Ultrasonic measurements of the bulk flow field in foams

The flow field of moving foams is relevant for basic research and for the optimization of industrial processes such as froth flotation. However, no adequate measurement technique exists for the local velocity distribution inside the foam bulk. We have investigated the ultrasound Doppler velocimetry (UDV), providing the first two-dimensional, non-invasive velocity measurement technique with an adequate spatial $\left(10\mathrm{mm}\right)$ and temporal resolution $\left(2.5\mathrm{Hz}\right)$ that is applicable to medium scale foam flows. The measurement object is dry aqueous foam flowing upward in a rectangular channel. An array of ultrasound transducers is mounted within the channel, sending pulses along the main flow axis, and receiving echoes from the foam bulk. This results in a temporally and spatially resolved, planar velocity field up to a measurement depth of $200\mathrm{mm}$, which is approximately one order of magnitude larger than those of optical techniques. A comparison with optical reference measurements of the surface velocity of the foam allows to validate the UDV results. At $2.5\mathrm{Hz}$ frame rate an uncertainty below 15 percent and an axial spatial resolution better than $10\mathrm{mm}$ is found. Therefore, UDV is a suitable tool for monitoring of industrial processes as well as the scientific investigation of three-dimensional foam flows on medium scales.

Figure 1

Operating principle of ultrasound Doppler velocimetry in foam. The velocity $u$ at a location $d$ is estimated from the phase difference $\mathrm{\Delta }\phi$ of the reflected ultrasound wave over multiple pulses with an rate of $f_{\mathrm{PR}}$.

Figure 2

Arrangement of US-transducer array (A…E) and reference transducer R in the foam channel (a) the straight channel and (b) nozzle.

Figure 3

Part of an echo signal received by transducer B after a single transmission of transducer A at $t=0$ and the corresponding spectrum. The dashed lines mark a range gate of $\mathrm{\Delta }t=3.2\mu \mathrm{s}$.

Figure 4

Speed of sound in foam with different liquid fraction, derived from the time of flight between the reference transducer R and the transducer B and vice-versa. The value $\varphi =0$ represents the empty channel.

Figure 5

Signal intensity as a function of the foam liquid fraction. One transducer sends a pulse and the signal recorded by neighboring transducer is integrated over $0.3\mathrm{ms}$. The value $\varphi =0$ represents the empty channel. The noise level of the measurement setup is approximated as $5\times {10}^8[\mathrm{arb}.\mathrm{units}]$.

Figure 6

Foam flow measurement in the straight channel: (a) picture of the applied foam flow, indicating the measurement volumes, (b) resulting vertical velocity distribution of the foam for $11{\mathrm{cm}}^3/\mathrm{s}$, measured with optical image correlation. The white spots above transducer C are caused by optical blockage.

Figure 7

Vertical velocity distribution in the straight channel, measured by UDV. Each plot corresponds to one measurement region in Fig. 6. The dashed lines mark the standard deviation of the measurement and the solid green line the corresponding signal strength. The dash-dotted red line gives the expected distribution, derived from the optical measurement in Fig. 6.

Figure 8

Vertical velocity distribution in the channel with decreasing cross section, derived from image correlation.

Figure 9

Vertical velocity distribution in a nozzle, measured by UDV. The dashed lines mark the standard deviation of the measurement and the green line the corresponding signal strength. The dash-dotted red line gives the expected distribution, derived from the optical measurement in Fig. 8.