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Sorting biological cells in heterogeneous cell populations is a critical task required in a variety of biomedical applications and therapeutics. Microfluidic methods are a promising pathway toward establishing label-free sorting based on cell intrinsic biophysical properties, such as cell size and compliance. Experiments and numerical studies show that microchannels decorated with diagonal ridges can be used to separate cell by stiffness in a Newtonian fluid. Here, we use computational modeling to probe stiffness-based cell sorting in ridged microchannels with a power-law shear thinning fluid. We consider compliant cells with a range of elasticities and examine the effects of ridge geometry on cell trajectories in microchannel with shear thinning fluid. The results reveal that shear thinning fluids can significantly enhance the resolution of stiffness-based cell sorting compared to Newtonian fluids. We explain the mechanism leading to the enhanced sorting in terms of hydrodynamic forces acting on cells during their interactions with the microchannel ridges.

The cross-stream inertial migration of neutrally buoyant particles in a power law fluid in a pressure-driven flow between two parallel walls is studied using three-dimensional numerical simulations. The particles are modeled as rigid and compliant spherical shells filled with a Newtonian fluid. Our simulations show that the particles in the flow equilibrate at stable off-center positions that depend on the particle size and fluid power exponent. In a shear thickening fluid, the equilibrium position is insensitive to the particle size. In a shear thinning fluid, an additional unstable off-center equilibrium position emerges for smaller particles, which leads to the accumulation of such particles at the channel centerline. We find that these equilibrium positions are insensitive to the magnitude of the channel Reynolds number and particle elasticity. The results of our study have applications to sorting, focusing, and separation of synthetic particles and biological cells.

The paper considers deposition of small aerosol particles inside a closed tube filled with a gas at resonance, when the flow is accompanied by periodic shock waves traveling back and forth along the tube. It is found that resonance gas oscillations cause vigorous aerosol deposition leading to a rapid concentration decrease. We study the effect of the Saffman lift and thermophoretic forces on particle trajectory in the boundary layer near the tube wall. The thermophoretic force arises due to gas heating by periodic shock waves, while the lift force is caused by the interaction of the shock with the viscous boundary layer. Both forces move particles toward the wall causing their deposition. The effect of turbulence on aerosol deposition is also considered. It is found that for particles less than 1 μm in diameter, the effect of turbulent fluctuations on their deposition is dominant, while for larger particles, the Saffman lift force prevails. The effect of the thermophoretic force is found to be slight. It is also found that at resonance the Saffman lift force causes instability in motion of large particles resulting in their rapid deposition. Our experiments of aerosol deposition in a resonance tube compare favorably with the results of the numerical study.

Periodic gas oscillations in closed tubes are investigated experimentally and numerically. At resonance, these oscillations are accompanied by shock waves traveling back and forth along the tube. Results of gas temperature and pressure measurements are reported. It is found that the gas temperature changes substantially along the tube. A two-dimensional numerical model of turbulent gas oscillations is developed and verified by a comparison with experiments. It is found that the experimental data of temperature and pressure inside the resonance tube are well correlated by the numerical model. Using the numerical model, turbulence and acoustic streaming at resonance are investigated. It is shown that the direction of gas streaming at resonance is opposite to that in nonresonant oscillations. A parametric investigation of resonant flow is performed in terms of the tube parameter e, acoustic Reynolds number Rea and dimensionless tube length Λ. In particular, it is found that the normalized pressure amplitude, as well as other flow characteristics, are functions of a single parameter E=Rea1/3/Λ. Useful correlations for flow characteristics are proposed in terms of tube dimensionless parameters.

Gas oscillations in a resonance tube are investigated experimentally and numerically. We found that for large amplitudes, heat interaction with the tube wall affects strongly gas flow for frequencies within the resonance band. A proposed model, accounting for heat interaction, shows good agreement with the experimental data.

We investigate the nonlinear dynamics of a two-layer system consisting of a thin liquid film and an overlying gas layer driven by the Marangoni instability induced by thermal waves propagating along the solid substrate. In the case of a stationary thermal wave with sufficiently large amplitude and Marangoni number, liquid film rupture takes place with a flattish wide trough. For sufficiently small but not too small frequencies of the thermal wave, a periodic structure consisting of localized drops interconnected by thin liquid bridges emerges. This train of drops travels unidirectionally along the heated substrate following the thermal wave. For larger thermal wave frequencies, the thickness of the bridges increases enabling fluid flow between the neighboring drops. The drop-train regimes may be utilized in microfluidic applications for directed transport of liquid content enclosed in drops formed by thermocapillary forces.

Using computational modeling, we examine the development of an unsteady laminar flow of a Newtonian fluid in a channel with sinusoidal walls. The flow is driven by a constant pressure gradient. The simulations reveal two types of unsteady flows occurring in sinusoidal channels. When the amplitude of the wavy walls is relatively small, vortices forming in the channel furrows are shed downstream. For larger wall wave amplitudes, vortices remain inside the furrows and exhibit periodic oscillations and topological changes. We present a phase diagram in terms of wall amplitude and driving pressure gradient separating different flow regimes. Our simulations establish the optimum wall amplitude and period leading to an unsteady flow at the minimum pressure gradient. The results are important for designing laminar heat/mass exchangers utilizing unsteady flows for enhancing transport processes.

We use three-dimensional computer simulations to examine the free swimming of an elastic plate plunging sinusoidally in a viscous fluid with a Reynolds number of 250. We find that the free swimming velocity is maximized when the swimmer is driven near the first natural frequency leading to larger swimmer deformations, and that the free swimming velocity is nearly linearly related to the trailing edge displacement. The maximum swimmer performance is found at a non-resonance frequency. The maximum performance takes place when the swimmer exhibits a deformation pattern in which the transverse displacement of the swimmer's center of mass is minimized, which in turn reduces viscous losses.

Using long wave theory and direct numerical solutions of the Navier–Stokes equations, we investigate thermocapillary flows arising in a thin liquid film covering a heated solid substrate with non-uniform temperature in the form of traveling thermal waves. Our results indicate that unidirectionally propagating interfacial waves are formed in the liquid film. The interfacial waves transport liquid, thereby creating a net pumping effect. We show that the frequency of thermal waves leading to the most efficient pumping is defined by their wave length and weakly depends on other system parameters. The results are useful for designing new methods for transporting liquids in open microfluidic devices.

Using three-dimensional computer simulations, we study the cross-stream inertial migration of neutrally buoyant deformable particles in a pressure-driven channel flow. The particles are modeled as elastic shells filled with a viscous fluid. We show that the particles equilibrate in a channel flow at off-center positions that depend on particle size, shell compliance, and the viscosity of encapsulated fluid. These equilibrium positions, however, are practically independent of the magnitude of channel Reynolds number in the range between 1 and 100. The results of our studies can be useful for sorting, focusing, and separation of micrometer-sized synthetic particles and biological cells.

Sorting and separation are key elements in many microfluidic processes. Here, we use computational modeling to design a hydrodynamic method for high-throughput separation of solid microparticles by size in microchannels. The rapid and high-resolution separation occurs due to a combination of two hydrodynamic effects: cross-stream inertial migration of particles and circulatory fluid flows created by periodic diagonal ridges protruding from opposite channel walls. This new continuous separation method operates in a wide range of Reynolds numbers, is insensitive to the magnitude of channel flow rate, and features simple design that can be readily integrated into microfluidic devices for massive sample analysis.

Stabilization of the Rayleigh-Taylor instability of a thin liquid film by the Marangoni effect arising from heating of the liquid at the gas-liquid interface in a bilayer setting is investigated. Solution of time-dependent Navier-Stokes and long-wave evolution equations in both two and three dimensions shows the emergence of nontrivial nonruptured steady states in the system when the applied temperature gradient exceeds a certain critical value.

Thermocapillary instability is one of the primary causes of a spontaneous rupture of thin films on heated walls. The film rupture may lead to an appearance of uncontrolled dry patches that significantly deteriorate the heat and mass transfer. In the present paper the thermocapillarity-induced film flow on a microstructured wall is studied in the framework of the long-wave theory. When the wall is heated or cooled, the solution predicts a film deformation caused by thermocapillarity. The linear stability analysis shows that the films on heated microstructured walls are less stable to the long-wave disturbances compared to the films on flat walls. The time-dependent film evolution is simulated and the effect of the wall structure on the film thinning and rupture is analyzed. It is shown that the wall topography exerts a profound effect on the dynamics of the film deformation and rupture, as well as on the size and the location of the dry patches. The full-scale direct volume-of-fluid simulations are used to verity the predictions of the long-wave theory. Good agreement is found for the small ratios between the groove depth and period. The agreement is further improved by including the effect of the convection heat transfer into the long-wave model.

Thermocapillary-induced motion in thin liquid films on a heated horizontal wall with parallel grooves on its upper surface is studied experimentally and numerically. The results of velocity and temperature measurements are reported. A numerical model for a liquid film on a structured wall is developed. The full incompressible Navier–Stokes equations and the energy equation are integrated by a finite difference algorithm, whereas the mobile gas-liquid interface is tracked by the volume-of-fluid method. The numerical model is verified by comparison with the experimental data showing a good agreement. The model is used to study flow patterns and film rupture caused by the thermocapillary forces. Heat transfer in the liquid is also investigated. In particular, it is found that the thermocapillary convection enhances heat transfer in liquid, though the effect depends on the shape of the wall surface.