Robert W. Barber

Bio: Robert W. Barber is an academic researcher from Daresbury Laboratory. The author has contributed to research in topics: Knudsen number & Slip (materials science). The author has an hindex of 21, co-authored 70 publications receiving 1948 citations. Previous affiliations of Robert W. Barber include Science and Technology Facilities Council.

Velocity boundary condition at solid walls in rarefied gas calculations

Abstract: Maxwell's famous slip boundary condition is often misapplied in current rarefied gas flow calculations (e.g., in hypersonics, microfluidics). For simulations of gas flows over curved or moving surfaces, this means crucial physics can be lost. We give examples of such cases. We also propose a higher-order boundary condition based on Maxwell's general equation and the constitutive relations derived by Burnett. Unlike many other higher-order slip conditions these are applicable to any form of surface geometry. It is shown that these "Maxwell-Burnett" boundary conditions are in reasonable agreement with the limited experimental data available for Poiseuille flow and can also predict Sone's thermal-stress slip flow - a phenomenon which cannot be captured by conventional slip boundary conditions.

Continuous cell washing and mixing driven by an ultrasound standing wave within a microfluidic channel

Abstract: Ultrasound standing wave radiation force and laminar flow have been used to transfer yeast cells from one liquid medium to another (washing) by a continuous field-flow fractionation (FFF) approach. Two co-flowing streams, a cell-free suspending phase (flow rate > 50% of the total flow-through volume) and a yeast suspension, were introduced parallel to the nodal plane of a 3 MHz standing wave resonator. The resonator was fabricated to have a single pressure nodal plane at the centre line of the chamber. Laminar flow ensured a stable interface was maintained as the two suspending phases flowed through the sound field. Initiation of the ultrasound transferred cells to the cell-free phase within 0.5 s. This particle transfer procedure circumvents the pellet formation and re-suspension steps of centrifuge based washing procedures. In addition, fluid mixing was demonstrated in the same chamber at higher sound pressures. The channel operates under negligible back-pressure (cross-section, 0.25 × 10 mm) and with only one flow convergence and one flow division step, the channel cannot be easily blocked. The force acting on the cells is small; less than that experienced in a centrifuge generating 100g. The acoustically-driven cell transfer and mixing procedures described may be particularly appropriate for the increasingly complex operations required in molecular biology and microbiology and especially for their conversion to continuous flow processes.

Challenges in Modeling Gas-Phase Flow in Microchannels: From Slip to Transition

Abstract: It has long been recognized that the fluid mechanics of gas-phase microflows can differ significantly from the macroscopic world. Non-equilibrium effects such as rarefaction and gas-surface interactions need to be taken into account, and it is well known that the no-slip boundary condition of the Navier-Stokes equations is no longer valid. Following ideas proposed by Maxwell, it is generally accepted that the Navier-Stokes equations can be extended into the slip-flow regime, provided the Knudsen number is less than 10− 1. Improvements in micro-fabrication techniques, however, are now enabling devices to be constructed with sub-micron feature sizes. At this scale, the flow will depart even further from equilibrium and will enter the transition regime. In recent years, there has been considerable success in the implementation of second-order slip-boundary conditions to extend the Navier-Stokes equations into the transition regime. Unfortunately, as yet, no consensus has been reached on the correct form of h...

Capturing Knudsen layer phenomena using a lattice Boltzmann model.

Abstract: In recent years, lattice Boltzmann methods have been increasingly used to simulate rarefied gas flows in microscale and nanoscale devices This is partly due to the fact that the method is computationally efficient, particularly when compared to solution techniques such as the direct simulation Monte Carlo approach However, lattice Boltzmann models developed for rarefied gas flows have difficulty in capturing the nonlinear relationship between the shear stress and strain rate within the Knudsen layer As a consequence, these models are equivalent to slip-flow solutions of the Navier-Stokes equations In this paper, we propose an effective mean-free path to address the Knudsen layer effect, so that the capabilities of lattice Boltzmann methods can be extended beyond the slip-flow regime The model has been applied to rarefied shear-driven and pressure-driven flows between parallel plates at Knudsen numbers between 001 and 1 Our results show that the proposed approach significantly improves the near-wall accuracy of the lattice Boltzmann method and provides a computationally economic solution technique over a wide range of Knudsen numbers

Biomimetic design of microfluidic manifolds based on a generalised Murray's law

Abstract: The relationship governing the optimum ratio between the diameters of the parent and daughter branches in vascular systems was first discovered by Murray using the principle of minimum work. This relationship is now known as Murray's law and states that the cube of the diameter of the parent vessel must equal the sum of the cubes of the daughter vessels. For symmetric bifurcations, an important consequence of this geometric rule is that the tangential shear stress at the wall remains constant throughout the vascular network. In the present paper, we extend this important hydrodynamic concept to arbitrary cross-sections and provide a framework for constructing a simple but elegant biomimetic design rule for hierarchical microfluidic networks. The paper focuses specifically on constant-depth rectangular and trapezoidal channels often employed in lab-on-a-chip systems. To validate our biomimetic design rule and demonstrate the application of Murray's law to microfluidic manifolds, a comprehensive series of computational fluid dynamics simulations have been performed. The numerical predictions are shown to be in very good agreement with the theoretical analysis, confirming that the generalised version of Murray's law can be successfully applied to the design of constant-depth microfluidic devices.

Fast parallel algorithms for short-range molecular dynamics

Abstract: Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Lattice-Boltzmann Method for Complex Flows

Abstract: With its roots in kinetic theory and the cellular automaton concept, the lattice-Boltzmann (LB) equation can be used to obtain continuum flow quantities from simple and local update rules based on particle interactions. The simplicity of formulation and its versatility explain the rapid expansion of the LB method to applications in complex and multiscale flows. We review many significant developments over the past decade with specific examples. Some of the most active developments include the entropic LB method and the application of the LB method to turbulent flow, multiphase flow, and deformable particle and fiber suspensions. Hybrid methods based on the combination of the Eulerian lattice with a Lagrangian grid system for the simulation of moving deformable boundaries show promise for more efficient applications to a broader class of problems. We also discuss higherorder boundary conditions and the simulation of microchannel flow with finite Knudsen number. Additionally, the remarkable scalability of the LB method for parallel processing is shown with examples. Teraflop simulations with the LB method are routine, and there is no doubt that this method will be one of the first candidates for petaflop computational fluid dynamics in the near future.

Micromachining a miniaturized capillary electrophoresis-based chemical analysis system on a chip

Abstract: Micromachining technology was used to prepare chemical analysis systems on glass chips (1 centimeter by 2 centimeters or larger) that utilize electroosmotic pumping to drive fluid flow and electrophoretic separation to distinguish sample components. Capillaries 1 to 10 centimeters long etched in the glass (cross section, 10 micrometers by 30 micrometers) allow for capillary electrophoresis-based separations of amino acids with up to 75,000 theoretical plates in about 15 seconds, and separations of about 600 plates can be effected within 4 seconds. Sample treatment steps within a manifold of intersecting capillaries were demonstrated for a simple sample dilution process. Manipulation of the applied voltages controlled the directions of fluid flow within the manifold. The principles demonstrated in this study can be used to develop a miniaturized system for sample handling and separation with no moving parts.

Microdroplets in microfluidics: an evolving platform for discoveries in chemistry and biology

Abstract: Microdroplets in microfluidics offer a great number of opportunities in chemical and biological research. They provide a compartment in which species or reactions can be isolated, they are monodisperse and therefore suitable for quantitative studies, they offer the possibility to work with extremely small volumes, single cells, or single molecules, and are suitable for high-throughput experiments. The aim of this Review is to show the importance of these features in enabling new experiments in biology and chemistry. The recent advances in device fabrication are highlighted as are the remaining technological challenges. Examples are presented to show how compartmentalization, monodispersity, single-molecule sensitivity, and high throughput have been exploited in experiments that would have been extremely difficult outside the microfluidics platform.