The effect of an insoluble surfactant on the stability of two-layer viscous flow in an inclined channel confined by two parallel walls is considered. A lubrication-flow model applicable to long waves and low-Reynolds-number-flow is developed, and pertinent nonlinear evolution equations for the interface position and surfactant concentration are derived. Linear stability analysis based on the lubrication-flow model and the inclusive equations of Stokes flow confirm the recent findings of Frenkel & Halpern (2002) and Halpern & Frenkel (2003) that the presence of an insoluble surfactant induces a Marangoni instability in certain regions of parameter space defined by the layer thickness and viscosity ratios. Numerical simulations based on both approaches show that the interfacial waves may grow and saturate into steep profiles. The lubrication-flow model is adequate in capturing the essential features of the instability for small and moderate wavenumbers.

The effect of an insoluble surfactant on the stability of the gravity-driven flow of a liquid film down an inclined plane is investigated by a normal-mode analysis. Numerical solutions of the Orr–Sommerfeld equation reveal the occurrence of a stable Marangoni mode and a possibly unstable Yih mode, and demonstrate that the primary role of the surfactant is effectively to raise the critical Reynolds number at which instability is first encountered.

Using micro-sized channels to manipulate fluids is the essence of microfluidics which has wide applications from analytical chemistry to material science and cell biology research.Recently, using microfluidic-based devices for pharmaceutical research, in particular for the fabrication of micro-and nano-particles, has emerged as a new area of interest. The particles that can be prepared by microfluidic devices can range from micron size droplet-based emulsions to nano-sized drug loaded polymeric particles. Microfluidic technology poses unique advantages in terms of the high precision of the mixing regimes and control of fluids involved in formulation preparation. As a result of this, monodispersity of the particles prepared by microfluidics is often recognised as being a particularly advantageous feature in comparison to those prepared by conventional large-scale mixing methods. However, there is a range of practical drawbacks and challenges of using microfluidics as a direct micron-and nano-particle manufacturing method. Technological advances are still required before this type of processing can be translated for application by the pharmaceutical industry. This review focuses specifically on the application of microfluidics for pharmaceutical solid nanoparticle preparation and discusses the theoretical foundation of using the nanoprecipitation principle to generate particles and how this is translated into microfluidic design and operation.

The gravity-driven flow of a liquid film down an inclined wall with periodic indentations in the presence of a normal electric field is investigated. The film is assumed to be a perfect conductor, and the bounding region of air above the film is taken to be a perfect dielectric. In particular, the interaction between the electric field and the topography is examined by predicting the shape of the film surface under steady conditions. A nonlinear, non-local evolution equation for the thickness of the liquid film is derived using a long-wave asymptotic analysis. Steady solutions are computed for flow into a rectangular trench and over a rectangular mound, whose shapes are approximated with smooth functions. The limiting behaviour of the film profile as the steepness of the wall geometry is increased is discussed. Using substantial numerical evidence, it is established that as the topography steepness increases towards rectangular steps, trenches, or mounds, the interfacial slope remains bounded, and the film does not touch the wall. In the absence of an electric field, the film develops a capillary ridge above a downward step and a slight depression in front of an upward step. It is demonstrated how an electric field may be used to completely eliminate the capillary ridge at a downward step. In contrast, imposing an electric field leads to the creation of a free-surface ridge at an upward step. The effect of the electric field on film flow into relatively narrow trenches, over relatively narrow mounds, and down slightly inclined substrates is also considered.

A sequence of increasingly refined interpolation grids over the triangle is proposed, with the goal of achieving uniform convergence and ensuring high interpolation accuracy. The number of interpolation nodes, N , corresponds to a complete mth-order polynomial expansion with respect to the triangle barycentric coordinates, which arises by the horizontal truncation of the Pascal triangle. The proposed grid is generated by deploying Lobatto interpolation nodes along the three edges of the triangle, and then computing interior nodes by averaged intersections to achieve threefold rotational symmetry. Numerical computations show that the Lebesgue constant and interpolation accuracy of the proposed grid compares favorably with those of the best-known grids consisting of the Fekete points. Integration weights corresponding to the set of Lobatto triangle base points are tabulated.