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Simulation of Machining with Cutting Liquids Based on Atomistic Force Fields

von Martin Lautenschläger

Within the last decades there has been enormous progress regarding manufacturing techniques. Those amongst others lead to the miniaturization of devices, and thus, of channels and ducts, too. Therefore, the investigation of nanoscale fluid flows and its dynamic behavior has become practically relevant, especially in the fields of microsystems engineering, chemistry and biology.

Since within such nanoscale fluid flows the characteristic lengths are in the order of molecular diameters, the fluid behavior and its properties may be dominated by effects which are neglected in macroscopic flows. Due to the high surface-to-volume ratio in channels, those can be surface effects, slip flow, viscous dissipation and intermolecular forces. Therefore, conventional hydrodynamic theories and flow models such as the Navier-Stokes equations with no-slip boundary condition are not necessarily applicable anymore. Instead, the understanding of the highly complex real effects has to be preceded by the systematic investigation of the individual phenomena, particularly in the linear response regime. But also beyond, where the system is far away from thermal and mechanical equilibrium, it is necessary to obtain a description of the fluid exceeding the linear response regime as well.

In the present work, this fluid behavior and the related nanoscale phenomena are investigated. Beside the nanoscale fluid flow, the fluid properties, transport phenomena and their dependencies on geometrical and model parameters are examined. For those cases molecular dynamic simulations seem to be the only approach using first principles to get a valid detailed insight.
Therefore, in a first step, a software tool for the investigation of non-equilibrium molecular dynamics such as fluid flows and transport phenomena was developed based on the molecular dynamics simulation program ls1 mardyn. Thereby, focus was laid on the connection between continuum fields and microscopic expressions. Thus, with reference to Fig. 1, the stress field and the energy flux, as well as local fluid and flow properties can be calculated and evaluated on a length scale of molecular diameters.

At the moment, this program is applied to the basic scenario of a nanoscale planar Couette flow. On the one hand, local fluid and flow properties are calculated. That means, e.g. the density, the pressure, the temperature, the fluid viscosity, and the fluid thermal conductivity are evaluated on the length scale of molecular diameters (see Fig. 1). This is necessary to calculate profiles of the relevant magnitudes and get a detailed insight into nanoscale effects, even in the nonlinear regime. Moreover, comparing the fluid properties calculated for wall-driven Couette flows with bulk properties calculated by the Green-Kubo equilibrium method, effects of the wall on the fluid properties can be observed.
On the other hand, the fluid-solid interfacial effect on the flow properties is taken into account. It is described with a method using Navier-Stokes equations with an effective slip boundary condition and the energy equation with a temperature jump due to a thermal resistance (Kapitza resistance) at the boundary. This is schematically described in Fig. 2. Here, velocity and temperature profiles are compared with their analytical hydrodynamic solutions. The nanoscopic flow effects can be adapted using the expressions for the boundary conditions given in Fig. 2, too.

The characteristic parameters for velocity and temperature profiles are the slip length Ls and the Kapitza length Lk, respectively. Both depend on lots of geometrical and material influencing factors. That can be for example the thermodynamic state of the fluid, its transport properties, the channel geometry, or the surface roughness, lattice properties and wettability of the wall. Since the cross-linking is complex, here, first results for the dependence of Ls and Lk on the surface wettability and the channel diameter at a constant fluid pressure and shear rate are shown. In Fig. 2 it can be seen that the slip length decreases with increasing solid-fluid interaction. Moreover, the effect of multilayer locking, i.e. the negative slip length for the strong interaction and the weak dependence on the channel size are obvious. Additionally, it can be observed that the thermal resistance length increases with increasing solid-fluid interaction and increasing channel diameter.
Beside those exemplary studies, extensive parameter variations are necessary to formulate predictive correlations that can be used to connect nanoscale flows to the continuum description via boundary conditions.

Fig. 1: Simulation results of a nanoscale planar Couette flow showing (from the left to the right) the discrete particles, the density and pressure distribution, where for the latter the red color means a high, while the blue color means a low magnitude

Fig. 2: Schematic correlation between analytical hydrodynamic solution and simulation results for velocity and temperature profiles of planar Couette flows using adapted boundary conditions (top) and results for Ls and Lk in dependence on a model parameter ε and the channel size D (bottom)

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