Evgeniy Shapiro

In Situ Fabrication of Cross-Linked Protein Membranes by Using Microfluidics

We report a novel technique for preparing cross‐linked protein membranes within microchannels by using an interfacial cross‐linking reaction. Glass microchannels with a Y input were assembled by using a simple adhesive bonding technique to achieve dual, parallel laminar flows. Membrane formation utilised an interfacial reaction at the liquid–liquid interface, which involved bovine serum albumin (aqueous solution with a flow rate of 300 μL min−1) and terephthaloyl chloride (xylene solution with a flow rate of 700 μL min−1), to form thin (∼25 μm) cross‐linked films along the length of the channel under the continuous pressure‐driven laminar flow. Such microfabricated membranes could extend the separation potential of any microfluidic structure to provide a stable barrier layer. Furthermore, degradation of the membrane was possible by using an alkali sodium dodecyl sulfate solution, which led to the complete disappearance of the membrane. These membranes could facilitate additional modification to allow for different permeability properties by controlled degradation. The one‐step in situ membrane‐fabrication methodology reported here generated precisely localised membranes and avoided the complexities of subcomponent assembly, which require complicated alignment of small, preformed membranes. This methodology could become the basis for sophisticated microseparation systems, biosensors and several “lab‐on‐a‐chip” devices.

Mesoscale flow and heat transfer modelling and its application to liquid and gas flows

Advances in micro and nanofluidics have influenced technological developments in several areas, including materials, chemistry, electronics and bio-medicine. The phenomena observed at micro and nanoscale are characterised by their inherent multiscale nature. Accurate numerical modelling of these phenomena is the cornerstone for enhancing the applicability of micro and nanofluidics in the industrial environment. We investigated different strategies for applying macroscopic boundary conditions to microscopic simulations. Continuous rescaling of atomic velocities and velocity distribution functions, such as Maxwell-Boltzmann or Chapman-Enskog, were investigated. Simulations were performed for problems involving liquids and gases under different velocity and temperature conditions. The results revealed that the selection of the most suitable method is not a trivial issue and depends on the nature of the problem, availability of computational resource and accuracy requirement.

An Efficient Multi-Scale Modelling Approach for ssDNA Motion in Fluid Flow

The paper presents a multi-scale modelling approach for simulating macromolecules in fluid flows. Macromolecule transport at low number densities is frequently encountered in biomedical devices, such as separators, detection and analysis systems. Accurate modelling of this process is challenging due to the wide range of physical scales involved. The continuum approach is not valid for low solute concentrations, but the large timescales of the fluid flow make purely molecular simulations prohibitively expensive. A promising multi-scale modelling strategy is provided by the meta-modelling approach considered in this paper. Meta-models are based on the coupled solution of fluid flow equations and equations of motion for a simplified mechanical model of macromolecules. The approach enables simulation of individual macromolecules at macroscopic time scales. Meta-models often rely on particle-corrector algorithms, which impose length constraints on the mechanical model. Lack of robustness of the particle-corrector algorithm employed can lead to slow convergence and numerical instability. A new FAst Linear COrrector (FALCO) algorithm is introduced in this paper, which significantly improves computational efficiency in comparison with the widely used SHAKE algorithm. Validation of the new particle corrector against a simple analytic solution is performed and improved convergence is demonstrated for ssDNA motion in a lid-driven micro-cavity.

Linear stability of ice growth under a gravity-driven water film

In this paper we consider linear stability of ice growth under a gravity-driven water film on a sloping wall. First, we derive an analytic solution of the stability problem in the long-wave limit, which shows that the presence of the ice layer generates an additional wave mode. Further, using a long-wave solution as an initial guess, we find the additional wave mode in the numerical solution of the complete Orr-Sommerfeld problem and investigate its behavior numerically for a wide range of problem parameters. We show that the ice mode can become unstable even at moderate Reynolds numbers, and that the ice layer alters the behavior of the mode corresponding to the waves on the liquid film surface. We also demonstrate that the presence of the ice layer stabilizes wave disturbances on the water surface and that, depending on the angle of the incline, the critical Reynolds number of the surface mode can be either increased or decreased.

On ice-induced instability in free-surface flows

The problem of stability of a water-coated ice layer is investigated for a free-surface flow of a thin water film down an inclined plane. An asymptotic (double-deck) theory is developed for a flow with large Reynolds and Froude numbers which is then used to investigate linear two-dimensional, three-dimensional and nonlinear two-dimensional stability characteristics. A new mode of upstream-propagating instability arising from the interaction of the ice surface with the flow is discovered and its properties are investigated. In the linear limit, closed-form expressions for the dispersion relation and neutral curves are obtained for the case of Pr= 1. For the general case, the linear stability problem is solved numerically and the applicability of the solution with Pr= 1 is analysed. Nonlinear double-deck equations are solved with a novel global-marching-type scheme and the effects of nonlinearity are investigated. An explanation of the physical mechanism leading to the upstream propagation of instability waves is provided.

Microfluidic Cell Optimization for Polymer Membrane Fabrication

Dual-fluid laminar flow in microchannels can be utilised through microfabrication to create polymer membranes at the interface between aqueous and organic solutions. In order to enable smooth membrane growth it is necessary not only to maintain a stable interface between the aqueous and organic phase, but also to minimise near-wall stresses, which affect membrane attachment at the initial stages of membrane formation. The characteristics of the dual-fluid flow in the entrance region of the micro-channel can be significantly affected by the geometry of the inlet and flow rates involved. We present a numerical study of the effects of the inlet geometry on the flow development and near-wall stresses in xylene/water flows, which represent the initial stages of nylon 6,6 membrane formation on the interface between an aqueous solution of hexamethylenediamine and adipoyl chloride solution in xylene. The shape of the inlets considered here varies from a T-inlet (90 degrees inlet angles) to an M-inlet (0 degrees inlet angles). We show that although higher flow rates are needed in order to contain reagents to the narrow region near the interface, the increase of the flow rate leads to significant increase of the shear stresses with the maximum values being obtained in the entrance region thus preventing membrane attachment. CFD validation against experimental data for rhodamine diffusion broadening in a microfluidic is also presented.Copyright

On the patterns of interaction between shear and interfacial modes in plane air–water Poiseuille flow

The current work deals with the numerical analysis of linear stability problems in a stratified plain Poiseuille flow of air over water with equal layer heights. The interaction and branch exchange between Tollmien–Schlichting instability in air and interfacial instability is discovered and investigated. This effect is shown to stabilize disturbances with wavelengths of the order of channel height for interfacial waves and to produce a closed stable region inside the neutral curve of the interfacial mode. The behaviour of three unstable modes in the problem, corresponding to Tollmien–Schlichting type instability in air and water layers and interfacial instability respectively, has been studied in detail. Neutral conditions for all three modes and the stable region have been calculated.

Mechanical behaviour of DNA molecules—Elasticity and migration

A novel multi-scale simulation method developed to describe mesoscale phenomena occurring in biofluidic devices is presented. The approach combines the macro-scale modelling of the carrier fluid and the micro-scale description of the transported macromolecules or compounds. Application of the approach is demonstrated through mesoscale simulations of DNA molecules. The investigated phenomena include elastic relaxation of dsDNA molecules and migration of ssDNA molecules in a microchannel flow. The results of the first study demonstrate that the elastic behaviour of the DNA molecules can be captured sucessfully. The second study proves that the migration of ssDNA in pressure-driven microchannel flows can be explained by the hydrodynamic interaction with the carrier liquid.

Comparison of High‐order Finite Volume and Discontinuous Galerkin Methods on 3D Unstructured Grids

The paper presents a direct comparison of convergence properties of finite volume and discontinuous Galerkin methods of the same nominal order of accuracy. Convergence is evaluated on tetrahedral grids for an advection equation and manufactured solution of Euler equations. It is shown that for the test cases considered, the discontinuous Galerkin discretisation tends to recover the asymptotic range of convergence on coarser grids and yields a lower error norm by comparison with the finite volume discretisation.

FALCO: Fast Linear Corrector for Modelling DNA-Laden Flows

The paper concerns the development of a numerical algorithm for improving the efficiency of computational fluid dynamics simulations of transport of biomolecules in microchannels at low number densities. For this problem, the continuum approach based on the concentration field model becomes invalid, whereas time scales involved make purely molecular simulations prohibitively computationally expensive. In this context, meta-models based on coupled solution of fluid flow equations and equations of motion for a simplified mechanical model of biomolecules provide a viable alternative. Meta-models often rely on particle-corrector algorithms, which impose length constraints on the mechanical DNA model. Particle-corrector algorithms are not sufficiently robust, thus resulting in slow convergence. A new geometrical particle corrector algorithm — called FALCO — is proposed in this paper, which significantly improves computational efficiency in comparison with the widely used SHAKE algorithm. It is shown that the new corrector can be related to the SHAKE algorithm by an appropriate choice of Lagrangian multipliers. Validation of the new particle corrector against a simple analytic solution is performed and the improved convergence is demonstrated for a macromolecule motion in a micro-cavity. This work has been supported in part by the European Commission under the 6th Framework Program (Project: DINAMICS, NMP4-CT-2007-026804).Copyright