Effusion
In physics and chemistry, effusion is the process in which a gas escapes from a container through a hole of diameter considerably smaller than the mean free path of the molecules.
[1] Such a hole is often described as a pinhole and the escape of the gas is due to the pressure difference between the container and the exterior.
Conversely, when the diameter is larger than the mean free path of the gas, flow obeys the Sampson flow law.
In medical terminology, an effusion refers to accumulation of fluid in an anatomic space, usually without loculation.
Specific examples include subdural, mastoid, pericardial and pleural effusions.
The word effusion derives from the Latin word, effundo, which means "shed", "pour forth", "pour out", "utter", "lavish", "waste".
Effusion from an equilibrated container into outside vacuum can be calculated based on kinetic theory.
[2] The number of atomic or molecular collisions with a wall of a container per unit area per unit time (impingement rate) is given by:
assuming mean free path is much greater than pinhole diameter and the gas can be treated as an ideal gas.
on the container is punched to become a small hole, the effusive flow rate will be
The average velocity of effused particles is
Combined with the effusive flow rate, the recoil/thrust force on the system itself is
An example is the recoil force on a balloon with a small hole flying in vacuum.
effuses (typically expressed as the number of molecules passing through the hole per second) is then[4] Here
is the gas pressure difference across the barrier,
Assuming the pressure difference between the two sides of the barrier is much smaller than
, the average absolute pressure in the system (i.e.
is the volumetric flow rate of the gas,
is the average pressure on either side of the orifice, and
At constant pressure and temperature, the root-mean-square speed and therefore the effusion rate are inversely proportional to the square root of the molecular weight.
Gases with a lower molecular weight effuse more rapidly than gases with a higher molecular weight, so that the number of lighter molecules passing through the hole per unit time is greater.
Scottish chemist Thomas Graham (1805–1869) found experimentally that the rate of effusion of a gas is inversely proportional to the square root of the mass of its particles.
[5] In other words, the ratio of the rates of effusion of two gases at the same temperature and pressure is given by the inverse ratio of the square roots of the masses of the gas particles.
represent the molar masses of the gases.
This equation is known as Graham's law of effusion.
The effusion rate for a gas depends directly on the average velocity of its particles.
Thus, the faster the gas particles are moving, the more likely they are to pass through the effusion orifice.
Such a solid forms a vapor at low pressure by sublimation.
The vapor slowly effuses through a pinhole, and the loss of mass is proportional to the vapor pressure and can be used to determine this pressure.
[4] The heat of sublimation can also be determined by measuring the vapor pressure as a function of temperature, using the Clausius–Clapeyron relation.
