Recent experiments on transient disturbance growth in boundary layers indicate that disturbances generated by surface roughness undergo suboptimal growth. The implication is that the receptivity mechanism governing the distribution of disturbance energy among the continuous spectrum of damped Orr-Sommerfeld/Squire modes produces energy distributions that are significantly different from the theoretical optimum. Experiments presented here are intended to investigate how the amplitude and diameter of cylindrical roughness elements arranged in a spanwise array affect various features of transient growth. The objective is to infer how or to what extent the roughness features affect the continuous spectrum and to use this information as a foundation for future receptivity models. The results show that the energy of stationary disturbances varies as Re k 2 and that the streamwise distance over which the disturbances grow increases slightly with increasing Re k . As the roughness diameter is varied, dramatic changes in the qualitative nature of the resulting transient growth occur. Both the variation of the growth length with Re k and the behavioral changes with roughness diameter indicate that the energy distribution among the continuous modes is a strong function of roughness features and that an accurate and sophisticated receptivity model will be necessary to accurately predict transient growth.

The role of surface roughness in boundary layers continues to be a topic of significant interest, especially with regard to how controlled roughness might be used to delay laminar-to-turbulent transition. Although it may be useful for control, large-amplitude roughness may itself lead to transition. In an effort to understand the breakdown mechanics associated with large-amplitude surface roughness, experiments are conducted to investigate the steady and unsteady disturbances generated by three-dimensional roughness elements whose amplitudes are close to the critical roughness-based Reynolds number Re k for roughness-induced transition. Measurements are obtained in a flat-plate boundary layer downstream of a spanwise array of cylindrical roughness elements at both subcritical and supercritical values of Re k . The steady disturbance field has strong shear in the wall-normal and spanwise directions, and the unsteady streamwise velocities in the roughness elements' wake show evidence of hairpin vortices. The locations of maximum fluctuation intensity correspond to the locations of inflection points in the steady flow streamwise velocity, and this suggests that the fluctuations may result from a Kelvin-Helmholtz-type instability. Temporal power spectra indicate an unstable band of frequencies from 300 to 800 Hz. The Strouhal number associated with the 650-Hz fluctuations that are often observed to be the strongest give Sr = 0.15, a value that is in good agreement with previous findings. At supercritical Re k , rapid transition takes place when the unsteady disturbances reach nonlinear amplitudes. The disturbance growth rates indicate that in this situation transition can be understood as a competition between the unsteady disturbance growth and the rapid relaxation of the steady flow that tends to stabilize these disturbances. NomenclatureD = roughness diameter E = steady disturbance energy e f = unsteady disturbance energy in a frequency band centered at f f = frequency H = shape factor, δ * /θ k = roughness height N = number of samples Re k = roughness-based Reynolds number,Ū (k)k/ν Re = unit Reynolds number, U ∞ /ν Sr = Strouhal number of unsteady vortex shedding, f δ * /U ∞ U = spanwise-invariant streamwise basic state velocity U = steady streamwise disturbance velocity U ∞ = freestream velocity u = unsteady streamwise disturbance velocity x, y, z = streamwise, wall-normal, and spanwise coordinates x k = streamwise location of the roughness array α = spatial growth rate δ = boundary-layer length scale, [(x − x vle )/Re ] 1/2 δ * = displacement thickness λ k = roughness spacing η = Blasius coordinate, y/δ θ = momentum thickness ν = kinematic viscosity Subscripts c = centerline crit = critical rms = root-mean-square

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Micro-convection caused by ponderomotive forces of the self-magnetic field of a magnetic fluid in the Hele-Shaw cell under the action of a vertical homogeneous magnetic field is studied both experimentally and numerically. It is shown that a non-potential magnetic force at magnetic Rayleigh numbers greater than the critical value causes fingering at the interface between the miscible magnetic and non-magnetic fluids. The threshold value of the magnetic Rayleigh number depends on the smearing of the interface between fluids. Fingering with its subsequent decay due to diffusion of particles significantly increases the mixing at the interface. Velocity and vorticity fields at fingering are determined by particle image velocimetry measurements and qualitatively correspond well to the results of numerical simulations of the micro-convection in the Hele-Shaw cell carried out in the Darcy approximation, which account for ponderomotive forces of the self-magnetic field of the magnetic fluid. Gravity plays an important role at the initial stage of the fingering observed in the experiments.

Highly monodispersed emulsions can be produced in microfluidic flow-focusing junctions (Anna et al 2003 Appl. Phys. Lett. 82 364–6, Baroud et al 2010 Lab Chip 10 2032–45). This is the reason why many industrial processes in the medical industry among others are based on droplet manipulation and involve at some point a step of dripping within a junction. However, only a few studies have focused on the flow field inside and outside the droplet, even though it is a necessary step for understanding the physical mechanism involved and for modeling the droplet formation process. Water-in-oil emulsions are produced in flow-focusing junctions of square cross sections. The fluids constituting the emulsion are (i) a 5.0 mPa·s silicon oil for the oil phase and (ii) distilled water containing 2.0 wt% of sodium dodecyl sulfate surfactant for the aqueous phase. Time-resolved shadow particle images are acquired using a microscale particle image velocimetry (µPIV) system and flow fields are calculated using an adaptive PIV algorithm in combination with dynamic masking. Inside the microchannel and in the permanent regime, the droplet has an internal circulation that has been well established by Sarrazin et al (AICHE J. 52 4061–70). But during the formation of a droplet in a flow-focusing junction, the flow field is not so well known, and the circulation in the finger flows forward along the sides and returns along the center. The mechanism can be described in terms of four distinct steps: droplet growth, necking, rupture, and recoil. The liquid expelled from the neck just before rupture is also well observed. The flow field and mixing are measured in detail during a complete cycle of formation of a main droplet and satellite droplets using high-speed imaging. This allows us to develop a better understanding of the different forces that are present and of the physical mechanism of droplet formation.