Simulation of gas separation effect in microchannel with moving walls

Numerical simulation of a free-molecular gas flow through plane microchannel with walls performing forced curving motion according to sine law is presented. It is shown that the probability of gas molecules to pass through the channel significantly depends on relation between wave speed of walls harmonic oscillations and characteristic thermal speed of gas molecules. It is then shown how this effect can be utilized for gas separation, and the comprehensive study of the influence of the main parameters (channel width and length, wave amplitude and length, etc.) on the magnitude of effect is performed.     

Topology optimization of a no-moving-part valve incorporating Pareto frontier exploration

No-moving-part (NMP) valves, such as Tesla valves, are engineered fluid channels whose flow resistance depends on the flow direction. They have no moving parts and do not deform, but rely on inertial forces of the fluid to preferentially allow flow in one direction while strongly inhibiting flow in the reverse direction. NMP valves have significant advantages over active valves in terms of their reliability and easy manufacturability. Several previous studies have explored optimum designs of NMP valves, and the most widely used indicator of NMP valve performance is diodicity, defined as the ratio of the pressure drop of reverse flow to that of the forward flow. However, higher diodicity does not necessarily imply a lower pressure drop for the forward flow, and if this pressure drop is too high, significant pumping power is required, which makes the NMP valve inefficient for use in pumping applications. Therefore, for the design NMP valves, treating the forward and reverse flow pressure drops independently in a multiobjective formulation is preferable to optimization of the diodicity alone. In this paper, we propose a bi-objective topology optimization method for an optimum design of an NMP valve. One objective function is to minimize the pressure drop in the forward flow, and the other is to maximize the pressure drop in the reverse flow. A numerical example is provided to illustrate the effectiveness of the proposed method.     

Transport Processes at Partial Accommodation by the Walls of a Rectangular Channel

This paper considers a flow of rarefied gas with a specular-diffuse reflection of gas molecules from a model of a rectangular cross section of channel walls in the free regime. We assume that the channel maintains a constant pressure gradient. Mass and heat flows are obtained as a function of the tangential momentum’s accommodation coefficient and the ratio between the linear dimensions of the channel’s cross section. Similar results presented in the literature are compared.     

Rarefaction and compressibility effects on steady and transient gas flows in microchannels

The main theoretical and experimental results from the literature about steady pressure-driven gas microflows are summarized. Among the different gas flow regimes in microchannels, the slip flow regime is the most frequently encountered. For this reason, the slip flow regime is particularly detailed and the question of appropriate choice of boundary conditions is discussed. It is shown that using second-order boundary conditions allows us to extend the applicability of the slip flow regime to higher Knudsen numbers that are usually relevant to the transition regime.The review of pulsed flows is also presented, as this kind of flow is frequently encountered in micropumps. The influence of slip on the frequency behavior (pressure gain and phase) of microchannels is illustrated. When subjected to sinusoidal pressure fluctuations, microdiffusers reveal a diode effect which depends on the frequency. This diode effect may be reversed when the depth is shrunk from a few hundred to a few m.Thermally driven flows in microchannels are also described. They are particularly interesting for vacuum generation using microsystems without moving parts.     

Liquid and gas flows in microchannels of varying cross section: a comparative analysis of the flow dynamics and design perspectives

This paper presents a comparative study of the flow of liquid and gases in microchannels of converging and diverging cross sections. Towards this, the static pressure across the microchannels is measured for different flow rates of the two fluids. The study includes both experimental and numerical investigations, thus providing several useful insights into the local information of flow parameters as well. Three different microchannels of varying angles of convergence/divergence (4°, 8° and 12°) are studied to understand the effect of the angle on flow properties such as pressure drop, Poiseuille number and diodicity. A comparison of the forces involved in liquid and gas flows shows their relative significance and effect on the flow structure. A diodic effect corresponds to a difference in the flow resistance in a microchannel of varying cross section, when the flow is subjected alternatively to converging and diverging orientations. In the present experiments, the diodic effect is observed for both liquid and gas as working fluids. The effect of governing parameters—Reynolds number and Knudsen number, on the diodicity is analysed. Based on these results, a comparison of design perspectives that may be useful in the design of converging/diverging microchannels for liquid and gas flows is provided.     

Simulation of transport processes in the Couette flow problem under incomplete accommodation of the tangential momentum of gas molecules by channel walls

The Couette flow problem has been used as an example for the proposed analytical method for calculating macro parameters of gas in channels, the thickness of which is comparable with the mean free path of gas molecules by means of simple numerical procedures. As a basic equation, the linearized BGK (Bhatnagar-Gross-Krook) model of the Boltzmann kinetic equation is used, and the boundary condition on the channel walls is taken to be the model of a specular-diffuse reflection. For different values of the channel thickness and the coefficient of accommodation of the tangential momentum of gas molecules by the channel walls, the profiles of the gas mass velocity in the channel have been constructed and the values of the nonzero component of the viscous stress tensor and the gas mass flow per unit channel width have been calculated. A comparison with similar results published in the press has been made.     

The effect of the microfluidic diodicity on the efficiency of valve-less rectification micropumps using Lattice Boltzmann Method

The efficiency of the valve-less rectification micropump depends primarily on the microfluidic diodicity (the ratio of the backward pressure drop to the forward pressure drop). In this study, different rectifying structures, including the conventional structures (nozzle/diffuser and Tesla structures), were investigated at very low Reynolds numbers (between 0.2 and 60). The rectifying structures were characterized with respect to their design, and a numerical approach was illustrated to calculate the diodicity for the rectifying structures. In this study, the microfluidic diodicity was evaluated numerically for different rectifying structures including half circle, semicircle, heart, triangle, bifurcation, nozzle/diffuser, and Tesla structures. The Lattice Boltzmann Method (LBM) was utilized as a numerical method to simulate the fluid flow in the microscale. The results suggest that at very low Reynolds number flow, rectification and multifunction micropumping may be achievable by using a number of the presented structures. The results for the conventional structures agree with the reported results.     

Numerical simulation of novel gas separation effect in microchannel with a series of oscillating barriers

A free-molecular gas flow through the microchannel with a series of oscillating microbarriers is studied. Barriers are oscillating with high frequency in the plane, perpendicular to the axis of the channel. It is shown that probability of passing through the channel for gas molecules significantly depends on relation of oscillations frequency, molecules thermal speed and distance between barriers. Presented effect can be used for separation of gases with different molecular masses due to discrepancy of their thermal speeds. The nature of this phenomenon is studied for different values of frequencies, characteristic sizes and number of barriers. Special attention is paid to comparison of different laws of gas–surface interactions.     

Bi-objective topology optimization of asymmetrical fixed-geometry microvalve for non-Newtonian flow

Fixed-geometry microvalves such as Tesla microvalves rely on the inertial forces of the fluid to allow flow in the desired direction while inhibiting flow in undesired direction. In the traditional topology optimization design methods of fixed-geometry microvalves, single objective function is used to minimize the energy dissipation of forward flow. And several previous studies have widely used diodicity to indicate the performance of fixed-geometry microvalves, which is defined as the ratio of the pressure drop of reverse flow to that of the forward flow. However, higher diodicity does not reflect the degree of forward energy dissipation, leading to a significant pumping power is required to drive flow. Therefore, treating the forward flow pressure drop and its performance independently by a bi-objective formulation is preferable to design fixed-geometry microvalve. This paper proposes a bi-objective topology optimization design method and uses the regularization constraint to design asymmetrical fixed-geometry microvalve for non-Newtonian flow. Several numerical examples with different bifurcation angles, Darcy number and weight coefficients of the bi-objective functions are studied and the validity of the topology optimization method presented in this paper is demonstrated.

     

Computational investigation and parametrization of the pumping effect in temperature-driven flows through long tapered channels

The temperature-driven rarefied gas flow and the associated pumping effects through long channels with linearly diverging or converging cross sections are computationally investigated. The implemented kinetic modeling is well known and relies on the infinite capillary methodology coupled with the mass conservation principle along the channel. The net mass flow rate and the induced pressure difference between the channel inlet and outlet are parametrized in terms of the geometrical and operational data including the channel inclination and the inlet pressure. Specific attention is given to the diode effect. The investigated flow setups include (a) the maximum pressure difference scenario with zero net mass flow rate (maximum pumping effect), (b) the maximum net mass flow rate scenario with equal inlet and outlet pressures and (c) all intermediate flow cases where both the net mass flow rate and the pressure difference are different than zero. In the first limit case, the pressure difference is always increased with the channel inclination and, depending on the inlet pressure, it may be larger for either the diverging or converging channel. In the second limit case, the mass flow rate is always decreased when the channel inclination is increased and it is always higher for the diverging channel. In both limit cases, optimum operation scenarios, in terms of the diode effect and the overall performance, are extracted. For intermediate cases, the characteristic curves of the net mass flow rate versus the pressure difference have been developed, indicating that the mass flow rate is inversely proportional to the pressure difference. The results strongly depend on the channel inclination. The present work may support decision making on the suitability of tapered channel flow to meet certain pumping specifications and the design of cascade-type thermally driven micropumps.     

Analysis of Stokes flow in microchannels with superhydrophobic surfaces containing a periodic array of micro-grooves

Superhydrophobic surfaces have been demonstrated to be capable of reducing fluid resistance in micro- and nanofluidic applications. The objective of this paper is to present analytical solutions for the Stokes flow through microchannels employing superhydrophobic surfaces with alternating micro-grooves and ribs. Results are presented for both cases where the micro-grooves are aligned parallel and perpendicular to the flow direction. The effects of patterning the grooves on one or both channel walls are also analyzed. The reduction in fluid resistance has been quantified in terms of a dimensionless effective slip length, which is found to increase monotonically with the shear-free fraction and the periodic extent of each groove–rib combination normalized by the channel half-height. Asymptotic relationships have been derived for the normalized effective slip length corresponding to large and small limiting values of the shear-free fraction and the normalized groove–rib period. A detailed comparison has been made between transverse and longitudinal grooves, patterned on one or both channel walls, to assess their effectiveness in terms of enhancing the effective slip length. These comparisons have been carried out for small and large limiting values, as well as finite values of the shear-free fraction and normalized groove–rib period. Results for the normalized effective slip length corresponding to transverse and longitudinal grooves are further applied to model the Stokes flow through microchannels employing superhydrophobic surfaces containing a periodic array of micro-grooves inclined at an angle to the direction of the applied pressure gradient. Results are presented for the normalized effective slip lengths parallel to the direction of the applied pressure gradient and the normalized cross flow rate perpendicular to the direction of the applied pressure gradient.     

Effect of operating conditions and liquid physical properties on the size of monodisperse microbubbles produced in a capillary embedded T-junction device

The aim of this study was to investigate the effect of operating parameters such as liquid flow rate, gas inlet pressure, and capillary diameter as well as the influence of the physical properties of the liquid, in particular viscosity, on the generation of monodisperse microbubbles in a circular cross section T-junction device. Aqueous glycerol solutions with viscosities ranging from 1- to 100 mPa s were used in the experiments. The bubble diameter generated was studied for systematically varied combinations of gas inlet pressure, liquid flow rate, and liquid viscosity with a fixed capillary inner diameter of 150 μm for the liquid and gas inlet channels as well as the outlet channel. In addition, the effect of channel geometry on bubble size was studied using capillaries with inner diameters of first 100 and then 200 μm. In all the experiments the distance between the coaxial capillaries at the junction was set to be 200 μm. All the microbubbles produced in this study were highly monodisperse (polydispersity index <1 %) and it was found, as expected, that bubble formation and size were influenced by the ratio of liquid to gas flow rate, capillary size, and liquid viscosity. The experimental data were then compared with empirical scaling laws derived for rectangular cross-section junctions. In contrast with these previous studies, which have found bubble size to be dependent on either the flow rate ratio (the squeezing regime) or capillary number (the dripping regime), in this experimental study bubble size was found to depend on both capillary number and flow ratio.     

Diffusion of fluid confined to nanotube with rectangular cross section

A dynamical model is proposed to study self-diffusion coefficient by confining the fluid in rectangular nanotube. The theoretical model is based on the consideration that the confinement affects the movement at atomic level. The model predicts that the diffusion parallel to walls of channel is different from that of diffusion perpendicular to the walls. Near the walls the dynamics of fluid has been found to slow down to an extent that below a certain value of ratio of width to the diameter of particle, the molecules behave as if these belong to solid. The results are contrasted with the result obtained from the model based on similar considerations for a fluid confined only in one direction. It is found that tendency of freezing near the wall increases due to confinement from second direction. Empirical relation which governs the behavior of diffusion coefficient as function of distance from the confining walls has also been proposed. The effect of confinement is more pronounced for denser fluids than for dilute fluid.     

Large-eddy simulation of streamwise-rotating turbulent channel flow

In many engineering and industrial applications the investigation of rotating turbulent flow is of great interest. Whereas some research has been done concerning channel flows with a spanwise rotation axis, only few investigations have been performed on channel flows with a rotation about the streamwise axis. In the present study an LES of a turbulent streamwise-rotating channel flow at Re_τ = 180 is performed using a moving grid method. The three-dimensional structures and the details of the secondary flow distribution are analyzed and compared with experimental data. The numerical-experimental comparison shows a convincing agreement as to the overall flow features. The results confirm the development of a secondary flow in the spanwise direction, which has been found to be correlated to the rotational speed. Furthermore, the findings show the distortion of the main flow velocity profile, the slight decrease of the streamwise Reynolds stresses in the vicinity of the walls, and the pronounced increase of the spanwise Reynolds stresses at higher rotation rates near the walls and particularly in the symmetry region. As to the numerical set-up it is shown that periodic boundary conditions in the spanwise direction suffice if the spanwise extent of the computational domain is larger than 10 times the channel half width.     

Single-step replicable microfluidic check valve for rectifying and sensing low Reynolds number flow

This paper presents a new microfluidic check valve well suited for low Reynolds number flow rate sensing, micropump flow rectification, and flow control in lab-on-a-chip devices. The valve uses coupling between fluid movement in a channel and an elastomeric column (flap) suspended in the fluid path to generate a strong anisotropic flow resistance. Soft lithography-based molding techniques were used to fabricate the valve, allowing for a low-cost, single-step fabrication process. Three valves—having heights of 25, 50, and 75 μm, respectively—were fabricated and experimentally evaluated; the best of them demonstrated a maximum fluidic diodicity of 4.6 at a Reynolds number of 12.6 and a significant diodicity of 1.6 at the low Reynolds number of 0.7. The valve’s notable low Reynolds number response was realized by adopting a design methodology that balances the stiffness of the elastomer flap and adhesion forces between the flap and its seat. A pair of elastomer check valves integrated with a miniature membrane actuator demonstrated a flow rectification efficiency of 29.8%. The valve’s other notable features include a wide bandwidth response, the ability to admit particles without becoming jammed, and flow rate sensing capability based on optical flap displacement measurements.     

Lattice Boltzmann modeling of microchannel flows in the transition flow regime

Owing to its kinetic nature and distinctive computational features, the lattice Boltzmann method for simulating rarefied gas flows has attracted significant research interest in recent years. In this article, a lattice Boltzmann (LB) model is presented to study microchannel flows in the transition flow regime, which have gained much attention because of fundamental scientific issues and technological applications in various micro-electro-mechanical system (MEMS) devices. In the model, a Bosanquet-type effective viscosity is used to account for the rarefaction effect on gas viscosity. To match the introduced effective viscosity and to gain an accurate simulation, a modified second-order slip boundary condition with a new set of slip coefficients is proposed. Numerical investigations demonstrate that the results, including the velocity profile, the non-linear pressure distribution along the channel, and the mass flow rate, are in good agreement with the solution of the linearized Boltzmann equation, the direct simulation Monte Carlo (DSMC) results, and the experimental results over a broad range of Knudsen numbers. It is shown that taking the rarefaction effect on gas viscosity into consideration and employing an appropriate slip boundary condition can lead to a significant improvement in the modeling of rarefied gas flows with moderate Knudsen numbers in the transition flow regime.     

Simulation of mixed electroosmotic/pressure-driven flows by utilizing dissipative particle dynamics

In this paper, we present an extension of dissipative particle dynamics method in order to study the mixed electroosmotic/pressure-driven micro- or nano-flows. This method is based on the Poisson–Boltzmann equation and has a great potential to resolve the electric double layer (EDL). Hence, apart from studying the bulk flow, it also provides a strong capability in order to resolve the complex phenomena occur inside the EDL. We utilize the proposed method to study the pure electroosmotic and also the mixed electroosmotic/pressure-driven flow through the straight micro-/nano-channels. The obtained results are in good agreement with the available analytical solutions. Furthermore, we study the electroosmotic flow and motion of DNA molecules through a T-shaped micro-channel. We show that neglecting the EDL and utilizing the slip wall boundary condition model can result in crucially misleading hydrodynamic characteristics if the EDL is comparable to the width of the channel. Finally, we utilize the presented method in order to study the complex flow patterns, which are created due to the heterogeneous distribution of the electric potential of the walls. These complex flow patterns usually are utilized in order to enhance the efficiency of mixing process in micro-/nano-length scales. In addition, we show that they can also be utilized effectively in order to separate the different macro-molecules such as polymers, DNA molecules and so on, according to their length of chain.     

Modeling oscillatory flows in the transition regime using a high-order moment method

We present results using three different continuum-based models to study oscillatory flow in the transition regime. Data obtained from numerical solutions of the Boltzmann equation and the direct simulation Monte Carlo method, are used to assess the ability of the continuum models to capture important rarefaction effects. We further highlight the need to consider two Knudsen numbers: one based upon the length scale and the other upon the time scale. It is found that the regularized 26 moment model can follow kinetic theory in the early transition regime in terms of both Knudsen numbers but the regularized 13 moment equations can only be used up to the upper limit of the hydrodynamic regime. However, the subtle interplay of the length and time scales on oscillatory non-equilibrium flow causes the Navier–Stokes equations to fail even in the hydrodynamic regime. In addition, the effect of modifying the accommodation coefficient is also considered. It is found that reducing the accommodation coefficient on the stationary wall alone will increase the motion of the gas. However, gaseous movement will be reduced by changing both walls from diffusive to specular reflection.     

Numerical investigation of dynamics of elliptical magnetic microparticles in shear flows

We study the rotational dynamics of magnetic prolate elliptical particles in a simple shear flow subjected to a uniform magnetic field, using direct numerical simulations based on the finite element method. Focusing on paramagnetic and ferromagnetic particles, we investigate the effects of the magnetic field strength and direction on their rotational dynamics. In the weak field regime (below a critical field strength), the particles are able to perform complete rotations, and the symmetry property of particle rotational speed is influenced by the direction and strength of the magnetic field. In the strong field regime (above a critical strength), the particles are pinned at steady angles. The steady angle depends on both the direction and strength of the magnetic field. Our results show that paramagnetic and ferromagnetic particles exhibit markedly different rotational dynamics in a uniform magnetic field. The numerical findings are in good agreement with theoretical prediction. Our numerical investigation further reveals drastically different lateral migration behaviors of paramagnetic and ferromagnetic particles in a wall-bounded simple shear flow under a uniform magnetic field. These two kinds of particles can thus be separated by combining a shear flow and a uniform magnetic field. We also study the lateral migration of paramagnetic and ferromagnetic particles in a pressure-driven flow (a more practical flow configuration in microfluidics), and observe similar lateral migration behaviors. These findings demonstrate a simple but useful way to manipulate non-spherical microparticles in microfluidic devices.     

A slip model for micro/nano gas flows induced by body forces

A slip model for gas flows in micro/nano-channels induced by external body forces is derived based on Maxwell’s collision theory between gas molecules and the wall. The model modifies the relationship between slip velocity and velocity gradient at the walls by introducing a new parameter in addition to the classic Tangential Momentum Accommodation Coefficient. Three-dimensional Molecular Dynamics simulations of helium gas flows under uniform body force field between copper flat walls with different channel height are used to validate the model and to determine this new parameter.