Session P10: Suspensions: Instability (3:10pm - 3:55pm CST)

Wavy regime of a colloidal falling film

Thin liquid films are observed in a wide range of scenarios, of both natural and engineering importance. Tear film formation, glaciers flowing down mountains and coating flows are some of the classical examples of shallow liquid flows where viscous effects are important. A lot of work has been done in the case of gravity driven falling films. Yih (1963) in his pioneering study carried out a linear stability analysis and identified a long wavelength instability in a falling film. Subsequently Benney (1966) derived a nonlinear long wave equation describing the evolution of the film height that reproduced the linear stability predictions as a limiting scenario. However with the introduction of particles brings in new physics - concentration dependent viscosity, shear-induced migration, normal stresses, etc. In this work, we analyze the dynamics of a particle-laden gravity driven falling film. The particles evolve by being both advected by the background flow while also diffusing due to Brownian motion. Both the linear and the non-linear regimes are studied by developing models using the lubrication approximation. The non-linear regime is studied using a Benney-like amplitude expansion and also a weighted residual approach in conjunction with the lubrication approximation.   

Shallow gravity driven particle-laden flows - Role of normal stresses

We study the stability of particle-laden falling films with the inclusion shear-induced migration and particle normal stresses.. In absence of particles, Yih (1963) in his pioneering study carried out a linear stability analysis and identified a long wavelength instability in a falling film. The presence of particles alters the rheology of the system with the alteration of local shear stress and also through an additional particle normal stress thus coupling with the momentum balance. This is done by using a form of particle stress that is inclusive of both the isotropic thermal stress and the stress due to shear induced migration (Frank et al. 2003). The shear induced stresses are described by constitutive models based on the suspension balance model (Nott \& Brady 1994, Morris \& Boulay 1999). The momentum balance and the particle evolution equations are linearised to arrive at a generalized Orr-Sommerfeld system using which the stability of the system is studied, both numerically and asymptotically in the long wavelength limit. Subsequently, the role of in-homogeneous particle concentration and anisotropic particle stresses on the interfacial stability is explored.   

Effect of Inertial Migration of Particles on Hysteresis in Suspension Taylor–Couette Flow

In this work, we present an experimental investigation into the influence of inertial migration of particles on flow transitions of a suspension in Taylor-Couette geometry with a stationary outer cylinder and rotating inner cylinder. This was considered for neutrally buoyant particles of size $d_p=230$ $\mu$m in the circular Couette flow (CCF) and Taylor vortex flow (TVF) states of a suspension at a concentration of $\phi=0.10$. While the effect of suspended particles on inertial flow transitions was recently investigated [Majji~\textit{et al}. (JFM 835, 936 (2018)), Ramesh~\textit{et al}. (JFM 870, 901 (2019)], the role of inertial migration of particles on flow transitions and observed flow structures has not been established for Taylor-Couette flow. This study considers the hysteresis effects associated with particles by focusing on the influence of non-uniform particle distribution due to particle migration in the CCF and TVF on flow transitions away from these initial states, relative to the case with uniform particle distribution, when the Reynolds number is rapidly changed. Clear evidence of the role of inertial migration and the resulting nonuniform particle fraction in the hysteretic behavior is established by our work.   

Instabilities in Polar Magnetic Suspensions

The stability of an active suspension of polar motile micromagnets is analyzed theoretically. We formulate the collective dynamics using a kinetic continuum model and Fokker-Planck formalism. Using a perturbation analysis, we obtain governing equations to leading order in polar length and study the stability of the suspension and transition from disordered to ordered state using linear stability analysis.   

Reversibility and instability of concentrated suspensions in oscillatory channel flow

The motion of individual particles has been tracked experimentally in a non-Brownian suspension of non-buoyant spheres (volume fraction between 0.2 and 0.4) subject to a square-wave oscillatory flow in a Hele-Shaw cell at low Reynolds numbers. We investigated the evolution of the suspension structure and velocity profile, as well as the microscopic reversibility of the particle trajectories, as a function of the amplitude A and period T of the oscillating flow. At short times, the flow is parallel with a blunted parallel velocity and a corresponding increase of particle concentration at the center of the channel, consistent with previous results and shear-induced migration models. The reversibility of the motion of the particles from one period to the next is strong in the center region but much weaker close to the walls. At longer times, an instability induces an exponential growth in the motion of the particles transverse to the flow, forming a periodic structure or recirculating zones along the channel. The wavelength and transverse velocity have been studied as a function of A and T. The reversibility of the particle motion is strongly reduced in this regime. We also discuss the presence of a threshold value in the cumulative strain for the appearance of the instability.