Computation of Shear Viscosity: A Systems Approach

Macroscopic material transport properties such as viscosity, diffusivity, conductivity, etc., may be computed by using molecular level simulation such as molecular dynamics or Monte Carlo methods. This computation is time consuming since simulations over sufficiently long times are needed to ensure that the assumed statistical properties are satisfied. As a result, such tools are useful in gaining insight and understanding of the underlying mechanisms behind observed physical phenomena, but are not amenable to material property design or material process control. In this paper, we focus on the computation of shear viscosity of a fluid-like material. We take a systems approach by regarding viscosity as a scalar input/output map from shear stress to shear strain rate. Linearizing this map about an equilibrated trajectory results in a linear time varying system. By freezing the time along the equilibrated trajectory, we obtain a set of linear time invariant systems. These systems are usually unstable, but may be transformed to stable systems by weighing all signals with sufficiently fast decaying exponential functions. Viscosity is then estimated directly from the frequency responses of these systems. Model reduction such as approximate balanced truncation may be applied to further reduce model complexity and computation load. This approach has a potential computation advantage since extensive simulation runs using high order molecular dynamics model are not required. Our long term objective is to develop efficient computation methods to facilitate rapid material and process design iterations. To illustrate the approach described in this paper and compare it with the traditional molecular dynamics methods, we have included the simulation results involving a simple LeonardJones fluid.