1 3 Microfluid Nanofluid (2016) 20:46 DOI 10.1007/s10404-016-1713-6 RESEARCH PAPER “Law of the nano-wall” in nano-channel gas flows Murat Barisik 1 · Ali Beskok 2 Received: 6 October 2015 / Accepted: 1 February 2016 © Springer-Verlag Berlin Heidelberg 2016 (Tagawa et al. 2007; Juang et al. 2007), hydrogen storage units (Chalk and Miller 2006; Furukawa and Yaghi 2009; Cho et al. 2011), gas separation membranes (Li et al. 2011; Venna and Carreon 2009; Yave et al. 2010) and shale gas reservoirs (Loucks et al. 2009; Chong et al. 2010; Michel et al. 2011). These flows exhibit substantially different physics from continuum descriptions due to (1) rarefaction, (2) surface force field and (3) surface adsorption. Contri- butions of these effects on gas transport differ depending on the pore/channel size, gas pressure, gas–surface interac- tions and chemistry. While rarefaction effects can be esti- mated using kinetic theory (KT)-based procedures such as solution of the Boltzmann transport equation or direct simulation Monte Carlo, surface force field and adsorption effects require molecular-level resolution mostly accessible by molecular dynamics (MD). Gas flows evolve through intermolecular collisions determined by the mean free path, which is an intrinsic length scale for momentum transport. Ratio of the mean free path to a characteristic length, such as the channel height, gives Knudsen number (Kn) that determines the degree of rarefaction, leading to continuum, slip, transi- tion and free-molecular flow regimes (Karniadakis et al. 2005). MD simulations of gas flows require computational domains that are at least one mean free path long in the stream-wise and lateral directions in order not to suppress gas–gas collisions. This results in large simulation domains dominated by an excessive number of wall molecules, creating challenges for classical non-equilibrium MD. We addressed this problem by developing the smart wall molecular dynamics (SWMD) algorithm, which enabled MD simulations of nanoscale gas flows with 3D molecu- lar surfaces for the first time in the literature (Barisik et al. 2010). Abstract Molecular dynamics simulations of force- driven nano-channel gas flows show two distinct flow regions. While the bulk flow region can be determined using kinetic theory, transport in the near-wall region is dominated by gas–wall interactions. This duality ena- bles definition of an inner-layer scaling, y * , based on the molecular dimensions. For gas–wall interactions deter- mined by Lennard–Jones potential, the velocity distribution for y * ≤ 3 exhibits a universal behavior as a function of the local Knudsen number and gas–wall interaction parame- ters, which can be interpreted as the “law of the nano-wall.” Knowing the velocity and density distributions within this region and using the bulk flow velocity profiles from Beskok–Karniadakis model (Beskok and Karniadakis in Microscale Thermophys Eng 3(1):43–77, 1999), we outline a procedure that can correct kinetic-theory-based mass flow rate predictions in the literature for various nano-channel gas flows. Keywords Wall force field effects · Scale effects · Nano- flows · Mass flow rate · Smart wall molecular dynamics 1 Introduction Gas flows in nanoscale domains are observed in a wide range of applications including the magnetic disk drives * Ali Beskok abeskok@smu.edu 1 Mechanical Engineering Department, Izmir Institute of Technology, 35430 Izmir, Turkey 2 Mechanical Engineering Department, Southern Methodist University, Dallas, TX 75275-0337, USA