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Fluid flow at the macroscale, as in water through a pipe, is typically dominated by physical processes in the bulk of the fluid. What goes on at the surfaces confining the material is normally of little interest and is hidden inside a simple boundary condition that assumes no slip. Near an interface and at the nanoscale, however, where the surface-to-volume ratio is much larger than commonly encountered, the story is not always so simple. An international research collaboration* has now investigated the case in which the applied stresses are weak and linked to the liquid/air surface tension. The researchers have put in evidence a molecular adsorption mechanism on atomically smooth surfaces which drastically alters the interaction between the flowing liquid and the bounding solid. These works were published on March 21st in the journal Nature Communications.
As a result of transient chain adsorption, slip lengths obtained in dewetting and levelling experiments can differ by orders of magnitude between experiments, even for the same liquids and the same surfaces
Wolfgang Pauli suggested that the devil invented surfaces, where e.g. matter from the outside world can play havoc on the no-slip boundary condition described above. The recent work of Ilton and co-workers harnesses this havoc, leading to a new appreciation of polymer flow at the nanoscale and near surfaces.
At the nanoscale, and near a solid substrate, what is the boundary condition that should be assumed? In 1823, Navier surmised that this question could be answered by Newton, who taught us in his third law about action-reaction force pairs. Navier postulated that the stress at the solid/liquid boundary should thus be continuous, with the stress in the liquid at the interface being equal to that on the solid. Writing down the stresses there, Navier introduced a so-called slip length which characterizes in terms of a length scale the strength of flow at the surface through a typical ratio: that of the liquid/liquid friction, or the viscosity, and the solid/liquid friction. Putting in typical numbers, it is found that slip lengths are normally just a couple of nanometres for simple fluids. So, as we already saw for large scale flows, the slip length is so small typically that we can normally consider that there is no flow at the boundary. This was then the condition that was assumed for about a century and a half.
The pitch-drop experiment example
In the mid-twentieth century, polymer materials were industrialized and device miniaturization became more and more important and lucrative. Polymer molecules are extended in space and tend to overlap strongly with one another in a material, like long, entangled spaghetti noodles after they are cooked. In the 60’s and 70’s, Edwards and de Gennes determined that as a result of this molecular entanglement, polymer liquids could have comparatively huge viscosities. A striking illustration is the pitch-drop experiment at the University of Queensland, Australia. This experiment has been running since 1927, and the flowing polymeric liquid involved has been shown to have a viscosity 100 billion times that of water. Given that Navier’s stress balance is dependent on the viscosity, the “negligible slip length” statement clearly needed to be revisited for polymeric liquids.
Inspired by industrial polymer flows involving surfaces, de Gennes noted indeed that Navier’s stress balance could lead to slip lengths as large as a few hundred micrometres, orders of magnitude larger than the smaller, nanometric slip lengths expected for non-macromolecular liquids. This would however be the case only for so-called ideal surfaces, with which the molecules have no interaction. Modern surface science has allowed for the creation of such surfaces, which are atomically smooth and typically hydrophobic (that is, interacting weakly with the liquid resting on top of the surface). In 2009, Bäumchen and co-workers employed experiments in which liquid polymer films drying off (termed “dewetting”) of those ideal substrates were shown to exhibit the huge slip lengths predicted by de Gennes a couple of decades earlier. The typical stresses involved in these experiments were a bit violent, approaching the pressure of the atmosphere.
The recently published study by Ilton and co-workers used a new experimental approach in which a non-uniform liquid-film topography smooths out due to surface tension. In these new experiments, data from the same liquids and the same surfaces as in the 2009 work are found to be at odds with the predictions of de Gennes and the results of the Bäumchen dewetting studies. Here, the authors invoked “Pauli’s principle” described in the first paragraph. The stresses applied in these surface relaxation experiments are much weaker (typically two orders of magnitude) than in the dewetting experiments, even while both of the flows are driven by surface tension. In their rationalization of the data, Ilton et al. considered that the surfaces used —even though atomically smooth and well described as ideal for the dewetting experiments— could actually “hang on” flowing molecules and thus slow them down. This molecular adsorption caused orders of magnitude deviations in the slip lengths measured, which could be understood in the context of a model that assumes few polymer chains transiently attached to the surface. The picture that has emerged is not one of the existence of a simple passive solid, but one in which the substrate responds differently under different experimental conditions. If pushed weakly enough, these atomically smooth substrates can hold the flowing molecules; yet a harder push as in a dewetting experiment makes the molecules slide along the substrate easily. These results fuel the active ongoing research about molecular effects in nanoscale flows.
*The collaboration comprises researchers from McMaster University in Canada, the LOMA laboratory (University of Bordeaux / CNRS), the Gulliver laboratory (ESPCI Paris-PSL University / CNRS), the Department of Physics of Ecole Normale Supérieure, and the Max Planck Institute for Dynamics and Self Organisation in Germany.
Associated Publication :
Adsorption-induced slip inhibition for polymer melts on ideal substrates, Ilton et al., Nature Communications 2018
DOI: 10.1038/s41467-018-03610-4
https://www.nature.com/articles/s41467-018-03610-4
Recently published:
Surface energy of strained amorphous solids, Schulman et al., Nature communications (2018) 9 : 982
doi:10.1038/s41467-018-03346-1
https://www.nature.com/articles/s41467-018-03346-1
This work sheds new fundamental light on the understanding of amorphous solid surfaces, and their interaction with liquids.
Researchers contact
Joshua McGraw : joshua.mcgraw@espci.fr
Elie Raphaël : elie.raphael@espci.fr
Thomas Salez : thomas.salez@u-bordeaux.fr