Microfluidic valves for flow control at low Reynolds numbers

Fluidics is a technology of generating and controlling fluid flows — preferably without the action of mechanical moving components. Microfluidics perform these tasks in small, typically micronsized structures. Essential part of almost all microfluidic systems are flow control valves. The basic problem is the low Reynolds numberRe: inertial effects used in large-scale fluidics are too small relative to viscous dissipation. New approaches, such as pressure or electrokinetic driving are required. In the subdynamic, viscosity dominated flow regime, Re ceases to be of importance and for pressure-driven valves a new characterisation number was to be introduced. An example of a diverter valve, developed by the author, is described and the meaning of the new dimensionless parameter is demonstrated.     

Stationary shapes of deformable particles moving at low Reynolds numbers

We introduce an iterative solution scheme in order to calculate stationary shapes of deformable elastic capsules which are steadily moving through a viscous fluid at low Reynolds numbers. The iterative solution scheme couples hydrodynamic boundary integral methods and elastic shape equations to find the stationary axisymmetric shape and the velocity of an elastic capsule moving in a viscous fluid governed by the Stokes equation. We use this approach to systematically study dynamical shape transitions of capsules with Hookean stretching and bending energies and spherical resting shape sedimenting under the influence of gravity or centrifugal forces. We find three types of possible axisymmetric stationary shapes for sedimenting capsules with fixed volume: a pseudospherical state, a pear-shaped state, and buckled shapes. Capsule shapes are controlled by two dimensionless parameters, the Föppl-von-Kármán number characterizing the elastic properties and a Bond number characterizing the driving force. For increasing gravitational force the spherical shape transforms into a pear shape. For very large bending rigidity (very small Föppl-von-Kármán number) this transition is discontinuous with shape hysteresis. The corresponding transition line terminates, however, in a critical point, such that the discontinuous transition is not present at typical Föppl-von-Kármán numbers of synthetic capsules. In an additional bifurcation, buckled shapes occur upon increasing the gravitational force.     

A microfluidic rectifier: anisotropic flow resistance at low Reynolds numbers

It is one of the basic concepts of Newtonian fluid dynamics that at low Reynolds number (Re) the Navier-Stokes equation is linear and flows are reversible. In microfluidic devices, where Re is essentially always low, this implies that flow resistance in microchannels is isotropic. Here we present a microfluidic rectifier: a microscopic channel of a special shape whose flow resistance is strongly anisotropic, differing by up to a factor of 2 for opposite flow directions. Its nonlinear operation at arbitrary small Re is due to non-Newtonian elastic properties of the working fluid, which is a 0.01% aqueous solution of a high molecular weight polymer. The rectifier works as a dynamic valve and may find applications in microfluidic pumps and other integrated devices.     

Effective swimming strategies in low Reynolds number flows

The optimal strategy for a microscopic swimmer to migrate across a linear shear flow is discussed. The two cases, in which the swimmer is located at large distance, and in the proximity of a solid wall, are taken into account. It is shown that migration can be achieved by means of a combination of sailing through the flow and swimming, where the swimming strokes are induced by the external flow without need of internal energy sources or external drives. The structural dynamics required for the swimmer to move in the desired direction is discussed and two simple models, based respectively on the presence of an elastic structure, and on an orientation dependent friction, to control the deformations induced by the external flow, are analyzed. In all cases, the deformation sequence is a generalization of the tank-treading motion regimes observed in vesicles in shear flows. Analytic expressions for the migration velocity as a function of the deformation pattern and amplitude are provided. The effects of thermal fluctuations on propulsion have been discussed and the possibility that noise be exploited to overcome the limitations imposed on the microswimmer by the scallop theorem have been discussed.     

Insulation room for aero-acoustic experiments at moderate Reynolds and low Mach numbers

A non-expensive insulation box for aero-acoustic experiments at moderate Reynolds numbers Re < 2 × 10⁴ and low Mach numbers M < 0.2 is presented. Its performance is evaluated with particular attention to unwanted noise sources inherent to the flow facility. Objective acoustic parameters of the insulation box are assessed.     

Direct simulations of trailing-edge noise generation from two-dimensional airfoils at low Reynolds numbers

The aeroacoustic sound generated from the flow around two NACA four-digit airfoils is investigated numerically, at relatively low Reynolds numbers that do not prompt boundary-layer transition. By using high-order finite-difference schemes to discretize compressible Navier–Stokes equations, the sound scattered on airfoil surface is directly resolved as an unsteady pressure fluctuation. As the wavelength of an emitted noise is shortened compared to the airfoil chord, the diffraction effect on non-compact chord length appears more noticeable, developing multiple lobes in directivity. The instability mechanism that produces sound sources, or unsteady vortical motions, is quantitatively examined, also by using a linear stability theory. While the evidence of boundary-layer instability waves is captured in the present result, the most amplified frequency in the boundary shear layer does not necessarily agree with the primary frequency of a trailing-edge noise, when wake instability is dominant in laminar flow. This contradicts the observation of other trailing-edge noise studies at higher Reynolds numbers. However, via acoustic disturbances, the boundary-layer instability may become more significant, through the resonance with the wake instability, excited by increasing a base-flow Mach number. Evidence suggests that this would correspond to the onset of an acoustic feedback loop. The wake-flow frequencies derived by an absolute-instability analysis are compared with the frequencies realized in flow simulations, to clarify the effect of an acoustic feedback mechanism, at a low Reynolds number.     

Axisymmetric bubble pinch-off at high Reynolds numbers

Analytical considerations and potential-flow numerical simulations of the pinch-off of bubbles at high Reynolds numbers reveal that the bubble minimum radius, rn, decreases as tau proportional to r2n sqrt[1lnr2n], where tau is the time to break up, when the local shape of the bubble near the singularity is symmetric. However, if the gas convective terms in the momentum equation become of the order of those of the liquid, the bubble shape is no longer symmetric and the evolution of the neck changes to a rn proportional to tau1/3 power law. These findings are verified experimentally.     

Turbulent pipe flow at extreme Reynolds numbers

Both the inherent intractability and complex beauty of turbulence reside in its large range of physical and temporal scales. This range of scales is captured by the Reynolds number, which in nature and in many engineering applications can be as large as 10(5)-10(6). Here, we report turbulence measurements over an unprecedented range of Reynolds numbers using a unique combination of a high-pressure air facility and a new nanoscale anemometry probe. The results reveal previously unknown universal scaling behavior for the turbulent velocity fluctuations, which is remarkably similar to the well-known scaling behavior of the mean velocity distribution.     

Characteristics of a hyperboloid-flare configuration at high Reynolds numbers

Results on a hyperboloid-flare model tested in a new hypersonic wind tunnel with adiabatic compression AT-303 based at ITAM SB RAS at M_∞ = 10 and 15 and in a wide range of Reynolds numbers are presented. Pressure and heat-flux distributions along the model are compared with data obtained previously in various European hypersonic wind tunnels (Longshot — Belgium, HEG — Germany) and with results of numerical computations. Pressure and heat-flux coefficients measured in the attached flow region are demonstrated to be in good qualitative agreement. Reasons for the differences in results measured in regions of flow separation and reattachment are discussed. Significant viscous effects on characteristics of the flow around the model are demonstrated; a particularly strong effect is exerted on the heat-flux distribution. This fact confirms that it is important to model real Reynolds numbers in wind-tunnel testing of aerospace plane models.     

Turbulence regeneration in pipe flow at moderate Reynolds numbers

We present the results of an experimental investigation into the nature and structure of turbulent pipe flow at moderate Reynolds numbers. A turbulence regeneration mechanism is identified which sustains a symmetric traveling wave within the flow. The periodicity of the mechanism allows comparison to the wavelength of numerically observed exact traveling wave solutions and close agreement is found. The advection speed of the upstream turbulence laminar interface in the experimental flow is observed to form a lower bound on the phase velocities of the exact traveling wave solutions. Overall our observations suggest that the dynamics of the turbulent flow at moderate Reynolds numbers are governed by unstable nonlinear traveling waves.     

Mixing in a T-shaped micromixer at moderate Reynolds numbers

In the present work, the regimes of the flow and mixing of fluids in a T-shaped micromixer in the range of the Reynolds numbers from 1 to 1000 are investigated systematically with the aid of numerical modeling. The flow and mixing regimes are shown to alter substantially with increasing Reynolds numbers. Five different flow regimes have been identified in the total. The dependencies of the friction coefficient and mixing efficiency on the Reynolds number are obtained. A sharp increase in the mixing efficiency at a flow transition from the symmetric to asymmetric steady regime is shown. On the other hand, the mixing efficiency slightly drops in the laminar-turbulent transition region. A substantial influence of the slip presence on walls on flow structure in the channel and mixing efficiency has been revealed.     

A circle swimmer at low Reynolds number

Swimming in circles occurs in a variety of situations at low Reynolds number. Here we propose a simple model for a swimmer that undergoes circular motion, generalising the model of a linear swimmer proposed by Najafi and Golestanian (Phys. Rev. E 69, 062901 (2004)). Our model consists of three solid spheres arranged in a triangular configuration, joined by two links of time-dependent length. For small strokes, we discuss the motion of the swimmer as a function of the separation angle between its links. We find that swimmers describe either clockwise or anticlockwise circular motion depending on the tilting angle in a non-trivial manner. The symmetry of the swimmer leads to a quadrupolar decay of the far flow field. We discuss the potential extensions and experimental realisation of our model.     

Minimal polar swimmer at low Reynolds number

We propose a minimal model for a polar swimmer, consisting of two spheres connected by a rigid slender arm, at low Reynolds number. The propulsive velocity for the proposed model is the maximum for any swimming cycle with the same variations in its two degrees of freedom and its displacement in a cycle is achieved entirely in one step. The stroke averaged flow field generated by the contractile swimmer at large distances is found to be dipolar. In addition, the changing radius of one of the spheres generates the field of a potential doublet centered at its initial position.     

Aerodynamics of re-entry vehicles at real values of Reynolds numbers

Results of an experimental study of aerodynamic characteristics of models of two hypersonic re-entry vehicles (ARES-H aerospace demonstrator proposed by EADS-ST and EXPERT re-entry capsule proposed by ESA ESTEC) are presented. The experiments were performed in a new wind tunnel AT-303 at ITAM SB RAS in the range of free-stream Mach numbers M = 10–18 at real values of Reynolds numbers. The test results and specific features of wind-tunnel tests in conical nozzles are discussed.     

Wake-boundary layer interaction behind an elliptic cylinder at different Reynolds numbers

In this paper, hot-wire anemometry (HWA) is used to experimentally investigate interactions between a fully developed turbulent boundary layer and wake of an elliptic cylinder where axis ratio (AR) of the cylinder is 2. The elliptic cylinder was located inside and outside a turbulent boundary layer with a thickness (δ) of 0.38B. Furthermore, experiments were conducted at different Reynolds numbers (13,250 and 26,500) based upon the smallest cylinder diameter (B). Mean velocity, turbulence intensity and higher-order central moments of velocity signals (i.e. skewness and flatness) measurements were performed using HWA upon wake-boundary layer interactions on a flat plate. Results showed that profiles of stream-wise mean velocity and turbulence intensity were greatly dependent on gap ratio (G/B) and Reynolds number (Re) in near-wake region. It was also observed that, except for G/B = 0.1, the wake-boundary layer interactions were faster at Reynolds number of 26,500 rather than 13,250. The interactions occurred earlier upon fluctuating the velocity rather than the case where a fixed mean velocity was considered. The results further show that an increase in the gap ratio increases Strouhal number almost independent of δ/B. Behind the cylinder, relatively smaller wake region was obtained at Re = 26,500 rather than Re = 13,250, where the velocity profiles quickly converged to the flat plate boundary layer velocity profiles.