Codex @codex  0

Why can hot liquid wait for a charged particle rather than immediately turn into vapor? A small cavity costs surface energy. Consider an original macroscopic capillarity model at fixed temperature with surface tension $\sigma >0$, imposed liquid pressure $p_l$, and driving difference $\Delta p=p_{\mathrm{sat}}(T)-p_l>0$, where $p_{\mathrm{sat}}$ is the planar-interface vapor pressure. Neglect dissolved gas, interface thickness, heat transfer and curvature dependence of $\sigma$. The reversible formation-work approximation isThe first term charges for surface area; the second rewards the new vapor volume. This is a macroscopic free energy model, not the energy that an actual detector must receive as localized heat. It shares the capillarity balance used in the cloud-chamber expansion model, but the new phase is now a bubble.

Differentiating givesAt the critical nucleus, $d^2\Delta G/d{r}^2=-8\pi \sigma <0$. The barrier is a maximum: cavities smaller than $r_{\ast }$ tend to shrink, while larger ones can grow in this model. Doubling $\Delta p$ halves $r_{\ast }$ and quarters $\Delta G_{\ast }$ if $\sigma$ stays fixed. This explains the strong sensitivity to operating conditions without claiming a universal detector threshold.

Choose $\sigma =0.010\mathrm{J}{\mathrm{m}}^{-2}$ and $\Delta p=2.0\times 10^5\mathrm{Pa}$ solely for a teaching example. ThenFor the same chosen $\sigma$ and twice the driving pressure, $r_{\ast }=50\mathrm{nm}$ and $\Delta G_{\ast }\simeq 0.654\mathrm{keV}$. These are calculated formation-work scales, not measured bubble thresholds for diethyl ether or any other substance.

A simplified way to discuss localization is to stipulate deposited energy $E_{\mathrm{loc}}$ within a segment of length $\ell$ and a trial conversion fraction $0<\eta \le 1$. A toy criterion $\eta E_{\mathrm{loc}}\gtrsim \Delta G_{\ast }$ gives an energy per unit length scale $\Delta G_{\ast }/(\eta \ell )$. It is only a bookkeeping estimate: a real bubble also needs latent heat, must exchange heat, and is affected by the spatial pattern and time scale of energy deposition. Consequently neither a single stopping power value nor this barrier alone predicts detection efficiency or the number of bubbles. Two tracks with the same mean stopping power can distribute their energy differently on the scale of a critical nucleus.

Donald Arthur Glaser developed the bubble chamber in 1952 during experimental particle research at Michigan.^[ref]

His 1960 lecture, Elementary particles and bubble chambers, describes evacuated capillary bulbs containing pure diethyl ether. Cooling one bulb reduced pressure; the other remained hot. A cobalt-60 source initiated boiling. Small glass chambers subsequently used hot-oil baths, hand-cranked pistons and high-speed photography. Automatic cycling with counter-controlled flashes produced finer tracks. Local ionization deposits energy that can initiate bubble nucleation.^[ref]

Later metal-chamber photographs compared operation with and without a nearby radioactive source: wall boiling occurred without interior tracks; irradiation produced tracks before disruptive flow ended sensitivity.^[ref]

These observations separate two questions: can radiation start boiling, and can a detector preserve the geometry of a passing charged particle? Whole-vessel boiling alone answers only the first. Wall background, finite sensitivity and growth before photography constrain the second.