Extraction of Tangential Momentum and Normal Energy Accommodation Coefficients by Comparing Variational Solutions of the Boltzmann Equation with Experiments on Thermal Creep Gas Flow in Microchannels

In the present paper, we provide an analytical expression for the first- and second-order thermal slip coefficients, σ1,T and σ2,T, by means of a variational technique that applies to the integrodifferential form of the Boltzmann equation based on the true linearized collision operator for hard-sphere molecules. The Cercignani-Lampis scattering kernel of the gas-surface interaction has been considered in order to take into account the influence of the accommodation coefficients (αt, αn) on the slip parameters. Comparing our theoretical results with recent experimental data on the mass flow rate and the slip coefficient for five noble gases (helium, neon, argon, krypton, and xenon), we found out that there is a continuous set of values for the pair (αt, αn) which leads to the same thermal slip parameters. To uniquely determine the accommodation coefficients, we took into account a further series of measurements carried out with the same experimental apparatus, where the thermal molecular pressure exponent γ has been also evaluated. Therefore, the new method proposed in the present work for extracting the accommodation coefficients relies on two steps. First of all, since γ mainly depends on αt, we fix the tangential momentum accommodation coefficient in such a way as to obtain a fair agreement between theoretical and experimental results. Then, among the multiple pairs of variational solutions for (αt, αn), giving the same thermal slip coefficients (chosen to closely approximate the measurements), we select the unique pair with the previously determined value of αt. The analysis carried out in the present work confirms that both accommodation coefficients increase by increasing the molecular weight of the considered gases, as already highlighted in the literature.

EXISTENCE OF SOLUTIONS OF A BOUNDARY VALUE PROBLEM FOR THE FOUR VELOCITY BROADWELL MODEL

Existence and boundedness is proved for the solutions of a boundary value problem for the two-dimensional Broadwell model in a rectangle. The influence of the orientation of the model in relation to the sides of the rectangle on the form of the boundary value problem is analysed. Exact solutions are found and use to determine accommodation coefficients at the boundaries of a fluid flow in a rectangular box.

Establishing a data-based scattering kernel model for gas–solid interaction by molecular dynamics simulation

Scattering kernel models for gas–solid interaction are crucial for rarefied gas flows and microscale flows. However, most existing models depend on certain accommodation coefficients (ACs). We propose here to construct a data-based model using molecular dynamics (MD) simulation and machine learning. The gas–solid interaction is first modelled by 100 000 MD simulations of a single gas molecule reflecting on the wall surface, which is fulfilled by GPU parallel technology. The results showed a correlation of the reflection velocity with the incidence velocity in the same direction, and also revealed correlations that may exist in different directions, which are neglected by the traditional gas–solid interaction model. Inspired by the sophisticated Cercignani–Lampis–Lord (CLL) model, two improved scattering kernels were constructed to better reproduce the probability density of velocity determined from MD simulation. The first one adopts variable ACs which depend on the incidence velocity and the second one combines three CLL-like kernels. All the parameters in the improved kernels are automatically chosen by the machine learning method. Compared with the numerical experiments of a molecular beam, the reconstructed scattering kernels are basically consistent with the MD results.

Temperature Dependent Entropy Driven Water Uptake in Phase Separated Aerosol from Steered Molecular Dynamics and Intrinsic Surface Analysis

<p>Dynamic water uptake by aerosol is a major driver of cloud droplet activation and growth. Interfacial mass transfer— that governs water uptake if the mean free path of molecules in the vapour phase is comparable to particle size — is represented in models by the mass accommodation coefficient. Although widely used, this approach neglects <em>i</em>) other internal interfaces (e.g., liquid-liquid that may be important for water uptake), and, <em>ii</em>) fluctuations of the liquid surface from capillary waves that modulate the surface and induce ambiguity in the estimation of mass accommodation coefficients. These issues can be addressed if the full path of the water molecule – from vapour to the bulk aqueous phase - is considered.<span> </span></p><p>We demonstrate, using steered molecular simulations, that a full treatment of the water uptake process reveals important details of the mechanism. The simulations are used to reconstruct the free energy profile of water transport across a vapour/hydroxy cis-pinonic acid/water double interface at 300 K and 200 K. In steered molecular dynamics the transferred molecule is pulled with a finite velocity along an aptly chosen reaction coordinate and the work exerted is used to reconstruct the free energy profile. Due to the finite velocity pulling, this method takes the effect of friction on the transport mechanism into account, which is important for phases of considerably different friction coefficients and is neglected by<span>  </span>quasi equilibrium free energy methods. Free energy profiles are used to estimate surface and bulk uptake coefficients and are decomposed into entropic and enthalpic contributions.<span> </span></p><p>Surface accommodation coefficients are unity at both temperatures, while bulk uptake at 300 K from the internal interface is strongly hindered (k<sub>b</sub>=0.05) by the increased density and molecular order in the first layer of the aqueous phase, which results in decreased orientational entropy. The difference between bulk and surface uptake coefficients also implies that water accumulates in the organic shell, which cannot be predicted using a single uptake coefficient for the whole particle. The minimum of the free energy profile at the organic/water interface, rationalised by increased conformational entropy due to local mixing and the depleted system density, results in a concentration gradient which helps maintain low surface tension and phase separation. Low surface tensions may explain increased CCN activity. These entropic features of the free energy profiles diminish at low temperature, which invokes a completely different mechanism of water uptake. Our results point out the need to describe water uptake in aerosol growth models using a temperature dependent parametrisation.</p>

Characterization of spinning rotor gauge-3 using orific flow system and static expansion system

This article elucidates the calibration of newly procured spinning rotor gauge (SRG 3) from MKS Instruments, USA using primary vacuum standards: Orifice flow system (OFS) and Static expansion system (SES) established at National Physical Laboratory, India (NPLI) in the range of 10^-4 Pa to 1 Pa and further compared with manufacturer reported value which was calibrated by transfer standard of National Institute of Standards & Technology (NIST). The key parameters to calculate the pressure measured by SRG is the accommodation coefficients. The accommodation coefficients for N₂ gas obtained using OFS, SES, and calibration report form NIST USA (SRG2) are 0.957, 0.961, and 0.954 respectively.