Unified slip boundary condition for fluid flows

Abstract

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 Maxwell's 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.

Role of the rate of surface dilatation in determining microscopic dynamic contact angle

“…The presence of linear strain rate is further evident on looking at the tangential component of fluid velocity, next to the wall ( figure 7(a)). In line with previous numerical (Denniston & Robbins, 2001;Thalakkottor & Mohseni, 2016;Qian et al, 2003) and experimental (Rathnasingham & Breuer, 2003) findings, a sharp increase in slip is observed in the vicinity of the contact point. As a result of slip, there is an increase in the magnitude of the tangential component of linear strain rate (du/dx) near the moving contact line ( figure 7(b)).…”

“…The occurrence of linear strain rate (du/dx) in the vicinity of the contact line, leads to an increase in linear stress (P xx ) along the interface, see figure 8(a). The existence of a gradient in linear strain rate (or convective acceleration) and linear stress, in the vicinity of the contact line, and its importance in accurately defining the slip boundary condition have been discussed by Thalakkottor & Mohseni (2016) and Qian et al (2003), respectively. The gradient in linear stress, increases the anisotropy of the stress tensor (P xx = P yy ).…”

Nonequilibrium molecular dynamics simulations of nanoconfined fluids at solid-liquid interfaces

“…18,[35][36][37][38] Thus, a constant temperature is maintained along the channel (see Appendix A). With the Langevin thermostat, the total force acting on the kth atom is…”

Moving contact lines and dynamic contact angles: a ‘litmus test’ for mathematical models, accomplishments and new challenges

“…Very soon it has been shown [27] that it is the no-slip condition that is responsible for the singularity and that any slip condition used instead makes shear stress integrable [28]. Furthermore, as it turned out, the form of the slip condition has an asymptotically vanishing effect on the flow in the far field, i.e., on the scale large compared with the size of the region near the contact line where no slip is replaced by slip [28], whilst the far-field flow is that described by Huh and Scriven. This happy outcome provided a fertile ground for many theoretical exercises [29][30][31][32][33][34][35][36] all proposing, again and again, the 'right' slip conditions and then applying the result to model problems. Sometimes, a slip condition is not even formulated in its mathematical form, and the proposed model is numerical from the start, with the singularity removed via mesh-dependent 'numerical slip' implicitly built into the discretization of the problem [37,38].…”