Molecular, Dynamics, Tangential, Momentum, Accommodation, Coefficient


The Tangential Momentum Accommodation Coefficient (TMAC) is used to improve the accuracy of fluid flow calculations in the slip flow regime. Under such conditions (indicated by Knudsen number greater than 0.001), the continuum assumption that a fluid velocity at a solid surface is equal to the surface velocity is inaccurate because relatively significant fluid "slip" occurs at the surface. Prior work has not led to a method to quickly estimate a value for TMAC - it is frequently assumed. In this work, Molecular Dynamics techniques are used to study the impacts of individual gas atoms upon solid surfaces to understand how approach velocity, crystal geometry and interatomic forces affect the scattering of the gas atoms, specifically from the perspective of tangential momentum. It is a logical step in the development of a comprehensive technique to estimate total coefficient values to be used by those investigating flows in micro- and nano-channels or on orbit spacecraft where slip flow occurs. TMAC can also help analysis in transitional or free molecular regimes of flow. The gas - solid impacts were modeled using Lennard Jones potentials. Solid surfaces were modeled with approximately 3 atoms wide by 3 atoms deep by 40 or more atoms long. The crystal surface was modeled as a Face Centered Cubic (100). The gas was modeled as individual free gas atoms. Gas approach angles were varied from 10 degrees to 70 degrees from normal. Gas speed was either specified directly or by way of a ratio relationship with the Lennard-Jones energy potential (Energy Ratio). In order to adequately model the trajectories and maintain conservation of energy, very small time steps (on the order of 0.0005 [tau] , where [tau] is the natural time unit) were used. For each impact the initial and final tangential momenta were determined and after a series of many impacts, a value of TMAC was calculated for those conditions. The modeling was validated with available experimental data for He gas atoms at 1770 m/s impacting Cu over angles ranging from 10° to 70°. The model agreed within 3% of the experimental values and correctly predicted that the coefficient changes with angle of approach. Molecular Dynamics results estimate TMAC values from a high of 1.2 to a low of 0.25, generally estimating a higher coefficient at the smaller angles. TMAC values above 1.0 indicate backscattering, which has been experimentally observed in numerous instances. The ratio of final to initial momenta, when plotted for a given sequence of gas atoms spaced across a lattice cycle typically follows a discontinuous curve, with continuous portions indicating forward and back scattering and discontinuous portions indicating multiple bounces. Increasing the Energy Ratio above a value of 5 tends to decrease the coefficient at all angles. Adsorbed layers atop a surface influence the coefficient similar to their Energy Ratio. The results provide encouragement to develop the model further, so as to be able in the future to evaluate TMAC for gas flows with Maxwell temperature distributions involving numerous impact angles simultaneously.


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Graduation Date





Kapat, Jayanta


Doctor of Philosophy (Ph.D.)


College of Engineering and Computer Science


Mechanical, Materials and Aerospace Engineering

Degree Program

Mechanical Engineering








Release Date

January 2006

Length of Campus-only Access


Access Status

Doctoral Dissertation (Open Access)