorption asymmetry between the vane faces. Key experiments with the all-black radiometer have confirmed the role of edge thermal gradients in producing the radiometric force, providing evidence for the thermal transpiration model proposed by Osborne Reynolds and later refined by Martin Knudsen. Historically, variants like the all-black radiometer were used in early 20th-century studies on radiometer behavior, including those by Albert Einstein in 1924 exploring edge effects and molecular kinetics.

Horizontal Vane Radiometer

The horizontal vane radiometer, also known as the Hettner radiometer, represents a specialized variant of the Crookes radiometer designed to isolate specific radiometric forces through geometric reconfiguration. In this setup, the vanes are oriented horizontally, lying parallel to the axis of rotation rather than perpendicular to it as in the standard vertical-vane design. This configuration was pioneered in the 1920s by physicists M. Czerny and G. Hettner to experimentally measure the thermal slip—or creep—of gases along surfaces with temperature gradients, providing early empirical evidence for edge-driven gas flows in rarefied conditions.^[38] Constructionally, the device mirrors the Crookes radiometer in its use of a sealed glass bulb maintaining a partial vacuum, typically at pressures ranging from 1.33 Pa to 33.33 Pa to ensure mean free paths on the order of millimeters. The vanes, often four in number and mounted on a low-friction spindle, measure approximately 1 cm in width (with experimental variants including narrow 8 mm × 16 mm and wide 16 mm × 16 mm sizes) and 0.1 mm in thickness; one half of each vane is blackened (e.g., with ink on high-gloss photo paper) to create a lateral temperature gradient under illumination, while the other half remains reflective.^[39] This horizontal arrangement ensures that any temperature-induced gas interactions occur primarily along the vane edges rather than across the faces.^[27] When exposed to light in partial vacuum, the horizontal vane radiometer rotates with the cooler (reflective) side of the vanes leading, driven predominantly by thermal creep—a tangential force arising from uneven momentum transfer of gas molecules along the hotter edges toward cooler regions. Unlike the standard Crookes design, it experiences minimal Einstein effect (also termed photophoretic force), as the horizontal orientation eliminates the vertical asymmetry needed for net normal forces on vane faces.^[27] This purposeful isolation allows researchers to distinguish edge-based thermal creep from face-normal radiometric forces, revealing reduced rotation speeds without the compounding vertical effects; typical operation yields angular velocities peaking at 0.5–5 rpm under optimal pressures around 2.67–12 Pa and moderate illumination, with performance diminishing at higher or lower pressures due to viscous drag dominance.^[39] Key experimental findings from this variant underscore the role of horizontal-edge streaming in radiometric motion. Early work by Czerny and Hettner confirmed that gas flow directions align with thermal gradients, producing measurable shear forces even on uniformly heated plates adjacent to hotter sources.^[38] More recent 2010s investigations, employing kinetic theory and Direct Simulation Monte Carlo (DSMC) modeling, have validated these observations by simulating gas flows around the vanes, achieving qualitative agreement with experiments and quantitative matches within an order of magnitude for narrow-vane configurations; these studies further demonstrate that drag forces contribute comparably to thermal creep in determining peak speeds, enhancing models of rarefied gas dynamics.^[27]

Nanoscale Light Mills

In 2010, researchers at the University of California, Berkeley developed the first nanoscale light mill, a plasmonic motor capable of driving the rotation of a silica microdisk approximately 4,000 times larger in volume than the motor itself.^[40] The device consisted of a gammadion-shaped gold nanostructure, roughly 100 nm in size, embedded within the silica disk, which had a diameter on the order of micrometers. This innovation marked a significant step in miniaturizing the Crookes radiometer principle, shifting from macroscopic thermal effects to light-driven plasmonic torque for rotation.^[41] These nanoscale light mills are typically fabricated using microelectromechanical systems (MEMS) techniques, involving electron-beam lithography to pattern metallic nanostructures on silicon or silica substrates within low-pressure vacuum chambers. Laser light illuminates the structure, inducing rotation through either thermal gradients that drive photophoretic forces or plasmonic resonances that generate torque via light's angular momentum. For instance, in the Berkeley design, linearly polarized light at specific wavelengths (810 nm for counterclockwise rotation and 1,715 nm for clockwise) excites plasmon modes in the gold structure, producing measurable rotational motion without mechanical contact.^[40] Such designs operate effectively in partial vacuums, analogous to classical radiometers, but at scales where quantum and near-field effects enhance performance. The behavior of these devices includes rotation speeds reaching hundreds of hertz under focused laser illumination in controlled vacuum environments, with torque scaling proportionally to the illuminated area and light intensity. In ultra-low pressure conditions (below 10^{-3} Pa), the mills exhibit heightened sensitivity to incident light, enabling detection of low photon fluxes due to reduced damping from gas molecules. Advances in the 2020s have incorporated novel materials like nanocardboard—ultralight metamaterials with alumina face sheets and carbon nanotube coatings—for vanes that rotate at atmospheric pressure, achieving speeds up to 11.6 RPM under solar-like intensities (1.5 kW/m²). Graphene aerogel coatings on vanes have further boosted performance, yielding rotation rates 13–30 times higher than traditional carbon black coatings across a broad pressure range (10^{-4} to 10^2 Pa), with forces up to 1.4 × 10^{-6} N.^[42] These developments position nanoscale light mills as promising optomechanical sensors for detecting minute forces or pressures, and for testing vacuum quality in microfabrication environments through rotation response to residual gas interactions. Potential applications include integrated photonic devices and propulsion in microspacecraft. However, challenges persist in fabrication precision, as nanoscale features demand sub-10 nm alignment to maintain plasmonic or thermal asymmetry, and the radiometric force scales with device area (F ∝ size²), reducing absolute torque at smaller dimensions while paradoxically increasing relative sensitivity due to lower mass (∝ size³).^[40]

Applications

Educational and Demonstrative Uses

The Crookes radiometer has long served as a compelling tool in educational settings, particularly in lectures by its inventor, Sir William Crookes, who demonstrated it during the late 19th century to illustrate principles of vacuum science and radiant energy to scientific audiences.^[25] Crookes incorporated the device into presentations, such as his 1879 Bakerian Lecture to the Royal Society, where it helped visualize molecular pressures and the behavior of gases in low-pressure environments, thereby popularizing experimental vacuum techniques among researchers and the public.^[43] In classroom demonstrations, the radiometer is widely employed to illustrate how light acts as an energy carrier, the effects of partial vacuums on gas dynamics, and basic thermal physics concepts, making it a staple in high school optics and thermodynamics labs since the early 20th century.^[44] Students often observe the vanes' rotation under sunlight or incandescent lamps, experimenting with variables like light intensity or bulb evacuation to explore energy transfer, as outlined in inquiry-based modules that encourage hypothesis testing and data analysis.^[45] This hands-on approach aligns with physics curricula, such as those integrating wave absorption and transmission standards.^[46] The device's pedagogical value lies in its ability to challenge students' intuitions about radiation pressure and demonstrate kinetic theory of gases in action, serving as an accessible entry point to non-equilibrium thermodynamics without requiring complex equipment.^[32] By prompting discussions on why the vanes rotate toward the brighter side despite initial expectations of photon momentum, it fosters critical thinking and connects abstract concepts like molecular collisions to observable motion, as highlighted in teaching aids that compare it to related devices like the Hettner radiometer.^[47] Interactive exhibits featuring the radiometer appear in prominent science museums, such as the Science Museum Group in London and the Smithsonian Institution, where it has been displayed since the late 19th century to engage visitors with "light-powered" rotation that requires no electrical wires, emphasizing self-contained energy conversion.^[48] These installations, often part of thermodynamics or optics galleries, allow public interaction to highlight vacuum effects and light's thermal influence, drawing crowds with its mesmerizing spin under gallery lighting.^[49] Modern adaptations include affordable DIY kits that enable students to construct simplified versions using household materials like foil and jars, often paired with LED or incandescent lights for indoor testing, promoting maker education in physics. Post-2020, online simulations have expanded remote learning options, with interactive models allowing virtual manipulation of light sources and pressure levels to mimic the device's behavior and reinforce conceptual understanding.^[50]

Practical and Technological Implementations

The Crookes radiometer has served as a qualitative vacuum gauge for measuring low pressures in the range of approximately 1 to 10 Pa since the late 1880s, with rotational speed indicating pressure levels through viscous drag on the vanes.^[4] This historical application relied on observing the device's spin rate, optimal around 8 Pa, to assess partial vacuums in laboratory settings. Modern vacuum measurement devices, such as digital spinning rotor gauges (SRGs), which operate on the related principle of gas drag on a spinning rotor, provide precise measurements and are widely used in semiconductor manufacturing for process control in high-vacuum environments like thin-film deposition.^[51] The thermal interaction mechanism underlying the Crookes radiometer has inspired radiometric detectors employed in infrared (IR) spectroscopy, where heat-induced gas motion or expansion detects radiation intensity.^[52] Nanoscale variants, drawing from the original design, are being explored for advanced sensing, including potential applications in photon detection within quantum optics experiments during the 2020s.^[40] Experimental micro-scale light mills, miniaturized versions of the Crookes radiometer, have been developed to harvest energy from ambient light for powering microelectromechanical systems (MEMS) devices, such as tiny mirrors in medical imaging tools. These prototypes generate sufficient torque for practical motion but achieve efficiencies around 10^{-6}, with ongoing improvements in materials and design.^[53] Beyond technical applications, Crookes radiometers feature in artistic contexts, including kinetic sculptures and installations like Luke Jerram's solar-powered chandeliers, where arrays of spinning vanes create dynamic visual effects from light exposure.^[54] The device has been proposed for use in meteorology to enable rough estimations of solar radiation intensity through vane rotation speed, serving as an inexpensive alternative to thermopile sensors for weather stations.^[55] Despite these implementations, the Crookes radiometer and its derivatives suffer from low power output, typically on the order of nanowatts, and high sensitivity to ambient temperature fluctuations, which restrict their suitability for high-precision or high-power applications.^[4]

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[PDF] Sir William Crookes (1832–1919) Biography with special reference ...
2), promoted electric lighting, invented the radiometer. 1873–1876, and the spinthariscope. He was the author in. 1871 of the book Select Methods of Chemical ...Missing: date | Show results with:date<|separator|>
[17]
Invisible resource: William Crookes and his circle of support, 1871–81
Jan 5, 2009 · Crookes's paper, sent to the Royal Society, 30 November 1879, was entitled, 'On the illumination of lines of molecular pressure and the ...
[18]
[PDF] The Loan Exhibition of Scientific Apparatus - Victorian Voices
ERY different in principle is the idea on which the present collection at South Kensington ... "Crooke's Radiometer," respecting the motive power of which ...
[19]
Attraction and Repulsion caused by Radiation - Nature
Published: 17 June 1875. Attraction and Repulsion caused by Radiation. WILLIAM CROOKES. Nature volume 12, page 125 (1875)Cite this article. 343 Accesses. 5 ...
[20]
XVIII. On repulsion resulting from Radiation.—Part II - Journals
Kooperation oder Konkurrenz?, ...
[21]
Crookes Radiometer, 1876-1895 - Science Museum Group Collection
Radiometer, with single, semi-cylindrical aluminium vanes (No. 20) on a wooden turned mahogany with leaded base, London, England, 1876-1895.
[22]
[PDF] HISTORY OF VACUUM DEVICES
In the 1870s William Crookes, with his assistant Charles Gimingham, attempted to achieve a vacuum “approaching perfection”. Figure 8 shows Crookes' first ...<|control11|><|separator|>
[23]
https://iopscience.iop.org/article/10.1088/2040-8986/ade8fb
[24]
Radiation pressure revisited: historical context and the role of ...
Maxwell, reflecting on phenomena such as comet tails in his correspondence ... This issue is clearly illustrated by the Crookes radiometer developed in ...
[25]
[PDF] The Force Driving the Crookes Radiometer
Within a minute, the rotation reached the highest speed, about 2 cycles per second. The results are similar to the experiments with none focused light sources.
[26]
William Crookes and the Radiometer - jstor
latter is entitled " On the Illumination of Lines of Molecular Pressure, and the Trajectory of Molecules "; its first paragraph is numbered 486. Crookes was ...
[27]
https://pubs.aip.org/aip/pof/article/28/3/037103/316377/A-horizontal-vane-radiometer-Experiment-theory-and
[28]
A horizontal vane radiometer: Experiment, theory, and simulation
These forces are most famously demonstrated by the Crookes radiometer. A thorough review of radiometric phenomena including historical accounts can be found in ...
[29]
[PDF] Enhanced radiometric forces - arXiv
Feb 3, 2004 · Abstract. Crookes' Radiometer exploits thermal forces arising from temperature gradients in rarefied gases. This instrument has remained ...Missing: 1910 | Show results with:1910
[30]
[PDF] Thermal Creep Force: Analysis And Application - DTIC
This chapter provides a historic overview of the Crookes radiometer, which led to the discovery of the thermal creep force. Chapter II presents the results ...
[31]
https://www.rs-online.com/designspark/diy-photon-propulsion-innovation-meets-designsparks-maker-sense
[32]
DIY Photon Propulsion – Innovation meets DesignSpark's maker ...
Apr 6, 2020 · The wheel of a Crookes radiometer turns with the reflecting ... 6.63*10-34 / (663 * 10-9) Ns = 2*10-27 Ns. to the mirror. As 1021 ...
[33]
Comparison of forces for the Crookes and Hettner radiometers
Jan 20, 2022 · 1. Introduction. The Crookes radiometer was invented by William Crookes in the nineteenth century (he originally observed the effect upon which ...Missing: invention reliable
[34]
A Horizontal Vane Radiometer: Experiment, Theory, and Simulation
Dec 8, 2015 · The existence of two motive forces on a Crookes radiometer has complicated the investigation of either force independently. The thermal creep ...
[35]
https://calhoun.nps.edu/server/api/core/bitstreams/19969a77-a0ad-496c-968a-04ffc74abdb7/content
[36]
[PDF] A horizontal vane radiometer: experiment, theory, and simulation
Dec 2, 2015 · (a) The Crookes radiometer experiences thermal creep forces and the Einstein effect. (b) The horizontal vane radiometer experiences thermal ...<|control11|><|separator|>
[37]
[PDF] Experimental and Numerical Analysis of Radiometric Forces ... - DTIC
Jan 13, 2009 · The shear force exerted on the lateral side of the radiometer vane was found to decrease the total radiometric force. Finally, various ...
[38]
[PDF] The dynamic mechanism of a moving Crookes radiometer
Nov 6, 2012 · A formula is derived to depict the total radiometric force for a wide range of Knudsen number. The kinetic equation is solved by the unified gas ...
[39]
https://arxiv.org/pdf/1512.02590
[40]
Messungen der thermischen Gleitung von Gasen
Zeitschrift für Physik. Messungen der thermischen Gleitung von Gasen. Download PDF. M. Czerny &; G. Hettner. 32 Accesses. 13 Citations. Explore all metrics ...Missing: thermal slip
[41]
[PDF] A Horizontal Vane Radiometer: Experiment, Theory, and Simulation
... Crookes radiometer is free to rotate around a spindle ... The gradient thus extends one mean free path further on each side in the gas than in the surface.
[42]
Light-driven nanoscale plasmonic motors | Nature Nanotechnology
Jul 4, 2010 · Light-driven nanoscale plasmonic motors. Download PDF. Letter; Published: 04 July 2010. Light-driven nanoscale plasmonic motors. Ming Liu ...Missing: PDF | Show results with:PDF
[43]
Nano-sized light mill drives micro-sized disk - Berkeley Lab
Jul 5, 2010 · Berkeley Lab researchers have created a nano-sized light mill motor powerful enough to drive micro-sized disks. With rotational speed and ...Missing: vacuum | Show results with:vacuum
[44]
Radiometric propulsion for sun-powered near-space aircraft ...
Jul 30, 2025 · The radiometric force is first observed on the Crookes radiometer ... radiometer experiments at a gas pressure of 1.5 Pa. The temperatures ...
[45]
V. The Bakerian Lecture.—On the illumination of lines of molecular ...
The Bakerian Lecture.—On the illumination of lines of molecular pressure, and the trajectory of molecules. William Crookes.
[46]
What is a Radiometer? - Educational Innovations Blog
Jan 11, 2012 · The radiometer is a light bulb-shaped device containing an object that looks like a weather vane (wings arranged in a circle like spokes of a wheel).
[47]
the radiometer using inquiry to teach energy conversions
The radiometer was invented in 1873 by the chemist Sir William Crookes. The radiometer is made from a glass bulb from which much of the air has been removed ...Missing: invention | Show results with:invention
[48]
[PDF] Radiometer - CommerceV3
Students can use the Radiometer to develop and use a model to describe how waves are reflected, absorbed, or transmitted through various materials. MS-PS4-2.
[49]
The Hettner Radiometer as a Teaching Aid - ResearchGate
Aug 7, 2021 · The vanes are black on one side and shiny on the other: the set of vanes then starts to rotate as soon as the radiometer is placed in light.
[50]
Crookes' Radiometer, 1878 | Science Museum Group Collection
Radiometer used to illustrate Sir W. Crookes' researches on the radiation of heat in high vacua: otheoscope (an instrument in which the driving surface is ...
[51]
The Smithsonian's First Radiometers
Apr 25, 2019 · While pursuing that project, Crookes discovered what he believed to be “repulsion resulting from radiation,” designed a “radiometer” to ...Missing: mechanism reliable
[52]
Crookes Radiometer: A Comedy of Errors
The original explanation was radiation pressure, which had recently been proposed by Maxwell. If this were true, however, the vanes would rotate in the opposite ...
[53]
https://phys.org/news/2010-06-classic-children-toy-tiny-motor.html
[54]
Solar radiometer vs pyranometer - Hukseflux
The main chamber of the Crookes solar radiometer is a glass bulb from which air has been removed until a partial vacuum is reached. A rod with four vertically ...Missing: construction materials<|control11|><|separator|>
[55]
Researchers Turn Classic Children's Toy Into Tiny Motor - Phys.org
Jun 30, 2010 · Researchers at the University of Texas at Austin have miniaturized a children's toy into a tiny motor that could one day power medical devices or harvest solar ...
[56]
Kinetic Chandeliers - Luke Jerram
These solar powered kinetic chandeliers consist of dozens of glass radiometers, which shimmer and flicker as they turn in the sunlight.Missing: Crookes | Show results with:Crookes