Coarse Grained Molecular Dynamics Simulations of Sub-Micron Liquid Cylinders and Jets

A coarse-grained molecular dynamics (MD) method, dissipative particle dynamics (DPD), is employed to simulate the breakup of liquid sub-micron liquid cylinders and jets. Consistent with prior findings employing MD, Rayleigh’s criterion for capillary breakup of inviscid liquid cylinders is shown to be applicable. Thermal fluctuations are the primary mechanism inducing instability and this leads to the formation of almost monodisperse drops. The parameters varied in the study include the cylinder radius, thermal length scale, viscosity, and surface tension. The breakup time does not show the same scaling dependence as in capillary breakup of liquid cylinders at the macroscale. The time variation of the radius at the point of breakup agrees with prior theoretical predictions from expressions derived with the assumption that thermal fluctuations lead to breakup. The thermal fluctuations accelerate the breakup of liquid jets at the submicron scale. The time evolution of minimum jet radius as given by prior theoretical analysis is recovered. Introduction The formation of drops from the breakup of sub-micron scale liquid cylinders and jets is important in many current and emerging applications, such as nanoscale machining, super-fine ink-jet printing, and drug-/gene-delivery to biological cells. The breakup of liquid cylinders and atomization of liquid jets at the macroscale has been a topic of study for over a century [14, 12], but sub-micron scale applications have gained in importance only recently. Computational studies of two-phase flows at the macroscale are complex because of the need to track highly deforming interfaces and develop numerical schemes which can be employed for compressible (gas) and incompressible (liquid) fluids [3]. At the sub-micron scale, the assumption that the fluid properties can be represented by statistical averaging may not hold. At this scale, molecular dynamics (MD) is an obvious choice as a numerical technique [10]. For example, it has been applied to study the behaviour of nanodrops [5] and mixing processes at the nanoscale [8]. Nevertheless, the method is computationally expensive. There are approaches which are computationally less expensive but which sacrifice precise information about dimensions and scales because of lack of adequate information about coarse graining. These approaches are, however, very useful to determine trends in physical behaviour at the sub-micron scale. In this work, the dissipative particle dynamics (DPD) approach will be applied to study the breakup of liquid nanocylinders and nanojets [4,6,7]. An important question here is whether the method can capture the physics associated with sub-micron liquid cylinder and jets. The Computational Model The DPD method is particle-based in which each particle represents millions of molecules. The governing equations are written down for the particles and the equations contain quantities which represent the collective behaviour of the millions of molecules they represent. A detailed description of the specific model employed here can be found in Ref. [15]. The position and velocity of a DPD particle i of unit mass are computed from Newton’s laws of motion