Тепловое скольжение

Тепловое скольжение — явление перемещения слоя газа, находящегося у поверхности твёрдого тела, поверхность которого нагрета неравномерно, в направлении к более высокой температуре. Наблюдается в среде, являющейся разреженным газом ^[1].

Качественное рассмотрение

Если поверхность тела нагрета неравномерно, то среди ударяющихся в одну точку молекул газа большую скорость имеют те, которые находятся со стороны большей температуры. Они передают телу разность тангенциальных импульсов в направлении, обратному градиенту температуры. По третьему закону Ньютона в приповерхностном слое газа появляется сила, направленная к более высокой температуре, куда при достаточно малой силе сопротивления будет происходить его перемещение.

Количественное рассмотрение

Пусть A — точка поверхности тела, ось X направлена в сторону увеличения температуры, координата точки A равна x. Усредняя, можно считать, что все попадающие в точку A молекулы имели последнее столкновение в плоскостях $x+{\overline {\lambda }}_{x}$ и $x-{\overline {\lambda }}_{x}$ , где $\lambda$ — длина свободного пробега газа. Если скорость скольжения газа равна u, то средние значения скорости молекулы вдоль оси X в этих плоскостях будут соответственно ${\overline {v}}_{x}(x+{\overline {\lambda }}_{x})-u$ и ${\overline {v}}_{x}(x-{\overline {\lambda }}_{x})+u$ . При стационарном скольжении прекратится передача тангенциального импульса от газа к телу и обратно. Тогда будет выполняться

${\overline {v}}_{x}(x+{\overline {\lambda }}_{x})-u={\overline {v}}_{x}(x-{\overline {\lambda }}_{x})+u$ ,

откуда

${u}={{\overline {\lambda }}_{x}{{d{\overline {v}}_{x}} \over {dx}}}$

Очевидно, что в силу изотропности пространства ${\overline {\lambda ^{2}}}=3{\overline {\lambda _{x}^{2}}}$ . Можно считать, что ${\overline {\lambda _{x}}}={{\overline {\lambda }} \over {\sqrt {3}}}$ . Теорема о равнораспределении даёт $mv_{x}^{2}\approx kT$ . Отсюда

$u\approx {{\lambda } \over {2}}{\sqrt {{k} \over {3mT}}}{{dT} \over {dx}}$

Следовательно, тепловое скольжение заметно в разреженных газах, для которых длина свободного пробега $\lambda$ велика.

См. также

Радиометрический эффект

Примечания

↑ Сивухин Д. В. Общий курс физики. — М.: Наука, 1975. — Т. II. Термодинамика и молекулярная физика. — 519 с.

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