Numerical analysis and computational testing of a high accuracy Leray‐deconvolution model of turbulence

We study a computationally attractive algorithm (based on an extrapolated Crank‐Nicolson method) for a recently proposed family of high accuracy turbulence models, the Leray‐deconvolution family. First we prove convergence of the algorithm to the solution of the Navier‐Stokes equations and delineate its (optimal) accuracy. Numerical experiments are presented which confirm the convergence theory. Our 3d experiments also give a careful comparison of various related approaches. They show the combination of the Leray‐deconvolution regularization with the extrapolated Crank‐Nicolson method can be more accurate at higher Reynolds number that the classical extrapolated trapezoidal method of Baker (Report, Harvard University, 1976). We also show the higher order Leray‐deconvolution models (e.g. N = 1,2,3) have greater accuracy than the N = 0 case of the Leray‐α model. Numerical experiments for the 2d step problem are also successfully investigated. Around the critical Reynolds number, the low order models inhibit vortex shedding behind the step. The higher order models, correctly, do not. To estimate the complexity of using Leray‐deconvolution models for turbulent flow simulations we estimate the models' microscale.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008     

Measurement of dynamical forces between deformable drops using the atomic force microscope. I. Theory

Recent experimental developments have enabled the measurement of dynamical forces between two moving liquid drops in solution using an atomic force microscope (AFM). The drop sizes, interfacial tension, and approach velocities used in the experiments are in a regime where surface forces, hydrodynamics, and drop deformation are all significant. A detailed theoretical model of the experimental setup which accounts for surface forces, hydrodynamic interactions, droplet deformation, and AFM cantilever deflection has been developed. In agreement with experimental observations, the calculated force curves show pseudo-constant compliance regions due to drop flattening, as well as attractive pull-off forces due mainly to hydrodynamic lubrication forces.     

Prototyping disposable electrophoresis microchips with electrochemical detection using rapid marker masking and laminar flow etching

Two novel methods are described for the fabrication of components for microchip capillary electrophoresis with electrochemical detection (microchip CEEC) on glass substrates. First, rapid marker masking is introduced as a completely nonphotolithographic method of patterning and fabricating integrated thin-film metal electrodes onto a glass substrate. The process involves applying the pattern directly onto the metal layer with a permanent marker that masks the ensuing chemical etch. The method is characterized, and the performance of the resulting electrode is evaluated using catecholamines. The response compares well with photolithographically defined electrodes and exhibits detection limits of 648 nM and 1.02 microM for dopamine and catechol, respectively. Second, laminar flow etching is introduced as a partially nonphotolithographic method of replicating channel networks onto glass substrates. The replication process involves applying a poly(dimethylsiloxane) (PDMS) mold of the channel network onto a slide coated with a sacrificial metal layer and then pulling solutions of metal etchants through the channels to transfer the pattern onto the sacrificial layer. The method is tested, and prototype channel networks are shown. These methods serve to overcome the time and cost involved in fabricating glass-based microchips, thereby making the goal of a disposable high performance lab-on-a-chip more attainable.     

Transient responses of a wetting film to mechanical and electrical perturbations

This article reports real-time observations and detailed modeling of the transient response of thin aqueous films bounded by a deformable surface to external mechanical and electrical perturbations. Such films, tens to hundreds of nanometers thick, are confined between a molecularly smooth mica plate and a deformable mercury/electrolyte interface on a protuberant drop at a sealed capillary tube. When the mercury is negatively charged, the water forms a wetting film on mica, stabilized by electrical double layer forces. Mechanical perturbations are produced by driving the mica plate toward or by retracting the mica plate from the mercury surface. Electrical perturbations are applied to change the electrical double layer interaction between the mica and the mercury by imposing a step change of the bias voltage between the mercury and the bulk electrolyte. A theoretical model has been developed that can account for these observations quantitatively. Comparison between experiments and theory indicates that a no-slip hydrodynamic boundary condition holds at the molecularly smooth mica/electrolyte surface and at the deformable mercury/electrolyte interface. An analysis of the transient response based on the model elucidates the complex interplay between disjoining pressure, hydrodynamic forces, and surface deformations. This study also provides insight into the mechanism and process of droplet coalescence and reveals a novel, counterintuitive mechanism that can lead to film instability and collapse when an attempt is made to thicken the film by pulling the bounding mercury and mica phases apart.     

Drainage of the air-water-quartz film: experiments and theory

Experimental results of the kinetics of drainage of the trapped water film between an approaching air bubble and a quartz plate have been analysed using recent theoretical advances in formulating and solving the flow problem in deformable films. Excellent agreement is obtained between experimental data and a model that assumes the bubble-water interface is tangentially immobile in its hydrodynamic response. The coupling between hydrodynamic pressure, disjoining pressure and film deformation is critical in determining the dynamic behaviour of the drainage process. The Reynolds parallel film model that omits the effects of film deformation predicts results that are qualitatively incorrect.     

Protective effects of extracts and flavonoids isolated from Scutia buxifolia Reissek against chromosome damage in human lymphocytes exposed to hydrogen peroxide

Flavonoids are claimed to protect against cardiovascular disease, certain forms of cancer and ageing, possibly by preventing initial DNA damage. Therefore, we investigated the protective effects of crude extract, ethyl acetate fraction and flavonoids (quercetin, quercitrin, isoquercitrin and rutin) isolated from the leaves from Scutia buxifolia against chromosome damage induced by H?O? in human lymphocytes by analyzing cellular growth rate, cell viability, mitotic index and chromosomal instability. We found a differential response among the compounds tested, with the ethyl acetate fraction being more effective than the crude extract, a difference perhaps related to the presence of the antioxidants identified and quantified by HPLC/DAD. In general, quercetin, isoquercitrin and rutin recovered the mitotic index and chromosomal instability more than quercitrin after treatment with hydrogen peroxide.     

Numerical study of a regularized barotropic vorticity model of geophysical flow

We study a Crank–Nicolson in time, finite element in space, numerical scheme for a Bardina regularization of the barotropic vorticity (BV) model. We derive the regularized model from the simplified Bardina model in primitive variables, present a numerical algorithm for it, and prove the algorithm is unconditionally stable with respect to the timestep size and optimally convergent in both space and time. Numerical experiments are provided that verify the theoretical convergence rates, and also that test the model/scheme on a benchmark double‐gyre wind forcing experiment. For the latter test, we find the proposed model/scheme gives a good coarse mesh approximation to the highly resolved direct numerical simulation of the BV model, and compares favorably to related regularization model results. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1492–1514, 2015     

Surveying FDA-approved drugs as new potential inhibitors of N-cadherin protein: a virtual screening approach

Since N-cadherin protein plays a remarkable role in cancer metastasis and tumor growth and progression, finding new effective inhibitors of this protein can be of high importance in cancer treatment. Nevertheless, few molecules have been introduced to inhibit N-cadherin protein to date. In this work, in order to find and present potent inhibitors, 3358 FDA-approved small molecules were docked against N-cadherin protein. All complexes with binding energy ??9 to ??8 kcal/mol were selected for protein-ligand interaction analysis. In the following, Tanimoto coefficient (T_c) was calculated for those molecules that established appropriate interactions with N-cadherin in order to compute the similarity score between them. Afterwards, molecular dynamics simulation and free energy calculations were done to estimate the stability and ability of the chosen ligands in complex with the target protein. Finally, seven small molecules among 3358 FDA-approved were suggested as potential inhibitors of N-cadherin protein.

     

Theory of non-equilibrium force measurements involving deformable drops and bubbles

Over the past decade, direct force measurements using the Atomic Force Microscope (AFM) have been extended to study non-equilibrium interactions. Perhaps the more scientifically interesting and technically challenging of such studies involved deformable drops and bubbles in relative motion. The scientific interest stems from the rich complexity that arises from the combination of separation dependent surface forces such as Van der Waals, electrical double layer and steric interactions with velocity dependent forces from hydrodynamic interactions. Moreover the effects of these forces also depend on the deformations of the surfaces of the drops and bubbles that alter local conditions on the nanometer scale, with deformations that can extend over micrometers. Because of incompressibility, effects of such deformations are strongly influenced by small changes of the sizes of the drops and bubbles that may be in the millimeter range. Our focus is on interactions between emulsion drops and bubbles at around 100 μm size range. At the typical velocities in dynamic force measurements with the AFM which span the range of Brownian velocities of such emulsions, the ratio of hydrodynamic force to surface tension force, as characterized by the capillary number, is ~ 10^{− 6} or smaller, which poses challenges to modeling using direct numerical simulations. However, the qualitative and quantitative features of the dynamic forces between interacting drops and bubbles are sensitive to the detailed space and time-dependent deformations. It is this dynamic coupling between forces and deformations that requires a detailed quantitative theoretical framework to help interpret experimental measurements. Theories that do not treat forces and deformations in a consistent way simply will not have much predictive power. The technical challenges of undertaking force measurements are substantial. These range from generating drop and bubble of the appropriate size range to controlling the physicochemical environment to finding the optimal and quantifiable way to place and secure the drops and bubbles in the AFM to make reproducible measurements. It is perhaps no surprise that it is only recently that direct measurements of non-equilibrium forces between two drops or two bubbles colliding in a controlled manner have been possible. This review covers the development of a consistent theory to describe non-equilibrium force measurements involving deformable drops and bubbles. Predictions of this model are also tested on dynamic film drainage experiments involving deformable drops and bubbles that use very different techniques to the AFM to demonstrate that it is capable of providing accurate quantitative predictions of both dynamic forces and dynamic deformations. In the low capillary number regime of interest, we observe that the dynamic behavior of all experimental results reviewed here are consistent with the tangentially immobile hydrodynamic boundary condition at liquid–liquid or liquid–gas interfaces. The most likely explanation for this observation is the presence of trace amounts of surface-active species that are responsible for arresting interfacial flow.