Session Z31: Microscale Non-Newtonian and Complex Flows II

A lubrication theory for permeable particles

Hydrodynamics interactions of permeable particles play a key role in applications including particle filtration processes and enhanced mass transport in fluidized catalytic reactors. This talk is about the effect of particle permeability on the hydrodynamic interactions of spherical particles immersed in viscous liquids. Under weak permeability conditions, K=k/a² << 1 , where k is the permeability and a is the reduced radius of the particles, the near-contact hydrodynamic interactions are qualitatively affected. A lubrication theory will be presented for permeable particles undergoing axisymmetric and transverse motions and the complete resistance matrix is derived. An integral Reynolds lubrication equation arises due to non-local coupling between pressure in the gap and the intraparticle pressure. Competition between liquid draining from the thin gap between two particles and draining into the particles imposes a characteristic lateral length scale L=K^1/5 a. By contrast to the singular resistances that characterize all near-contact relative motions of impermeable hard spheres, axisymmetric resistances and transverse rolling motions of contacting permeable particles are non singular. At contact, the axisymmetric mobility under the action of oppositely-directed forces is U/U₀=d₀ K^2/5, where U is the relative velocity, U₀ is the velocity in the absence of hydrodynamic interactions, and d₀=1.332. Under the action of a constant tangential force, a particle in contact with a permeable half-space rolls without slipping with velocity U/U₀=d₁ (d₂ + log K^-1)^-1, where d₁=3.125 and d₂=6.666; in shear flow, the same expression holds with d₁=7.280.   

Numerical investigation of the effect of particle concentration and size on the Dean's flow in a curved microchannel

Microfluidic devices have been widely employed for the purpose of clinical diagnostic tests, cell sorting, flow cytometry, particle manipulation, etc. Inertial microfluidics has been one of the most extensively used passive particle manipulation techniques, where hydrodynamic forces are used for sorting, or separating particles in a microchannel. Despite its popularity, there is a lacuna in our understanding of the particle-fluid two-phase transport in curved microchannels. In this study, we incorporate a multiphase Eulerian model to study such a two-phase transport in the presence of Dean flow in a curved microchannel. Firstly, we witness a significant shift of the location of maximum velocity away from the channel walls opposing the effect of Dean's flow at large particle concentrations. Secondly, we observe a massive modification of the counter-rotating vortices associated with the Dean's flow. We attribute such alterations in the typical Dean flow characteristics to the interphase interaction forces which oppose the effect of curvature-induced centrifugal force. Such an understanding of interphase interaction forces will be critical in designing better particle/cell focusing devices.   

Non-colloidal suspension Taylor-Couette flows: flow instabilities and hysteresis

We employed suspension balance model (SBM) and rheological constitutive laws to numerically examine the Taylor-Couette flow of concentrated, neutrally buoyant, and non-colloidal suspensions when the inner cylinder is rotating and the outer one is stationary. The bulk particle volume fraction was varied ϕ_b = 0.1 ~ 0.3, while the radius ratio of cylinders η and the particle size ratio ϵ (= d/a) were fixed at 0.877 and 60, respectively; d is the gap width of cylinders and a is the radius of particles. By varying the suspensions Reynolds number based on the rotating angular velocity and the effective viscosity of suspensions, we also analyzed the imapct of suspended particles on flow transition. Although in the model the inertial migration of particles is neglected, similar to the recent reported experiments, we observed the circular Couette flow (CCF) transitions via ribbons (RIB), spiral vortex flow (SVF), and wavy spiral vortex flow (WSVF) to wavy vortex flow (WVF). We also found a hysteresis during the transitions where the transitons to higher modes occur early for more dense suspensions. Friction and torque coefficients of the suspension flow are also computed and compared.   

Capillary Rise of Yield Stress Fluids

Cell & DNA solutions, blood, food, cosmetics, and polymer mixtures are examples of yield stress fluids (YSFs). They frequently wet narrow channels, as seen in a blood test for virus and a recovery of crude oil. In this talk, we present the capillary rise of various YSFs in vertical glass capillaries, and find a unique rise curve distinct from Newtonian fluids; the rise slows down to a plateau in the middle, followed by the sudden increase to the final equilibrium. We show that this plateau is originated from a competition between Laplace pressure and the yield stress. Furthermore, it is also found that the second rise from the plateau greatly depends on a liquid-solid transition speed or 'yielding rate'.    

Hydrodynamic instabilities in chemotactic thin-film active suspensions

In this work, we are interested in the hydrodynamic instabilities found in chemotactic thin-film suspensions of active swimmers. In the presence of an imposed attractant gradient, the preferential swimming exhibited by the swimmers gives rise to an anisotropic active stress within the suspension. Through a long-wave stability analysis, we show that the flow generated as a result gives rise to a new mode of instability associated with the film interface, in addition to modifying the instability mechanism predicted by Kasyap and Koch (2012). We further show that a coupling between the above two modes of instability destabilizes a suspension of pullers, which was previously shown to be unconditionally stable ( Kasyap and Koch (2012) & (2014) ). Additionally, we formulate a long-wave theory for the film evolution to ascertain the mechanism associated with the instabilities found in the system.   

Rod climbing effect modulated by the three-phase contact line behavior

We present an exposition on the rod climbing effect by replacing the bare rod with a silicone oil-coated rod. This revealed two key differences: (i) For a fixed rod rotation speed, an enhancement in the magnitude of the climbing height. For instance, climbing height increased from ~1.3 mm to ~2.6 mm at a rod rotation speed of 600 RPM. (ii) There exists a threshold rod rotation speed, ω_th for rod climbing to occur and this ω_th decreases on introduction of the oil-coated rod. We hypothesize that these differences can be explained by the altered behavior of the three-phase contact line at the rod-fluid interface in presence of an oil layer. Experimental evidence suggested that the contact line exhibits pinned mode with the bare rod and de-pinned mode with the oil-coated rod. We propose a new set of boundary conditions in terms of altered contact angle at the rod-fluid interface to incorporate the role of the contact line behavior. An agreement between the observed and the predicted climbing height using the Giesekus model confirms our hypothesis that the contact line behavior can modulate the rod climbing effect.   

Soft lubrication in the elastic Leidenfrost effect

When a hydrogel sphere is lowered onto a hot plate, its bottom begins to vaporize. The resulting vapor flow couples tightly to elastic deformations within the sphere. This results in two regimes of the so-called elastic Leidenfrost effect: steady-state floating or limit-cycle-like bouncing. Despite experimental evidence, a fundamental theory of these phenomena remains a challenge: How high above the hot plate does the sphere sit? What is the spatial profile of its underbelly? 

We explore an asymptotic theory of elastic Leidenfrost drops. Stiff sublimable solids support an increase in weight by sitting closer to the hot surface. We instead discover a super-squishy elastic limit, in which the underbelly of the sphere tends to a Hertzian contact profile. In this case, the larger the drop the higher it floats, due to increasing contact area. We capture this crossover in a single dimensionless parameter balancing vapor pressure against elastic stresses. We compare these theoretical predictions against simulations and experiments.  

We explore tailoring hydrogel motion using shape and connect Leidenfrost dynamics to the phenomena of soft lubrication underpinning, for example, the motion of human joints.   

The swelling and shrinking of a thermo-responsive hydrogel

Thermo-responsive hydrogels are a promising new material for creating controllable actuators for use on micro-scale devices, since they expand and contract significantly (absorbing or expelling fluid) in response to relatively small temperature changes. Understanding such systems can be difficult because of the spatially- and temporally-varying properties of the gel, and the complex relationships between the fluid dynamics, elastic deformation of the gel and chemical interaction between the polymer and fluid. We address this using a poro-elastic model, considering the dynamics of a thermo-responsive spherical hydrogel after a sudden change in the temperature that should result in substantial swelling or shrinking. We typically find that swelling and shrinking have qualitatively different behaviour: swelling happens smoothly from the edge, whereas shrinking results in the formation of an inwards-travelling spherical front that separates a swollen core and shrunken shell. An approximate analytical form for the front dynamics is developed that well-approximates the numerical solutions.   

Observation of Particle Drift in a Controlled Viscosity Gradient

We report the observation of drift by Brownian particles in a viscosity gradient inside a nanofluidic device. We set up a controlled viscosity gradientby pumping miscible fluids of known viscosity past either end of a 200 nm-deep, 100μm-long, and 150μm-wide glass channel. We tracked the motion of nanoscopic fluorescent spheres inside the channel. An analysis of the particles' stochastic trajectories based on the work of Frishman and Ronceray obtained the position-dependent self diffusivity of the particles, the mean drift, and the inferred force field. Particles were observed to drift in the direction of increasing diffusivity, consistent with the theory of Brownian motion with multiplicative noise in the an isothermal stochastic framework. We separately used electrodes to measure ionic currents flowing through the same nanofluidic channel in the direction of lower viscosity. The currents increased in proportion with the viscosity gradient.