Sampson flow is defined as fluid flow through an infinitely thin

orifice An orifice is any opening, mouth, hole or vent, as in a pipe, a plate, or a body * Body orifice, any opening in the body of a human or animal *Orifice plate, a restriction used to measure flow or to control pressure or flow, sometimes given specia ...

in the

viscous flow The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inter ...

regime for low Reynolds number. It is derived from an analytical solution to the Navier-Stokes equations. The below equation can be used to calculate the total volumetric flowrate through such an orifice: :

Q_S=\Delta P d^3 / 24 \mu

Here,

Q_S

is the volumetric flowrate in

m^3/sec

\Delta P

is the pressure difference in Pa,

d

is the pore diameter in m, and

\mu

is the fluid's dynamic viscosity in Pa·s. The flow can also be expressed as a molecular flux as: :

J_S=P_ \Delta P d/6\pi\mu k_BT

Here,

J_S

is the molecular flux in atoms/m²·sec,

P_

is the average of the pressures on either side of the orifice,

k_B

is the

Boltzmann constant The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constant, ...

, (

1.38\times10^

J/K), and

T

is the absolute temperature in K. Sampson flow is the macroscopic analog of

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. Such a hole is often described as a ''pinhole'' and the escape ...

flow, which describes stochastic

diffusion Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemica ...

of molecules through an orifice much smaller than the mean-free-path of the gas molecules. For pore diameters on the order of the mean-free-path of the fluid, flow will occur with contributions from the molecular regime as well as the viscous regime, obeying the dusty gas model according to the following equation: :

Q_=Q_S+Q_E

Here,

Q_

is the total volumetric flowrate and

Q_E

is the volumetric flowrate according to the law of

. As it turns out, for many gasses, we notice equal contributions from molecular and viscous regimes when the pore size is significantly larger than the mean-free-path of the fluid, for nitrogen this occurs at a pore diameter of 393 nm, 6.0× larger than the mean-free-path.

References

{{Reflist Fluid dynamics