Accommodation coefficient tangential momentum

When the fractions of molecules reflected specularly and diffusively are known, the slip length can be determined, as shovm by Maxwell. Maxwell introduced a tangential momentum accommodation coefficient defined as... 

The average incident tangential momentum is muh while the average scattered tangential momentum is muf. If the gas molecule equilibrates with the surface and the scattered momentum is zero, we have Knudsen cosine scattering and complete accommodation of the incident gas molecule with the surface. On the other extreme, if specular reflection occurs, the incident momentum is retained upon scattering and mut = muf. The momentum accommodation coefficient, / is introduced to describe the type of scattering that does occur, and it is defined by... 

In this relation, Fm, the tangential momentum accommodation coefficient, is a function of the interaction between gas molecules and the surface. If the surface is smooth and reflects the molecules specularly, F , will be zero. For diffuse reflections F =l. This means that all the tangential momentum is lost at the wall. Diffuse reflection results from the penetration of the molecules into interstices in the surface where multiple impacts occur before the molecules depart. 

Also, the tangential momentum accommodation coefficients obtained experimentally varied in range from 0.3 to 0.7, quite different from the conventional value of 1. This value range agreed with the earlier analytical work [11]. 

Fm, Tangential momentum accommodation coefficient K Molecular mean free path... 

Sazhin OV, Borisov SF, Sharipov F (2001) Accommodation coefficient of tangential momentum on atomically clean and contaminated surfaces. J Vac Sci Technol A 19(5) 2499-2503, Erratum 20(3) 957 (2002)... 

Nanoscale gas transport Shear-driven flow Surface force effects Tangential momentum accommodation coefficient... 

Overall the results show that the wall force field penetration depth is an additional length scale for gas flows in nano-channels, breaking dynamic similarity between rarefied and nanoscale gas flows solely based on the Knudsen and Mach numbers. Hence, one should define a new dimensionless parameter as the ratio of the force field penetration depth to the characteristic channel dimension, where wall effects cannot be neglected for large values of this dimensionless parameter. Additionally, the calculated tangential momentum accommodation coefficients for a specific gas-surface couple were found to be constant regardless of different base pressure, channel height, wall velocity, and Knudsen number. Results of different gas-surface couples reveal that TMAC is only dependent on the gas-surface couple properties and independent of the Knudsen number. 

In this equation, a is the tangential momentum accommodation coefficient, equal to unity for perfectly diffuse molecular reflection and zero for purely specular reflection. In Maxwell s model, MsUp overestimates the real velocity at the wall but leads to a rather good prediction of the velocity out of the Knudsen layer, as represented in Fig. 2. After non-dimensionalization with the characteristic length L, a reference velocity uo, and a reference temperature Tq, Eq. 10 is written as follows ... 

Knudsen accommodation coefficients of normal momentum, tangential momentum, energy, and thermal creep. The additional coefficients a y, a y, and ayy are... 

Here a22 is the tangential momentum accommodation coefficient, a2g and are "second-order" coefficients, is the Chapman-Enskog first-order approximation to the viscosity coefficient. Equation (2.68) is, of course, valid for general gas-surface scattering kernels (2.49). Equation (2.68) reduces approximately to... 

Let us look into some average parameter for defining gas-solid interaction from macroscopic point of view. Tangential momentum accommodation coefficient (momentum exchange of gas molecules with the solid surface defined as... 

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