Understanding the evolution of complex multiscale systems: Dynamic renormalization, non-equilibrium entropy and stochasticity

June 2013 - We have developed a novel methodology that enables the study the complex dynamics of dissipative systems characterized from the very beginning by dissipation of energy at any relevant scales. By means of a generic reduced equation which is also computationally efficient we tackle a fundamental problem in science and engineering: Many time-dependent problems are generally too complex to be fully resolved and hence some information (degrees of freedom) needs to be neglected. A central question is then how can one systematically and reliably reduce the complexity of such high-dimensional systems without neglecting essential information. Popular examples of this are models for weather and climate prediction, cell biology processes, non-linear networks, or economics. Phys. Rev. Lett. paper [pdf]

Dynamics of moving contact lines and diffuse interfaces

January 2015 - We revisited the classical matched asymptotic analysis of the moving contact line problem. The main result was to show that the inner and outer regions can match without the need for an intermediate region, as e.g. in the classical Hocking-Cox analysis. This new asymptotic framework was successfully exemplified in a wide spectrum of moving contact line problems. Not only we clarified the classical Hocking-Cox analysis which is cumbersome and difficult to implement in practice, but it also provided an elegant correction to a problem that has been treated incorrectly for several decades. J. Fluid Mech. paper [pdf]
July 2014 - We examine the nanoscale behavior of an equilibrium three-phase contact line in the presence of long-ranged intermolecular forces by employing a statistical mechanics of fluids approach, namely, density functional theory (DFT) together with fundamental measure theory (FMT). This enables us to evaluate the predictive quality of effective Hamiltonian models in the vicinity of the contact line. The work was selected in the Research Highlights from Physics of Fluids. Phys. Fluids paper [link]
February 2013 - For solid-liquid-gas systems the seminal study of Seppecher is often referred to when suggesting that diffuse-interface models resolve the moving contact line singularity. Whilst Seppecher’s work contains some discussion of the asymptotics, the analysis was largely incomplete, with asymptotic regions being probed without careful justification and the crucial behaviour close to the contact line only investigated numerically (a number of constraints were also imposed, e.g. 90° contact angles and fluids of equal viscosity). Moreover, Seppecher’s study has some errors in the solution forms given in an intermediate region (where the classical equations are assumed to hold). We demonstrated analytically that a diffuse-interface model can alleviate the moving contact line singularity with no-slip applied. The model also allows for rolling motion (due to mass transfer through the contact line through diffusion)  and microscopic contact angle variation dependent on flow conditions. E. Phys. J. E. paper [pdf]

Statistical mechanics of inhomogeneous classical fluids and dynamic density-functional theory (DDFT)

June 2016 - We generalised the dynamic DFT framework to systems of anisotropic particles to take into account both inertia and hydrodynamic interactions. Starting from the Liouville equation and utilising Zwanzig’s projection-operator techniques, we derived the kinetic equation for the Brownian particle distribution function, eventually obtaining a DDFT equation by utilising the tools of statistical mechanics. Whilst this equation has some similarities with previous DDFTs, it involves a translational-rotational coupling which affects the diffusivity of the (asymmetric) particles. Moreover, in the overdamped (high friction) limit, we recover a prefect agreement with previous DDFTs. J. Stat. Phys. paper [pdf]
June 2016 - Using microscopic classical density functional theory to model systems with realistic Lennard-Jones fluid–fluid and fluid–substrate intermolecular potentials, we unveiled continuous interfacial transitions, analagous to two-dimensional complete wetting, associated with the first-order prewetting line, which can occur on steps, patterned walls, grooves and wedges, and which are sensitive to both the range of the intermolecular forces and interfacial fluctuation effects.  The work was highlighted (link here) by the reviewers as being particularly significant to the community and featured at JPhys+ blog. J. Phys.: Condens. Matter paper [pdf]
February 2013 - In a very recent effort we have discovered and fully characterise a new phase transition in confined fluids. It is driven purely by geometry and we have referred to it as “capillary prewetting”. Phys. Rev. E paper [pdf]
December 2012 - The recent breakthrough here was to unify previous DDFTs and to rigorously formulate a general DDFT that takes into account inertia and hydrodynamic interactions, the combined effect of which was neglected in previous theories, even though they strongly influence non-equilibrium properties of the system. The work was highlighted as a labtalk news article for J. Phys.: Condens. Matter, as well as for inclusion in IOPselect. Phys. Rev. Lett. paper [pdf] J. Phys.: Condens. Matter paper [pdf] SIAM Multiscale Model. Simul. paper [pdf]
December 2011 - In a related project we showed that although DFT is a microscopic approach, it allows for the construction of a macroscopic quantity such as contact angle and hence it could offer a bridge between the micro-scale and macroscale in the moving contact line problem. J. Fluid Mech. paper [pdf]

Upscaling of the Cahn-Hilliard (CH) equation for interfacial dynamics in perforated/strongly heterogeneous domains

October 2012 - An effective macroscopic CH equation for such domains was derived rigorously by homogenisation theory for the first time. Our results were applied to wetting dynamics in porous media and to a single channel with strongly heterogeneous walls, also justifying rigorously phenomenological phase-field models introduced previously on an ad-hoc basis. Classical results such as Taylor-Aris dispersion are simple byproducts of our analysis. Proc. R. Soc. A paper [pdf]

Multiscale analysis and stochastic PDEs

October 2015 - We systematically developed a new framework and novel techniques for extracting coarse-grained models from time series with multiscale structure. Analysing complex phenomena from historical data comprises a tremendous challenge, since available data is often insufficient either because of the rare-event nature of the process or the coexistence of multiple time scales. A theoretical-computational framework capable of providing a systematic and rational estimation of relevant statistical quantitites was developed. The framework was tested with a wide spectrum of examples (from marine biology to paleoclimatic data), showing the accuracy and reliability of the algorithm, which obtained unbiased estimates. Phys. Rev. E. paper [pdf], J. Comp. Phys. paper [pdf], Multiscale Model. Simul paper [pdf]
February 2011 - We analysed the effects of noise on the long-term dynamics of spatially extended systems and showed that depending on the strength of noise, such systems can undergo several non-trivial state transitions including on-off intermittency and stabilised states. Phys. Rev. Lett. paper [pdf]

Contact line motion over random spatially heterogeneous substrates

February 2010 - We proved rigorously for the first time that the classical "Wenzel law", according to which substrate roughness enhances wetting, is in fact incorrect. Phys. Rev. Lett. paper [pdf]