In this paper, Part 7 of the thematic tutorial series "Acoustofluidics-exploiting ultrasonic standing waves, forces and acoustic streaming in microfluidic systems for cell and particle manipulation", we present the theory of the acoustic radiation force; a second-order, time-averaged effect responsible for the acoustophoretic motion of suspended, micrometre-sized particles in an ultrasound field.

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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 (mm in water at MHz frequencies). The acoustophoretic response of suspended microparticles is predicted and analyzed using parameter values typically employed in microchannel acoustophoresis.

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 ∆. This energy difference is compared with the activation temperature Ta extracted from the experimentally observed activated behavior of the 0.7 anomaly at low bias. We find ∆ = kBTa 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 ∆ below the chemical potential becomes thermally depopulated as the temperature is increased.PACS 73.61.-r, 73.23.-b

AlatraeL We generalize the Linear response theory of magnetoconductivity of disordered mdimensional electron gases lo include the case where a mnfinemenl potential is present in one of the two spatial directions. ?he theory allows Studies of the effect of suppression of backscattering due lo the aislence of spatially reparated edge stales m high magnetic fields. Explicit calculations of the conductivity are arried out for weak sgttering in two limits: the weak and the Strong mnfinement limit.

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 ¼ 377 mm of the channel.

The basic continuum fields are introduced, the mathematical notation is presented, and the governing equations in microfluidics are established. Examples of basic flow solutions are then presented, and equivalent circuit modeling for determining flow rates in microfluidic networks is introduced and discussed. Finally, a number of scaling laws in microfluidics are derived.

In the second part of the thematic tutorial series "Acoustofluidics--exploiting ultrasonic standing waves forces and acoustic streaming in microfluidic systems for cell and particle manipulation", we develop the perturbation theory of the acoustic field in fluids and apply the result in a study of acoustic resonance modes in microfluidic channels.