Henrik Bruus

A high‐level programming‐language implementation of topology optimization applied to steady‐state Navier–Stokes flow

We present a versatile high-level programming-language implementation of non-linear topology optimization. Our implementation is based on the commercial software package FEMLAB, and it allows a wide range of optimization objectives to be dealt with easily. We exemplify our method by studies of steady-state Navier–Stokes flow problems, thus extending the work by Borrvall and Petersson on topology optimization of fluids in Stokes flow (Int. J. Num. Meth. Fluids 2003; 41:77–107). We analyse the physical aspects of the solutions and how they are affected by different parameters of the optimization algorithm. A complete example of our implementation is included as FEMLAB code in an appendix. Copyright

Forces acting on a small particle in an acoustical field in a thermoviscous fluid

We calculate the acoustic radiation force from an ultrasound wave on a compressible, spherical particle suspended in a viscous fluid. Using Prandtl-Schlichting boundary-layer theory, we include the kinematic viscosity of the solvent and derive an analytical expression for the resulting radiation force, which is valid for any particle radius and boundary-layer thickness provided that both of these length scales are much smaller than the wavelength of the ultrasound wave (millimeters in water at megahertz frequencies). The acoustophoretic response of suspended microparticles is predicted and analyzed using parameter values typically employed in microchannel acoustophoresis.

Measuring the local pressure amplitude in microchannel acoustophoresis

A new method is reported on how to measure the local pressure amplitude and the Q factor of ultrasound resonances in microfluidic chips designed for acoustophoresis of particle suspensions. The method relies on tracking individual polystyrene tracer microbeads in straight water-filled silicon/glass microchannels. The system is actuated by a PZT piezo transducer attached beneath the chip and driven by an applied ac voltage near its eigenfrequency of 2 MHz. For a given frequency a number of particle tracks are recorded by a CCD camera and fitted to a theoretical expression for the acoustophoretic motion of the microbeads. From the curve fits we obtain the acoustic energy density, and hence the pressure amplitude as well as the acoustophoretic force. By plotting the obtained energy densities as a function of applied frequency, we obtain Lorentzian line shapes, from which the resonance frequency and the Q factor for each resonance peak are derived. Typical measurements yield acoustic energy densities of the order of 10 J/m(3), pressure amplitudes of 0.2 MPa, and Q factors around 500. The observed half wavelength of the transverse acoustic pressure wave is equal within 2% to the measured width w = 377 microm of the channel.

Reexamination of Hagen-Poiseuille flow: Shape dependence of the hydraulic resistance in microchannels

We consider pressure-driven, steady-state Poiseuille flow in straight channels with various cross-sectional shapes: elliptic, rectangular, triangular, and harmonic-perturbed circles. A given shape is characterized by its perimeter P and area A which are combined into the dimensionless compactness number C= P2/A, while the hydraulic resistance is characterized by the well-known dimensionless geometrical correction factor alpha. We find that alpha depends linearly on C, which points out C as a single dimensionless measure characterizing flow properties as well as the strength and effectiveness of surface-related phenomena central to lab-on-a-chip applications. This measure also provides a simple way to evaluate the hydraulic resistance for the various shapes.

Forthcoming Lab on a Chip tutorial series on acoustofluidics: Acoustofluidics—exploiting ultrasonic standing wave forces and acoustic streaming in microfluidic systems for cell and particle manipulation

Forthcoming lab on a chip tutorial series on acoustofluidics : Acoustofluidics - Exploiting ultrasonic standing wave forces and acoustic streaming in microfluidic systems for cell and particle manipulation

Bias and temperature dependence of the 0.7 conductance anomaly in quantum point contacts

The 0.7 (2e^2/h) conductance anomaly is studied in strongly confined, etched GaAs/GaAlAs quantum point contacts, by measuring the differential conductance as a function of source-drain and gate bias as well as a function of temperature. We investigate in detail how, for a given gate voltage, the differential conductance depends on the finite bias voltage and find a so-called self-gating effect, which we correct for. The 0.7 anomaly at zero bias is found to evolve smoothly into a conductance plateau at 0.85 (2e^2/h) at finite bias. Varying the gate voltage the transition between the 1.0 and the 0.85 (2e^2/h) plateaus occurs for definite bias voltages, which defines a gate voltage dependent energy difference

Acoustic radiation- and streaming-induced microparticle velocities determined by microparticle image velocimetry in an ultrasound symmetry plane

\Delta

Automated and temperature-controlled micro-PIV measurements enabling long-term-stable microchannel acoustophoresis characterization

. This energy difference is compared with the activation temperature T_a extracted from the experimentally observed activated behavior of the 0.7 anomaly at low bias. We find \Delta = k_B T_a which lends support to the idea that the conductance anomaly is due to transmission through two conduction channels, of which the one with its subband edge \Delta below the chemical potential becomes thermally depopulated as the temperature is increased.

Migration of cells in a social context

We present microparticle image velocimetry measurements of suspended microparticles of diameters from 0.6 to 10 μm undergoing acoustophoresis in an ultrasound symmetry plane in a microchannel. The motion of the smallest particles is dominated by the Stokes drag from the induced acoustic streaming flow, while the motion of the largest particles is dominated by the acoustic radiation force. For all particle sizes we predict theoretically how much of the particle velocity is due to radiation and streaming, respectively. These predictions include corrections for particle-wall interactions and ultrasonic thermoviscous effects and match our measurements within the experimental uncertainty. Finally, we predict theoretically and confirm experimentally that the ratio between the acoustic radiation- and streaming-induced particle velocities is proportional to the actuation frequency, the acoustic contrast factor, and the square of the particle size, while it is inversely proportional to the kinematic viscosity.

Acoustophoretic Synchronization of Mammalian Cells in Microchannels

We present a platform for micro particle image velocimetry (μPIV), capable of carrying out full-channel, temperature-controlled, long-term-stable, and automated μPIV-measurement of microchannel acoustophoresis with uncertainties below 5% and a spatial resolution in the order of 20 μm. A method to determine optimal μPIV-settings for obtaining high-quality results of the spatially inhomogeneous acoustophoretic velocity fields of large dynamical range is presented. In particular we study the dependence of the results on the μPIV interrogation window size and the number of repeated experiments. The μPIV-method was further verified by comparing it with our previously published particle tracking method. Using the μPIV platform we present a series of high-resolution measurements of the acoustophoretic velocity field as a function of the driving frequency, the driving voltage, and the resonator temperature. Finally, we establish a direct and consistent connection between the obtained acoustophoretic velocity fields, and continuous flow mode acoustophoresis, commonly used in applications.