= Thermal transpiration experiment with a glass microtube
Rojas Cardenas, Graur, Perrier and Méolans studied <thermal transpiration> in <helium> using a glass microtube of diameter $490\pm1\,\mathrm{\mu m}$ and length $3.05\pm0.01\,\mathrm{cm}$ in their 2012 experiment. They heated one reservoir, leaving the other near room <temperature>, and measured tube-end <temperatures> of $300$ and $351\,\mathrm K$. Three contact <thermometers> and an infrared camera checked the thermal conditions; the hot reservoir was warmer than the adjacent tube end, so heater <temperature> was not an adequate substitute for tube-end <temperature>. Two <capacitance diaphragm gauges> recorded the reservoir <pressures>; a third gauge supported calibration. https://www.jstage.jst.go.jp/article/jtst/7/3/7_437/_pdf/-char/en#page=4[Rojas Cardenas et al. (2012), An Experimental and Numerical Study of the Final Zero-Flow Thermal Transpiration Stage, §2.1]{ref}
\Image[/thermal-transpiration-bypass-and-flux.png]
{title=Thermal-transpiration measurement geometry and an ideal effusion comparison}
{description=The upper panel is a simplified apparatus schematic, not a reproduction of the experimental hardware. The lower panels compare one-way rates in a thin-hole toy model with $T_c=300\,\mathrm K$ and $T_h=351\,\mathrm K$; they are not measured capillary data.}
Their earlier 2011 paper explains the measurement sequence. A wide bypass links the reservoirs in parallel with the microtube. After isolating the gas supply and pump, keep the bypass open to equalize <pressures> with the <temperature> difference already established. Closing the bypass defines $t=0$. The hot-side <pressure> rises and the cold-side <pressure> falls; ultimately their slopes approach zero at unequal <pressures>. Repeating at different initial <pressures> changes the degree of rarefaction without changing the microtube. The 2011 study also compared <helium> and <nitrogen> and imposed <temperature> differences of $50$, $60$ and $70\,\mathrm K$. https://doi.org/10.1063/1.3561744[Rojas Cardenas et al. (2011), Thermal transpiration flow: A circular cross-section microtube submitted to a temperature gradient, measurement sequence]{ref}
The quantities to record are both $p_c(t)$ and $p_h(t)$, the reservoir volumes, and the <temperatures> relevant to their particle inventories. In an idealized reservoir of fixed volume $V_i$ and uniform fixed <temperature> $T_i$, the <ideal gas law> gives $\dot N_i=[V_i/(k_BT_i)]\dot p_i$, so opposite inventory changes test particle conservation. If <temperature> changes, differentiation instead gives $\dot N_i=(V_i/k_B)[\dot p_i/T_i-p_i\dot T_i/T_i^2]$: a thermal drift can imitate particle transfer. The authors' 2011 presentation explicitly checks this thermal correction when extracting an initial <mass flow rate> from the pressure slope. https://www.itep.kit.edu/downloads/12_Rojas.pdf#page=25[Rojas et al., IUVSTA 2011 presentation, mass-flow extraction and thermal correction]{ref}
The 2012 paper compares the final <pressure> ratio across near-free-molecular through slip conditions with a kinetic model and empirical corrections. It does not establish the thin-hole square-root law at every measured <pressure>. https://www.jstage.jst.go.jp/article/jtst/7/3/7_437/_pdf/-char/en[Rojas Cardenas et al. (2012), abstract and comparison of final pressure ratios]{ref} For a replication, useful additional controls follow from the interpretation: remove the <temperature> difference to test the null signal; reverse it to test the direction; check gauge zero offsets and leaks; and wait for stable <temperatures> before closing the bypass. These are suggested controls, not claims that the cited paper performed each one. A reproducible pressure split at zero net transfer makes the failure of a single continuum wall model observable, while the <Knudsen number> organizes which molecular and apparatus scales are competing.
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