Lava lamps, heat and buoyancy: sources & model

Watch real lava-lamp footage, then release a model blob. Discover why it can rise while cooling, hold it without stopping heat flow, and change the conditions until its journey stops.

What supports the explanation?

What this model assumes

1. The numerical fluids, dimensions, heat response and resistance are authored and restricted to a 40–60°C domain. They are not commercial wax or water measurements.
2. One parcel retains its mass and uses an equal-volume sphere. Real stretching, merging and splitting appear in the separately credited footage, not as solved model physics.
3. The surrounding temperature field is externally maintained. The carrier does not have a calculated flow or energy budget.
4. The force model is overdamped; resistance or support balances the driving force. There is no simulated inertia or measured viscosity.
5. The ideal center-travel boundaries do not model pooling, impact or detachment.
6. Thermal storage CΔT excludes the lamp, carrier, mechanical dissipation and other energy flows.
7. The footage has no measured temperature, material composition or distance scale. Color and shape count cannot supply those measurements.
8. Virtual temperatures and holds are investigative tools, not instructions to modify or heat a real lamp.
9. The names behind the motion: Thermal expansion is a change in size with temperature. Density is mass per volume. Buoyancy is the upward force from the surrounding fluid’s pressure distribution. Thermal inertia describes the time involved in changing stored thermal energy. Immiscible liquids remain separate phases; that alone does not guarantee a repeating lava-lamp cycle.
10. A small expansion can matter: Our authored parcel has mass 2 g. Its volume is 1.980198 mL at 40°C and 2.039604 mL at 60°C: an increase of 3%. Its density changes from 1010 to 980.5825 kg/m³. Its weight remains 0.01962 N. The radius of the equal-volume sphere grows by only about 0.99%; the model does not secretly double the blob to make expansion look dramatic.
11. Same height, opposite clues: At the midpoint the model liquid is 50°C, with density 997.009 kg/m³. A 44°C parcel has density 1003.976 kg/m³: it sinks while heat enters it. A 54°C parcel has density 989.226 kg/m³: it rises while heat leaves it. Relative density determines the driving force; a temperature difference determines heat flow. These are authored calculated examples, not measurements from the video.
12. The thermal model: The surrounding temperature is imposed as Ta(z) = Tbottom + (Ttop − Tbottom)z/H over a 0.24 m center-travel interval. The parcel follows dT/dt = (Ta − T)/τ. Its thermal capacitance is C = 4 J/K, giving heat flow Q̇ = C(Ta − T)/τ. In the default model τ = 240 s. These are teaching parameters, not a recovered commercial formula or operating recommendation.
13. A hold separates position from heat: At a fixed height, temperature approaches the local surroundings as T(t) = Ta + [T(0) − Ta]exp(−t/τ). A 40°C parcel held at the 60°C bottom reaches 52.6424°C after 240 model seconds. Its thermal energy has increased by 50.5696 J in this lumped budget. That is not the lamp’s total electrical use. The virtual holding tool supplies whatever support is needed to keep its position fixed.
14. Mass-consistent density and a force balance: The authored volume law is V = (m/1010)[1 + 0.0015(T − 40)] in SI units; density is m/V. The carrier has density 1000/[1 + 0.0003(Ta − 40)]. Buoyancy is ρcarrier gV and weight is mg. Free speed is their difference divided by an effective resistance coefficient, 0.05 N·s/m. This overdamped approximation has no independently simulated inertial acceleration. At a boundary or under a hold, an additional support force balances the difference.
15. Why quick exchange can lead to rest: With the same imposed 60-to-40°C field, changing the response time to 20 s makes this calculation approach an interior equilibrium: about 13.9749 cm above the lower travel boundary and 48.3542°C. The local densities and temperatures match there. The default 240 s model does not settle to that interior state. An equilibrium’s existence and its stability are different questions; neither result establishes a universal threshold for real lamps.
16. What an actual experiment adds: Gyüre and Jánosi studied heavy silicone fluid and salt solution, not commercial wax. Their apparatus often reached stationary arrangements; periodic exchange appeared under selected conditions. Their boundary-temperature signals were spatially averaged, not temperatures tracked inside a moving blob. The experiment shows why interfaces and heat transport deserve evidence beyond a colorful model. Its Figure 2 legend and caption disagree about symbol assignments, so we do not digitize that plot into a claimed wax calibration.
17. Melting is not the whole cycle: Manufacturer explanations describe wax melting during startup. Once liquid, a parcel can change temperature and relative density without repeatedly freezing and boiling. This model begins with liquid material. It omits initial melting, surface tension, splitting, merging, wall wetting, internal fluid motion and the energy evolution of the carrier.

What has been checked

Analytical reference cases, conservation or transition invariants, finite drawing commands, bounded setup parsing, discovery and route integrity are checked automatically. These checks do not establish anatomical fidelity, learner outcomes or browser/device compatibility. Independent subject review, learner trials, comprehensive accessibility review and browser video encoding checks remain pending.

Each source supports the associated claim. Sources do not certify this implementation or its visuals.

About the cover illustration

Frank Vincentz, Lava lamp (oT) 07 ies (2012), CC BY-SA 3.0 Unported. Source frame 2:15, full framing preserved, resized/WebP encoded. Source and license links accompany the real footage and downloadable provenance in the lesson. Actual visible shapes, not measured temperatures.