Counter-rotating suspension Taylor–Couette flow: pattern transition, flow multiplicity and the spectral evolution

Abstract

Inertial transitions in a suspension Taylor–Couette flow are explored for the first time via experiments in the counter-rotation regime (i.e. the rotation ratio $\varOmega =\omega _o/\omega _i<0$ , where $\omega _i$ and $\omega _o$ are the angular speeds of the inner and outer cylinders, respectively) up to a particle volume fraction $\phi \leq 0.2$ . The primary bifurcation from the circular Couette flow (CCF) is found to yield patterns similar to those in a particle-free Newtonian fluid, and is supercritical at $|\varOmega |\leq 0.5$ but becomes hysteretic at large $|\varOmega |=1$ . It is shown that the states with different numbers of vortices can coexist over a large range of shear Reynolds number $\mbox {Re}_s(\phi )$ , confirming multi-stable behaviour of the primary and higher-order states for any particle loading at $|\varOmega |\leq 0.5$ . A quasi-periodic state characterized by two incommensurate frequencies, namely, the modulated wavy vortices (MWV), is found at $\varOmega =-0.5$ as a tertiary bifurcation from the wavy Taylor vortices (WTV), with the stationary Taylor vortex flow (TVF) being the primary bifurcating state from CCF at $\phi \geq 0$ . A novel sequence of transitions ${\rm TVF}\to {\rm MWV}_1\to {\rm WTV}\to {\rm MWV}$ , with another variant of modulated vortices (MWV $_1$ ) appearing directly from TVF as a secondary bifurcation, may also occur even for the particle-free ( $\phi =0$ ) case; the coexistence/non-uniqueness of WTV and MWV states is demonstrated over a range of $\mbox {Re}_s$ values spanning the secondary and tertiary bifurcation loci. At $\varOmega =-1$ , the primary bifurcation yields an oscillatory state (spiral/helical vortex flow) that gives birth to another oscillatory state (interpenetrating spiral vortices) and a non-periodic state (non-propagating interpenetrating spirals, NIS) as secondary and tertiary bifurcations, respectively, with NIS being characterized by the absence of frequency peaks in the power spectrum of the scattered light intensity. For all transitions at $\varOmega < 0$ , the critical values of $\mbox {Re}_s^c(\phi )$ decrease with increasing $\phi$ , with more destabilizing effects of particles being found at larger $|\varOmega |$ . The effect of particle loading is found to (i) decrease the amplitude and (ii) increase the wavelength of wavy vortices, with the latter seeming to be responsible for the decreased propagation frequencies of azimuthal waves with increasing $\phi$ . The normalized rotation frequency of spiral vortices also decreases with increasing $\mbox {Re}_s$ and $\phi$ , and a scaling relation in terms of the relative viscosity is found to collapse the frequency data for all $\phi$ .

Flow transitions and effective properties in multiphase Taylor–Couette flow

“…Experiments by Ramesh et al (2019) are included in table 1 and the results are compared with this study. More recent works by Dash et al (2020), Singh et al (2022) and document the flow bifurcation sequence that leads to turbulence and the variations in the corresponding torque for inner-rotating and counter-rotating rheometers.…”

“…1992; Matas, Morris & Guazzelli 2003; Mueller, Llewellin & Mader 2010; Mahbubul, Saidur & Amalina 2012; Mendoza 2017; Baroudi, Majji & Morris 2020; Singh et al. 2022). Using an annular rheometer with a stationary inner cylinder and rotating outer cylinder, Hunt et al.…”

“…(2020), Singh et al. (2022) and Alam & Ghosh (2022) document the flow bifurcation sequence that leads to turbulence and the variations in the corresponding torque for inner-rotating and counter-rotating rheometers.…”

“…For suspensions, unconfined granular flows and fluidized beds, it is important to establish similar flow criteria, especially when making rheological measurements. Toroidal vortices have been observed in gaseous fluidized beds (Conway, Shinbrot & Glasser 2004), unfluidized granular media (Krishnaraj & Nott 2016) and neutrally buoyant particle suspensions (Linares-Guerrero, Hunt & Zenit 2017; Majji, Banerjee & Morris 2018; Ramesh, Bharadwaj & Alam 2019; Dash, Anantharaman & Poelma 2020; Alam & Ghosh 2022; Singh, Ghosh & Alam 2022). Despite their similar appearance, these vortical flows differ in their structure as well as in their inciting mechanisms.…”

Recent developments of turbulent emulsions in Taylor–Couette flow

“…In many natural and industrial processes, turbulent liquid flows contain dispersed droplets, bubbles or particles [13][14][15]. Turbulent multiphase flows in TC systems are investigated in various studies, including bubbly flows [16][17][18], particle-laden flows [19][20][21][22] and liquid-liquid dispersed flows [23]. The flow of emulsions (i.e.…”