Combining hydrodynamics and molecular kinetics to predict dewetting between a small bubble and a solid surface

This paper examined the dewetting between a small air bubble and a solid surface in deionised water. Hydrodynamics was used in conjunction with surface molecular kinetics to model and predict the velocity of the moving contact line as a function of the dynamic macroscopic contact angle. The dewetting hydrodynamics was modelled following the approach developed specifically for drops and bubbles using the (absolute) coordinate system with the origin located at the centre of the contact area, which does not move with the moving contact line. The model provides accurate corrections unavailable in the generic hydrodynamic theories developed by Voinov and Cox, and removes the need for a macroscopic length scale employed in their generic theories. Molecular kinetics was used to determine the contact angle of the inner region close to the contact line, where the hydrodynamic approach breaks down due to the singularity. Unlike the generic hydrodynamic theories, the inner (microscopic) angle in our combined model is not a constant (a fitting parameter) but is a function of the moving contact line velocity and other molecular properties of the interfaces. The combined model agreed with the experimental data and produced physically consistent values for the slip length, molecular jumping distance and frequency. The dissolved gases accumulated at the non-wetting solid-liquid interface may influence the slip length.     

XPS study of the major minerals in bauxite: gibbsite, bayerite and (pseudo-)boehmite

Synthetic corundum (Al2O3), gibbsite (Al(OH)3), bayerite (Al(OH)3), boehmite (AlO(OH)) and pseudoboehmite (AlO(OH)) have been studied by high resolution XPS. The chemical compositions based on the XPS survey scans were in good agreement with the expected composition. High resolution Al2p scans showed no significant changes in binding energy, with all values between 73.9 and 74.4 eV. Only bayerite showed two transitions, associated with the presence of amorphous material in the sample. More information about the chemical and crystallographic environment was obtained from the O1s high resolution spectra. Here a clear distinction could be made between oxygen in the crystal structure, hydroxyl groups and adsorbed water. Oxygen in the crystal structure was characterised by a binding energy of about 530.6 eV in all minerals. Hydroxyl groups, present either in the crystal structure or on the surface, exhibited binding energies around 531.9 eV, while water on the surface showed binding energies around 533.0 eV. A distinction could be made between boehmite and pseudoboehmite based on the slightly lower ratio of oxygen to hydroxyl groups and water in pseudoboehmite.     

Generalized Vector Quasivariational Inclusion Problems with Moving Cones

This paper deals with the generalized vector quasivariational inclusion Problem (P₁) (resp. Problem (P₂)) of finding a point (z ₀,x ₀) of a set E×K such that (z ₀,x ₀)∈B(z ₀,x ₀)×A(z ₀,x ₀) and, for all η∈A(z ₀,x ₀),

Galerkin finite element approximation of symmetric space-fractional partial differential equations

In this paper, symmetric space-fractional partial differential equations (SSFPDE) with the Riesz fractional operator are considered. The SSFPDE is obtained from the standard advection-dispersion equation by replacing the first-order and second-order space derivatives with the Riesz fractional derivatives of order 2β ∈ (0, 1) and 2α ∈ (1, 2], respectively. We prove that the variational solution of the SSFPDE exists and is unique. Using the Galerkin finite element method and a backward difference technique, a fully discrete approximating system is obtained, which has a unique solution according to the Lax-Milgram theorem. The stability and convergence of the fully discrete schemes are derived. Finally, some numerical experiments are given to confirm our theoretical analysis.     

Sharp estimates for approximations to a nonlinear backward heat equation

A nonlinear backward heat problem for an infinite strip is considered. The problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. In this paper, we use the Fourier regularization method to solve the problem. Some sharp estimates of the error between the exact solution and its regularization approximation are given.     

A nonlinear parabolic equation backward in time: Regularization with new error estimates

Consider a nonlinear backward parabolic problem in the form

     

Study of Phase Transformation of Guanosine 5′-Monophosphate in Drowning-Out Crystallization

The present study used a mechanistic approach to control the phase transformation of guanosine 5′-monophosphate (GMP) via the operating conditions of agitation and feed concentration during drowning-out crystallization. First, Fourier transform infrared and UV/vis spectrophotometry were successfully applied to monitor the mass fraction of GMP polymorphs (amorphous and hydrate crystalline GMPs) and GMP supersaturation, respectively, during the crystallization. The phase transformation of amorphous GMP into hydrate crystals was significantly influenced by the agitation, which promoted the mass transfer of GMP dissolution and growth. Therefore, the phase transformation was quickly finished when increasing the agitation speed. However, a high agitation caused breakage of the hydrate crystals, resulting in a reduced crystal size with a bimodal distribution. The phase transformation was also influenced by the GMP feed concentration, as the crystal growth was promoted and the crystal size increased when increasing the feed concentration up to 61 g/l. However, a further increase in the feed concentration caused secondary nucleation due to the induction of a high supersaturation level during the phase transformation, leading to a small crystal size with a bimodal distribution. In addition, the rectangular-shaped hydrate GMP crystals exhibited a higher growth rate in the b direction rather than the a direction. Therefore, the crystal morphology shifted from a long rectangle to a square when increasing the feed concentration.     

Bioanalysis in structured microfluidic systems

Microfluidic and lab-on-a-chip devices have attracted widespread interest in separation sciences and bioanalysis. Recent designs in microfluidic devices extend common separation concepts by exploiting new phenomena for molecular dynamics on a length scale of 10 mum and below, giving rise to novel manipulation tools and nonintuitive phenomena for microseparations. Here, we focus on three very recent developments for bioseparations based on tailored microfluidic systems: Single cell navigation, trapping and steering with subsequent on-chip lysis, protein separation and LIF detection (Section 3.1), then we report dielectrophoretic trapping and separation of large DNA fragments in structured microfluidic devices (Section 3.2). Finally, a paradoxial migration phenomenon based on thermal fluctuations, periodically arranged microchannels and a biased alternating current electric field is presented in Section 3.3.     

Endpoint estimates for Riesz transforms of magnetic Schrödinger operators

Let $A=-(\nabla-i\vec{a})^2+VLet be a magnetic Schr?dinger operator acting on L ²(R ⁿ ), n≥1, where and 0≤V∈L ¹ _loc. Following [1], we define, by means of the area integral function, a Hardy space H ¹ _A associated with A. We show that Riesz transforms (∂/∂x _k -i a _k )A ^-1/2 associated with A, , are bounded from the Hardy space H ¹ _A into L ¹. By interpolation, the Riesz transforms are bounded on L ^p for all 1<p≤2.     

Lattices generated by Chip Firing Game models: Criteria and recognition algorithms

It is well-known that the class of lattices generated by Chip Firing Games (CFGs) is strictly included in the class of upper locally distributive lattices (ULD). However a necessary and sufficient criterion for this class is still an open question. In this paper we settle this problem by giving such a criterion. This criterion provides a polynomial-time algorithm for constructing a CFG which generates a given lattice if such a CFG exists. Going further we solve the same problem on two other classes of lattices which are generated by CFGs on the classes of undirected graphs and directed acyclic graphs.