RARE Velocimetry of Shear Banded Flow in Cylindrical Couette Geometry

<p>A flow phenomena called ‘shear banding’ is often observed for a certain class of complex fluids, namely wormlike micellar solutions. Wormlike micelles are elongated flexible self-assembly structures formed by the aggregation of amphiphiles, which may entangle into a dynamic network above a certain concentration threshold. The entanglement results in the sample having both solid-like (elastic) and liquid-like (viscous) properties, an ambiguity commonly found in complex fluids. Under certain shear conditions, the flow couples with the structure of the micellar network, leading to the formation of (shear) bands with differing viscosity. The principle goal of this work is to address open questions regarding the temporal and spatial stability of shear banded flow. Shear banding is often studied in cylindrical Couette cells, where the fluid is sheared in a gap between differentially rotating concentric cylinders. For the sake of an accurate description of the flow in such a shear cell, the methodology for a 2D Nuclear Magnetic Resonance (NMR) velocimetry technique (known as PGSE-RARE), which offers high temporal and spatial resolution, is improved and refined. Two main challenges are identified and overcome. The first concerns the fact that the velocity imaging process operates on a Cartesian grid, whereas the flow in the Couette cell is of cylindrical symmetry. Numerical calculations and NMR simulations based on the Bloch equations, as well as experimental evidence, give insight on the appropriate selection of the fluid volume over which velocity information is accumulated and the preferred scheme through which the NMR image is acquired in the so-called k-space. The small extent of the fluid gap for the cells in use is the second challenge. In this respect, a variant of the velocimetry technique is developed, which offers ultra high resolution in the gap direction, necessary for a detailed description of the flow profile in the banded state. The refined methodology is applied in a thorough study of a certain wormlike micellar solution (‘10% CPCl’), which is known to exhibit spatiotemporal fluctuations and has been subject of numerous studies over the past 20 years. NMR results are supported by a recently developed 2D Rheo-USV (Ultrasonic Speckle Velocimetry) method, which offers an even higher temporal resolution. The two complementary methods show good agreement for averaged velocity profiles. In line with previous studies the fluid is found to follow a standard anomalous lever rule, which is characterized by a constant shear rate in the high viscosity band and a varying shear rate and proportion of the high shear rate band. In particular, the high resolution NMR variant allows a refined picture on the dynamics of the interface between the two bands. Furthermore, slip is observed for all investigated shear rates. The amount of slip, however, is found to strongly depend on the specifities of the Couette cells in use. Spatially and temporally resolved flow maps reveal various flow instabilities. Ultrasound measurements show vorticity structures in the order of the gap width. In the NMR case no such structures are observed due to the lower resolution in the axial direction. For higher shear rates the occurrence of turbulent bursts is detected for USV. No direct evidence of similar flow instabilities is found in the NMR case. Finally, broad distributions dominate the high shear rate band in temporally and spatially resolved velocity profiles, showing the fluctuative nature of the flow.</p>

RARE Velocimetry of Shear Banded Flow in Cylindrical Couette Geometry

<p>A flow phenomena called ‘shear banding’ is often observed for a certain class of complex fluids, namely wormlike micellar solutions. Wormlike micelles are elongated flexible self-assembly structures formed by the aggregation of amphiphiles, which may entangle into a dynamic network above a certain concentration threshold. The entanglement results in the sample having both solid-like (elastic) and liquid-like (viscous) properties, an ambiguity commonly found in complex fluids. Under certain shear conditions, the flow couples with the structure of the micellar network, leading to the formation of (shear) bands with differing viscosity. The principle goal of this work is to address open questions regarding the temporal and spatial stability of shear banded flow. Shear banding is often studied in cylindrical Couette cells, where the fluid is sheared in a gap between differentially rotating concentric cylinders. For the sake of an accurate description of the flow in such a shear cell, the methodology for a 2D Nuclear Magnetic Resonance (NMR) velocimetry technique (known as PGSE-RARE), which offers high temporal and spatial resolution, is improved and refined. Two main challenges are identified and overcome. The first concerns the fact that the velocity imaging process operates on a Cartesian grid, whereas the flow in the Couette cell is of cylindrical symmetry. Numerical calculations and NMR simulations based on the Bloch equations, as well as experimental evidence, give insight on the appropriate selection of the fluid volume over which velocity information is accumulated and the preferred scheme through which the NMR image is acquired in the so-called k-space. The small extent of the fluid gap for the cells in use is the second challenge. In this respect, a variant of the velocimetry technique is developed, which offers ultra high resolution in the gap direction, necessary for a detailed description of the flow profile in the banded state. The refined methodology is applied in a thorough study of a certain wormlike micellar solution (‘10% CPCl’), which is known to exhibit spatiotemporal fluctuations and has been subject of numerous studies over the past 20 years. NMR results are supported by a recently developed 2D Rheo-USV (Ultrasonic Speckle Velocimetry) method, which offers an even higher temporal resolution. The two complementary methods show good agreement for averaged velocity profiles. In line with previous studies the fluid is found to follow a standard anomalous lever rule, which is characterized by a constant shear rate in the high viscosity band and a varying shear rate and proportion of the high shear rate band. In particular, the high resolution NMR variant allows a refined picture on the dynamics of the interface between the two bands. Furthermore, slip is observed for all investigated shear rates. The amount of slip, however, is found to strongly depend on the specifities of the Couette cells in use. Spatially and temporally resolved flow maps reveal various flow instabilities. Ultrasound measurements show vorticity structures in the order of the gap width. In the NMR case no such structures are observed due to the lower resolution in the axial direction. For higher shear rates the occurrence of turbulent bursts is detected for USV. No direct evidence of similar flow instabilities is found in the NMR case. Finally, broad distributions dominate the high shear rate band in temporally and spatially resolved velocity profiles, showing the fluctuative nature of the flow.</p>

Bistabilities in two parallel Kármán wakes

Bistabilities of two equilibrium states discovered in the coupled side-by-side Kármán wakes are investigated through Floquet analysis and direct numerical simulation (DNS) with different initial conditions over a range of gap-to-diameter ratio ( $g^*= 0.2\text {--}3.5$ ) and Reynolds number ( $Re = 47\text {--}100$ ). Two bistabilities are found in the transitional $g^*-Re$ regions from in-phase (IP) to anti-phase (AP) vortex shedding states. By initialising the flow in DNS with zero initial conditions, the flow in the first bistable region (i.e. bistable IP/FF $_C$ at $g^*= 1.4 \text {--} 2.0$ , where FF $_C$ denotes the conditional flip-flop flow) attains flip-flop (FF) flow, it settles into the IP state by initialising the flow with an IP flow. The second bistability is observed between cylinder-scale IP and AP states at large $g^*$ ( $=$ 2.0–3.5). The transition from the FF $_C$ to IP is dependent on initial conditions and irreversible over the parameter space, meaning that the flow cannot revert back to the FF $_C$ state once it jumps to the IP state irrespective of the direction of $Re$ variations. Its counterpart for the bistable IP/AP state is reversible. We also found that the FF $_C$ flow in the first bistable region is primarily bifurcated from synchronised AP with cluster-scale features, possibly because the cluster-scale AP flow is inherently unstable to FF flow instabilities. It is demonstrated that the irreversible bistability exists in other interacting wakes around multiple cylinders. A good understanding of flow bistabilities is pivotal to flow control applications and the interpretation of desynchronised flow features observed at high $Re$ values.