Challenges of modelling the moving contact line problem and recent progress: bridging scales from the nano- to the macroscale

Monday, March 26, 2018 - 9:40am - 10:10am
Lind 305
Serafim Kalliadasis (Imperial College London)
The moving contact line problem occurs when modelling one fluid replacing another as it moves along a solid surface, a situation widespread throughout industry and nature. Classically, the no-slip boundary condition at the solid substrate, a zero-thickness interface between the fluids, and motion at the three-phase contact line are incompatible - leading to the well-known shear-stress singularity. At the heart of the problem is its multiscale nature: a nanoscale region close to the solid boundary where the continuum hypothesis breaks down, must be resolved before effective macroscale parameters such as contact line friction and slip, often adopted to alleviate the singularity [1], can be obtained.

Here we will review recent progress made by our group and ongoing work to rigorously analyse the moving contact line problem and related physics from the nano- to macroscopic lengthscales. Specifically, to capture nanoscale properties very close to the contact line and to establish a link to the macroscale behaviour, we employ elements from the statistical mechanics of classical fluids, namely density-functional theory (DFT) [2,3]. We formulate a new and general dynamic DFT (DDFT) [4] that carefully and systematically accounts for the fundamental elements of any classical fluid and soft matter system, a crucial step towards the accurate and predictive modelling of physically relevant systems. In a certain limit, our DDFT reduces to a non-local Navier-Stokes-like equation [5]. Work analysing the contact line in both equilibrium and dynamics using this equation will be presented [6,7]. A key property captured by our theory is the fluid layering at the wall-fluid interface. We demonstrate that the stratified fluid structure in the vicinity of the wall has a large effect on the compression and shearing properties of the fluid and determines the width of the shear region, in which effective slip is generated. In contrast, the region where compressive effects dominate is determined by the liquid-vapour interface width. We also scrutinize the effect of stratification on contact line friction and the dependence of the latter on the imposed temperature of the fluid [8].

Selected references

[1] D.N. Sibley, A. Nold and S. Kalliadasis 2015 The asymptotics of the moving contact line: cracking an old nut, J. Fluid Mech. 764, 445-462.
[2] P. Yatsyshin, N. Savva and S. Kalliadasis 2015 Wetting of prototypical one- and two-dimensional systems:
Thermodynamics and density functional theory, J. Chem. Phys. 142, Art. No. 034708.
[3] P. Yatsyshin, A.O. Parry and S. Kalliadasis 2016 Complete prewetting, J. Phys.: Condens. Matter 28, Art. No. 275001.
[4] B.D. Goddard, A. Nold, N. Savva, G.A. Pavliotis and S. Kalliadasis 2012 General dynamical density functional theory for classical fluids, Phys. Rev. Lett. 109, Art. No. 120603.
[5] B.D. Goddard, A. Nold, N. Savva, P. Yatsyshin and S. Kalliadasis 2013 Unification of dynamic density functional theory for colloidal fluids to include inertia and hydrodynamic interactions: derivation and numerical experiments, J. Phys.: Condens. Matter 25, Art. No. 035101.
[6] A. Nold, D.N. Sibley, B.D. Goddard and S. Kalliadasis 2014 Fluid structure in the immediate vicinity of an equilibrium three-phase contact line and assessment of disjoining pressure models using density functional theory, Phys. Fluids 26, Art. No. 072001.
[7] A. Nold, D.N. Sibley, B.D. Goddard and S. Kalliadasis 2015 Nanoscale fluid structure of liquid-solid-vapor contact lines for a wide range of contact angles, Math. Model. Nat. Phenom. 10, 111-125.
[8] A. Nold, PhD Thesis, Imperial College London (2016).

[Joint work with Benjamin D. Goddard (Edinburgh University), Andreas Nold (Max Planck Institute for Brain Research), Nikos Savva (Cardiff University), David N. Sibley (Loughborough University) and Peter Yatsyshin (Imperial College)]