Joseph J. Thalakkottor

Analysis of Boundary Slip in a Flow with an Oscillating Wall

(Dated: August 1, 2012)Molecular dynamic (MD) simulation is used to study slip at the fluid-solid boundary in an un-steady flow based on the Stokes second problem. An increase in slip is observed in comparison tothe steady flow for shear rates below the critical shear rate of the corresponding steady flow. Thisincreased slip is attributed to fluid inertial forces not represented in a steady flow. An unsteadymathematical model for slip is established, which estimates the increment in slip at the boundary.The model shows that slip is also dependent on acceleration in addition to the shear rate of fluid atthe wall. By writing acceleration in terms of shear rate, it is shown that slip at the wall in unsteadyflows is governed by the gradient of shear rate and shear rate of the fluid. Non-dimensionalizing themodel gives a universal curve which can be used to find the slip boundary condition at the fluid-solidinterface based on the information of shear rate and gradient of shear rate of the fluid. A governingnon-dimensional number, defined as the ratio of phase speed to speed of sound, is identified to helpin explaining the mechanism responsible for the transition of slip boundary condition from finiteto a perfect slip and determining when this would occur. Phase lag in fluid velocity relative towall is observed. The lag increases with decreasing time period of wall oscillation and increasingwall hydrophobicity. The phenomenon of hysteresis is seen when looking into the variation of slipvelocity as a function of wall velocity and slip velocity as a function of fluid shear rate. The causefor hysteresis is attributed to the unsteady inertial forces of the fluid.

Unified slip boundary condition for fluid flows.

Interface between two phases of matter are ubiquitous in nature and technology. Determining the correct velocity condition at an interface is essential for understanding and designing of flows over a surface. We demonstrate that both the widely used noslip and the Navier and Maxwell slip boundary conditions do not capture the complete physics associated with complex problems, such as spreading of liquids or corner flows. Hence, we present a unified boundary condition that is applicable to a wide-range of flow problems.Determining the correct matching boundary condition is fundamental to our understanding of several everyday problems. Despite over a century of scientific work, existing velocity boundary conditions are unable to consistently explain and capture the complete physics associated with certain common but complex problems, such as moving contact lines and corner flows. The widely used Maxwell and Navier slip boundary conditions make an implicit assumption that velocity varies only in the wall normal direction. This makes their boundary condition inapplicable in the vicinity of contact lines and corner points, where velocity gradient exists both in the wall normal and wall tangential directions. In this paper, by identifying this implicit assumption we are able to extend Maxwells slip model. Here, we present a generalized velocity boundary condition that shows that slip velocity is a function of not only the shear rate but also the linear strain rate. In addition, we present a universal relation for slip length, which shows that, for a general flow, slip length is a function of the principal strain rate. The universal relation for slip length along with the generalized velocity boundary condition provides a unified slip boundary condition to model a wide range of steady Newtonian fluid flows. We validate the unified slip boundary for simple Newtonian liquids by using molecular dynamics simulations and studying both the moving contact line and corner flow problems.

Analysis of Slip in a Flow with an Oscillating Wall

Over the past two decades several studies has been done to understand the molecular mechanism of slip in uids at the boundary. Most of the studies that were conducted have dealt with a steady ow. In this paper we use molecular dynamic simulations to study slip in an unsteady ow. Our numerical experiment is based on that of Stokes second problem for a continuum regime. The results show additional slip in comparison to the slip observed in a steady ow. An unsteady slip model is established by extending Maxwell’s slip theory for a steady ow to encapsulate unsteady ows. The model is used as an analogy to nd the parameters that in uence slip in uids. The model indicates that slip velocity of a uid is dependent on acceleration of the uid, in addition to its shear rate. Further the slip model is non-dimensionalized. It is seen that the type of ow has no bearing on the layering of uid layer at close proximity to the wall. The presence of hysteresis in an unsteady ow is also observed. This can be attributed to uid inertia which is governed by the acceleration and deceleration of the wall.

Modeling Slip at Triple Contact Point in a Two Phase Flow

Contact line motion has been a topic of interest for the past few decades. With the help of molecular dynamics simulations it is shown that Navier and Maxwell slip boundary conditions is incomplete in the case of flow near triple contact point and corner flow. Using the concept of Maxwell’s theory for slip in a single phase flow, a modified slip model is established that demonstrates the dependence of slip velocity on the velocity gradient tensor at the wall. The model shows that in addition to shear strain rate, slip velocity is also dependent on the linear strain rate and vorticity of the fluid flow. In the vicinity of the triple contact point the magnitude of linear strain rate is of the same order as that of vorticity and shear strain rate, hence it can not be neglected. Studying the behavior of these components of the velocity gradient tensor, along the wall, showed a sharp increase in their magnitude close to the triple contact point. The sharp increase in vorticity suggests the generation of vorticity at the triple contact point. This is of particular interest as vorticity is related to circulation and circulation plays an important role in various droplet based applications. In this paper non-Newtonian behavior of the fluid near the triple contact point is also demonstrated, as viscosity varies from the bulk value in the vicinity of the triple contact point.

Effect of Slip on Circulation Inside a Droplet

Internal recirculation in a moving droplet plays an important role in several droplet-based microfluidic devices as it enhances mixing, chemical reaction and heat transfer. The occurrence of fluid slip at the wall, which becomes prominent at high shear rates and lower length scales, results in a significant change in droplet circulation. Using molecular dynamics (MD) simulations, the presence of circulation in droplets is demonstrated and quantified. Circulation is shown to vary inversely with slip length, which is a measure of interface wettability. A simple circulation model is established that captures the effect of slip on droplet circulation. Scaling parameters for circulation and slip length are identified from the circulation model which leads to the collapse of data for droplets with varying aspect ratio (AR) and slip length. The model is validated using continuum and MD simulations and is shown to be accurate for droplets with high AR.

Velocity and thermal slip at the moving contact line

The no-slip boundary condition is known to produce stress and velocity singularity at the moving contact line. Recent molecular dynamics simulations have shown that this is not the case, rather in the vicinity of the contact line velocity slip is observed, with the contact line undergoing perfect slip. It is known that velocity slip is often accompanied by thermal slip, resulting in a temperature jump at the interface. The degree of thermal slip is defined by Kapitza length which is analogous to slip length and is of the same order of magnitude as it. It has been recently shown that the standard Navier and Maxwells velocity slip model is not sufficient to capture slip in the vicinity of moving contact line. Here we first present a universal velocity slip model and then explore using molecular dynamics simulations, the extent of thermal slip in the vicinity of the contact line and the impact it has on nano-/micro-fluidic applications.

Stress dependent slip boundary condition for single- and two-phase fluid flow on a substrate

In problems such as moving contact line and corner flows, fluid velocity adjacent to the wall varies spatially in direction normal and tangential to the wall. Navier and Maxwell slip models considered flows where velocity only changed in the wall normal direction. In this paper, molecular dynamics simulation is used to study the moving contact line problem. In the vicinity of the triple contact point, slip length is shown to be dependent on the local velocity gradient tensor and number density. Scaling for slip length and the velocity gradient tensor is identified; that helps collapse the data to give a universal curve for slip length. The universal curve helps relate slip length to the fluid-wall properties and the local flow parameters. Generalized slip model together with the universal curve, provide an accurate boundary condition for a wide range of steady flow problems without having to perform computationally expensive molecular dynamics simulations.

Effect of hydrodynamic and thermal slip on droplet based thermal management systems

Fluid flow in a microchannel is primarily laminar due to viscous forces dominating over body or inertia forces. Hence fluid circulation in a droplet greatly enhances heat transfer. As a result, slip at a wall-fluid interface could have a two fold affect on heat transfer in droplet based thermal systems; the first is a direct result of thermal slip at the fluid-wall interface, the second is due to hydrodynamic slip at the interface which leads to reduction of internal circulation and in turn reduction in heat transfer. In this paper molecular dynamic simulations are used to look at the effects of thermal and hydrodynamic slip separately and then to investigate the cumulative effect of them on heat transfer in moving droplets in a microchannel. The affect of hydrodynamic slip in an isothermal channel is studied and it is observed that circulation is inversely dependent on slip length. A simple model is established that captures this effect and it also shows that the effect of slip on circulation only becomes important when the length scale of the problem is comparable to the order of slip length.

Slip at the triple contact point in two phase flow in microchannels

Over the past two decades several studies have been conducted to understand the molecular mechanism of slip in fluids at the boundary and to better understand the movement of triple contact point in two phase flows. The paper studies this problem and investigates the cause and effects of the moving contact point. The results indicates that miscibility between the two fluids, hydrophobicity between fluid and wall, and the shear rate of the fluid are some of the fundamental parameters that determine the amount of slip at the triple contact point. Circulation inside a droplet and slip at the fluid-fluid interface are correlated and interlinked with the motion of a dynamic contact line. Knowing how these phenomenons affect contact line motion is required for a better understanding of the movement of triple contact point in two phase flow. This information would aide in developing a slip model for the triple contact point in a two phase flow.