The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

The dynamics and stability of thin liquid films have fascinated scientists over many decades: the observations of regular wave patterns in film flows down a windowpane or along guttering, the patterning of dewetting droplets, and the fingering of viscous flows down a slope are all examples that are familiar in daily life. Thin film flows occur over a wide range of length scales and are central to numerous areas of engineering, geophysics, and biophysics; these include nanofluidics and microfluidics, coating flows, intensive processing, lava flows, dynamics of continental ice sheets, tear-film rupture, and surfactant replacement therapy. These flows have attracted considerable attention in the literature, which have resulted in many significant developments in experimental, analytical, and numerical research in this area. These include advances in understanding dewetting, thermocapillary- and surfactant-driven films, falling films and films flowing over structured, compliant, and rapidly rotating substrates, and evaporating films as well as those manipulated via use of electric fields to produce nanoscale patterns. These developments are reviewed in this paper and open problems and exciting research avenues in this thriving area of fluid mechanics are also highlighted.

Dynamics and stability of thin liquid films

This article reports on the International Nanofluid Property Benchmark Exercise, or INPBE, in which the thermal conductivity of identical samples of colloidally stable dispersions of nanoparticles or “nanofluids,” was measured by over 30 organizations worldwide, using a variety of experimental approaches, including the transient hot wire method, steady-state methods, and optical methods. The nanofluids tested in the exercise were comprised of aqueous and nonaqueous basefluids, metal and metal oxide particles, near-spherical and elongated particles, at low and high particle concentrations. The data analysis reveals that the data from most organizations lie within a relatively narrow band (±10% or less) about the sample average with only few outliers. The thermal conductivity of the nanofluids was found to increase with particle concentration and aspect ratio, as expected from classical theory. There are (small) systematic differences in the absolute values of the nanofluid thermal conductivity among the various experimental approaches; however, such differences tend to disappear when the data are normalized to the measured thermal conductivity of the basefluid. The effective medium theory developed for dispersed particles by Maxwell in 1881 and recently generalized by Nan et al. [J. Appl. Phys. 81, 6692 (1997)], was found to be in good agreement with the experimental data, suggesting that no anomalous enhancement of thermal conductivity was achieved in the nanofluids tested in this exercise.

A Benchmark Study on the Thermal Conductivity of Nanofluids

Ice formation can have catastrophic consequences for human activity on the ground and in the air. Here we investigate water freezing delays on untreated and coated surfaces ranging from hydrophilic to superhydrophobic and use these delays to evaluate icephobicity. Supercooled water microdroplets are inkjet-deposited and coalesce until spontaneous freezing of the accumulated mass occurs. Surfaces with nanometer-scale roughness and higher wettability display unexpectedly long freezing delays, at least 1 order of magnitude longer than typical superhydrophobic surfaces with larger hierarchical roughness and low wettability. Directly related to the main focus on heterogeneous nucleation and freezing delay of supercooled water droplets, the observed ensuing crystallization process consisted of two distinct phases: one very rapid recalescent partial solidification phase and a subsequent slower phase. Observations of the droplet collision process employed for the continuous liquid mass accumulation up to the poin...

Are superhydrophobic surfaces best for icephobicity

The surface and interfaces of heterogeneous catalysts are essential to their performance as they are often considered to be active sites for catalytic reactions. With the development of nanoscience, the ability to tune surface and interface of nanostructures has provided a versatile tool for the development and optimization of a heterogeneous catalyst. In this Review, we present the surface and interface control of nanoparticle catalysts in the context of oxygen reduction reaction (ORR), electrochemical CO2 reduction reaction (CO2 RR), and tandem catalysis in three sections. In the first section, we start with the activity of ORR on the nanoscale surface and then focus on the approaches to optimize the performance of Pt-based catalyst including using alloying, core-shell structure, and high surface area open structures. In the section of CO2 RR, where the surface composition of the catalysts plays a dominant role, we cover its reaction fundamentals and the performance of different nanosized metal catalysts. For tandem catalysis, where adjacent catalytic interfaces in a single nanostructure catalyze sequential reactions, we describe its concept and principle, catalyst synthesis methodology, and application in different reactions.

/pdf/surface-and-interface-control-in-nanoparticle-catalysis-zdt0m6gwi0.pdf

Surface and Interface Control in Nanoparticle Catalysis.

In this paper we study the melting of a spherical nanoparticle. To match with experimental data, the model includes several new features such as size-dependent latent heat and a cooling boundary condition at the boundary. Melt temperature variation and density change are also included. A novel form of Stefan condition is used to determine the position of the melt front. Results show that melting times can be significantly faster than those predicted by previous theoretical models, primarily due to the latent heat variation.

A Model for Nanoparticle Melting with a Newton Cooling Condition and Size-Dependent Latent Heat

Systematic asymptotic methods are used to formulate a model for the extensional flow of a thin sheet of nematic liquid crystal. With no external body forces applied, the model is found to be equivalent to the so-called Trouton model for Newtonian sheets (and fi bers), albeit with a modi fied "Trouton ratio". However, with a symmetry-breaking electric field gradient applied, behavior deviates from the Newtonian case, and the sheet can undergo fi nite-time breakup if a suitable destabilizing field is applied. Some simple exact solutions are presented to illustrate the results in certain idealized limits, as well as sample numerical results to the full model equations.

Extensional flow of nematic liquid crystal under electric field gradient

Environmental applications of adsorption technology: From the experimental research to the mathematical modeling of the breakthrough curves

A mathematical model is developed for the two-dimensional flow of an incompressible Newtonian fluid which is being squeezed between two rigid, impermeable plates. The fluid viscosity varies linearly with temperature. The model is intended to elucidate a problem of air bubble entrapment which arises in the manufacture of panel material, particularly in the manufacture of ‘corner’ profiles. The results show that when the two plates have the same shape, the pressure gradient is such that bubbles are likely to be expelled throughout the contact, except in the central region. When a corner profile is manufactured it is likely that bubbles will be retained, thereby leading to flaws in the final product.

Variable viscosity squeeze films and bubble removal in the manufacture of panel material

In this paper we use the cellular automaton (CA) approach to model one-dimensional binary diffusion in solids. Employing a very simple state change rule we define an asynchronous CA model and take its continuum limit to obtain the governing equations of the problem. We show that in the limit where the number of cells tends to infinity the CA model approaches a continuous model derived in previous work. Thus, showing that the CA approach provides a new, simple method to study and model binary diffusion.

Cellular automaton model for substitutional binary diffusion in solids.

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