Journal

~ The factors determining the degree of dynamic wetting, which is characterized by the microscopic dynamic contact angle, have been the subject of much discussion. In this manuscript, it is analytically determined that the microscopic dynamic contact angle is dependent on the rate of surface dilatation in addition to the thermodynamic surface tension. It is argued that, in the vicinity of a moving contact line, this rate of surface dilatation results in a disparity between the thermodynamic and mechanical surface tensions, which are almost always assumed to be equal. It is also found that, in the case of forced wetting, the difference between the receding and advancing contact angles is primarily due to the rate of surface compression at the receding contact line and the rate of surface expansion at the advancing contact line. These findings, which are validated using molecular dynamics simulations, demonstrate that surface dilatation is an important factor responsible for the deviation of the microscopic dynamic contact angle from its static equilibrium value.

~ 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.

~ Internal recirculation in a moving droplet, enforced by the presence of fluid–fluid interfaces, plays an important role in several dropletbased microfluidic devices as it could enhance mixing, heat transfer, and chemical reaction. The effect of slip on droplet circulation is studied for two canonical steadystate problems: twophase Couette, boundarydriven, and Poiseuille, pressure/body forcedriven, flows. A simple model is established to estimate the circulation in a droplet and capture the effect of slip and aspect ratio on the droplet circulation. The circulation in a droplet is shown to decrease with increasing slip length in the case of a boundarydriven flow, while for a body force driven flow it is independent of slip length. Scaling parameters for circulation and slip length are identified from the circulation model. The model is validated using continuum and molecular dynamics (MD) simulations. The effect of slip at the fluid–fluid interface on circulation is also briefly discussed. The results suggest that active manipulation of velocity slip, e.g., through actuation of hydrophobicity, could be employed to control droplet circulation and consequently its mixing rate.

~ Molecular dynamics (MD) simulation is used to study slip at the fluidsolid boundary in an unsteady flow based on the Stokes’ second problem. An increase in slip is observed in comparison to the steady flow for shear rates below the critical shear rate of the corresponding steady flow. This increased slip is attributed to fluid inertial forces not represented in a steady flow. An unsteady mathematical 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 at the wall. By writing acceleration in terms of shear rate, it is shown that slip at the wall in unsteady flows is governed by the gradient of shear rate and shear rate of the fluid. Nondimensionalizing the model gives a time dependent yet universal curve, independent of wallfluid properties, which can be used to find the slip boundary condition at the fluidsolid interface based on the information of shear rate, gradient of shear rate of the fluid, and the instant of time during the cycle. A governing nondimensional number, defined as the ratio of phase speed to speed of sound, is identified to help in explaining the mechanism responsible for the transition of slip boundary condition from finite to a perfect slip and determining when this would occur. Phase lag in fluid velocity relative to wall is observed. The lag increases with decreasing time period of wall oscillation and increasing wall hydrophobicity. The phenomenon of hysteresis is seen when looking into the variation of slip velocity as a function of wall velocity and slip velocity as a function of fluid shear rate. The cause for hysteresis is attributed to the unsteady inertial forces of the fluid. The rate of heat generated by viscous shear is compared for an unsteady Stokes’ second problem and simple Couette flow and is shown to be higher for the unsteady flow.
Conference
 Accurate Representation of the Moving Contact Line and Interfacial Dynamics in Multiphase Flows
J. J. Thalakkottor and K. Mohseni, ASME Fluids Engineering Summer Conference (FEDSM) , Orlando, FL, 1216 July, 2020. (Accepted)  Continuum implementation of the unified slip boundary condition and microscopic dynamic contact angle for multiphase flows
J. J. Thalakkottor and B. Aboulhasanzadeh and K. Mohseni, 32nd Symposium on Naval Hydrodynamics , Hamburg, Germany, 510 August 2018.  A generalized model for dynamic contact angle
J. J. Thalakkottor and K. Mohseni, ASME Fluids Engineering Summer Conference (FEDSM) , Waikoloa, HI, July 30August 3, 2017.  A Universal Slip Boundary Condition for a FluidSolid Interface and its Implementation in a Continuum Solver
J. J. Thalakkottor and K. Mohseni, 31st Symposium on Naval Hydrodynamics , Monterrey, CA, 1116 September 2016.  Velocity and thermal slip at the moving contact line
J. J. Thalakkottor and K. Mohseni, 15th IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (ITherm) , 11391142, Las Vegas, NV, May 313 June 2016.  Stress dependent slip boundary condition for singleand twophase fluid flow on a substrate
J. J. Thalakkottor and K. Mohseni, 53rd AIAA Aerospace Sciences Meeting , AIAA paper 20151280, Kissimmee, FL, 59 January 2015.  Modeling slip at triple contact point in two phase flow
J. J. Thalakkottor and K. Mohseni, 52nd AIAA Aerospace Sciences Meeting , AIAA paper 20140067, National Harbor, MD, 1317 January 2014.  Effect of hydrodynamic and thermal slip on droplet based thermal management systems
J. J. Thalakkottor and K. Mohseni, 14th IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (ITherm) , Orlando, FL, 2730 May 2014.  Slip at the triple contact point in two phase flows in microchannels
J. J. Thalakkottor and K. Mohseni, 43rd AIAA Fluid Dynamics Conference , AIAA paper 20132974, San Diego, CA, 2427 June 2013.  Analysis of slip in a flow with an oscillating wall
J. J. Thalakkottor and K. Mohseni, 42nd AIAA Fluid Dynamics Conference , AIAA paper 20123158, New Orleans, LA, 2528 June 2012.
Talks
 Interfaces with mass: applications to vortex sheet dynamics and slip boundary conditions in viscous flows
A. C. DeVoria and J. J. Thalakkottor and K. Mohseni, The second joint SIAM/CAIMS annual meeting , Toronto, Canada, 610 July, 2020.  The disparity between thermodynamic and mechanical surface tension in the vicinity of the moving contact line
J. J. Thalakkottor and K. Mohseni, 72nd Annual Meeting of the APS DFD , P36.00001, Seattle, WA, November 2019.  Continuum explanation of the cause of slip at an interface
J. J. Thalakkottor and K. Mohseni, 71st Annual Meeting of the APS DFD , E07.00004, Atlanta, GA, November 2018.  The role of convective acceleration in determining the velocity and dynamic angle at the contact line
J. J. Thalakkottor and K. Mohseni, 70th Annual Meeting of the APS DFD , D38.00006, Denver, CO, November 2017.  The unified slip boundary condition: addressing the breakdown of the noslip boundary condition
J. J. Thalakkottor and K. Mohseni, 69th Annual Meeting of the APS DFD , G22.00003, Portland OR, November 2016.  A Universal Stress Dependent Slip Boundary Condition for Steady Fluid Flows
J. J. Thalakkottor and K. Mohseni, AIChE Annual Meeting , 591g, Salt Lake City, UT, November 2015.  Analysis of slip boundary condition in single and multiphase flows
J. J. Thalakkottor and K. Mohseni, 65th Annual Meeting of the APS DFD , BAPS.2012.DFD.M11.9, San Deigo, CA, November 2012  Moleculary dynamics simulation of flow in a channel with oscillating walls
J. J. Thalakkottor and K. Mohseni, 64th Annual Meeting of the APS DFD , BAPS.2011.DFD.M26.4, Baltimore, MD, November 2011