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In elastohydrodynamic lubrication (EHL) contact, the film thickness strongly depends on boundary slips, including velocity slip and thermal slip at the solid–lubricant interface. In the EHL studies published thus far, velocity slip at the solid–lubricant interface has been investigated individually without considering thermal slip. In this study, the effects of both types of boundary slip on film thickness were investigated simultaneously in rolling/sliding contact. Numerical simulations were conducted based on the modified Reynolds equation and energy equation by considering boundary slips on the sliding surface. The results indicate that the velocity slip causes a reduction in film thickness under pure rolling contact, while a shifted surface dimple is formed along the sliding direction due to both velocity slip and thermal slip under zero entrainment velocity (ZEV) contact.

Energetic Variational Approach is used to derive a novel thermodynamically consistent three-phase model of a mixture of Newtonian and visco-elastic fluids. The model which automatically satisfies the energy dissipation law and is Galilean invariant, consists of coupled Navier-Stokes and Cahn-Hilliard equations. Modified General Navier Boundary Condition with fluid elasticity taken into account is also introduced for using the model to study moving contact line problems. Energy stable numerical scheme is developed to solve system of model equations efficiently. Convergence of the numerical scheme is verified by simulating a droplet sliding on an inclined plane under gravity. The model can be applied for studying various biological or biophysical problems. Predictive abilities of the model are demonstrated by simulating deformation of venous blood clots with different visco-elastic properties and experimentally observed internal structures under different biologically relevant shear blood flow conditions.

This work describes a novel formulation for the simulation of Navier–Stokes problems including embedded objects. The new proposal is based on the use of a modified finite element space, which replaces the standard one within the elements intersected by the immersed geometry. The modified space is able to exactly reproduce the jumps happening at the embedded boundary while preserving the conformity across the faces intersected by the embedded object. The paper focuses particularly on the imposition of a slip boundary condition on the surface of the embedded geometry, proposing a new technique for the application of such constraint. The new proposal is carefully benchmarked using the results of a body fitted technique and of an alternative embedded approach. Potential applications of interest are also presented., Peer Reviewed, Postprint (author's final draft)

With the miniaturisation and increasing power density of electronic devices and energy systems, increasing the efficiency and effectiveness of heat removal is closely tied with technological advancement. Both microchannels and nanofluids have shown promise to enhance the internal convective heat transfer in literature, but both of these come at the cost of increased pumping power. In microchannels, this is due to the dominance of surface forces and in nanofluids, it is due to increased viscosity. The literature has also shown that superhydrophobic surfaces can be used to create shear-free regions with a channel which effectively reduces pumping power. At present, though, no study has investigated the combined heat and mass transfer impacts of implementing nanofluids in superhydrophobic microchannels. Therefore, the aim of this thesis is to advance this field of research by systematically experimentally investigating the combined heat and mass transfer implications of utilising superhydrophobic microchannels and nanofluids.In this work, various superhydrophobic microstructural geometries with different shear-free fractions were designed and fabricated. Firstly, hydrodynamic studies were conducted with pure water, which yielded good agreement with the analytical predictions. A maximum flow friction reduction of up to 26% was measured for pure water in these superhydrophobic microchannels. Following the hydrodynamic studies, heat transfer studies were performed. A figure of merit was used to examine the combined thermodynamic and hydrodynamic performance of the superhydrophobic microchannels compared with that of the smooth microchannel. It was observed that most of the superhydrophobic microchannels tested in this study had a measured figure of merit of more than unity ranging from approximately 1.03 to 1.28. This ultimately demonstrated that the hydrodynamic enhancement of superhydrophobic microchannels can overcome their disadvantage in heat transfer performance. In

回顧了高超聲速連續流部分的計算流體力學(CFD)方法,總結了近些年興起的氣體動理學格式。闡述了該格式的構造機制,強調了將物理規律直接用于構造數值方法的思路。結合一些應用實例,例如激波相互作用、激波邊界層相互作用以及邊界層分離等高超聲速問題,說明了這種構造思路給數值模擬帶來的優點。從高超聲速的發展歷程來看,氣體動理學格式的構造過程包含了更基礎的物理規律,而且具有多尺度的特性。這些特性有助于研究復雜的高超聲速問題。介觀或者微觀角度直接構造數值方法的發展趨勢為高超聲速計算工具指出了可能的發展方向。 For hypersonic flow simulation, a review of computation fluid dynamics (CFD) and a summary of gas kinetic scheme are presented in this paper. The mechanism underlying the construction of gas kinetic scheme is clarified by comparing it with the traditional CFD method. The importance of direct modeling and the implementation of the physical laws in a discretized space are emphasized. Through some classical hypersonic applications in recent years, such as the shock/shock interaction, shock wave/boundary layer interaction, and hypersonic boundary layer separation problems, the advantages of the methodology are also demonstrated. As a trend of CFD, the gas kinetic scheme includes more fundamental physical laws in its algorithm construction, and the multiple scale nature makes the kinetic scheme feasible for the hypersonic applications. The principle of direct modeling and the methodology of constructing numerical schemes from mesoscopic or microscopic flow dynamics would benefit the development of reliable flow solvers, especially for the high speed flow. ©, 2014, AAAS Press of Chinese Society of Aeronautics and Astronautics. All right reserved.

We develop a continuum hydrodynamic model for two-phase immiscible flows that involve electroosmotic effect in an electrolyte and moving contact line at solid surfaces. The model is derived through a variational approach based on the Onsager principle of minimum energy dissipation. This approach was first presented in the derivation of a continuum hydrodynamic model for moving contact line in neutral two-phase immiscible flows (Qian, Wang, and Sheng, J. Fluid Mech. 564, 333-360 (2006)). Physically, the electroosmotic effect can be formulated by the Onsager principle as well in the linear response regime. Therefore, the same variational approach is applied here to the derivation of the continuum hydrodynamic model for charged two-phase immiscible flows where one fluid component is an electrolyte exhibiting electroosmotic effect on a charged surface. A phase field is employed to model the diffuse interface between two immiscible fluid components, one being the electrolyte and the other a nonconductive fluid, both allowed to slip at solid surfaces. Our model consists of the incompressible Navier-Stokes equation for momentum transport, the Nernst-Planck equation for ion transport, the Cahn-Hilliard phase-field equation for interface motion, and the Poisson equation for electric potential, along with all the necessary boundary conditions. In particular, all the dynamic boundary conditions at solid surfaces, including the generalized Navier boundary condition for slip, are derived together with the equations of motion in the bulk region. Numerical examples in two-dimensional space, which involve overlapped electric double layer fields, have been presented to demonstrate the validity and applicability of the model, and a few salient features of the two-phase immiscible electroosmotic flows at solid surface. The wall slip in the vicinity of moving contact line and the Smoluchowski slip in the electric double layer are both investigated. © 2012 Global-Science Press.

We develop a continuum hydrodynamic model for two-phase immiscible flows that involve electroosmotic effect in an electrolyte and moving contact line at solid surfaces. The model is derived through a variational approach based on the Onsager principle of minimum energy dissipation. This approach was first presented in the derivation of a continuum hydrodynamic model for moving contact line in neutral two-phase immiscible flows (Qian, Wang, and Sheng, J. Fluid Mech. 564, 333-360 (2006)). Physically, the electroosmotic effect can be formulated by the Onsager principle as well in the linear response regime. Therefore, the same variational approach is applied here to the derivation of the continuum hydrodynamic model for charged two-phase immiscible flows where one fluid component is an electrolyte exhibiting electroosmotic effect on a charged surface. A phase field is employed to model the diffuse interface between two immiscible fluid components, one being the electrolyte and the other a nonconductive fluid, both allowed to slip at solid surfaces. Our model consists of the incompressible Navier-Stokes equation for momentum transport, the Nernst-Planck equation for ion transport, the Cahn-Hilliard phase-field equation for interface motion, and the Poisson equation for electric potential, along with all the necessary boundary conditions. In particular, all the dynamic boundary conditions at solid surfaces, including the generalized Navier boundary condition for slip, are derived together with the equations of motion in the bulk region. Numerical examples in two-dimensional space, which involve overlapped electric double layer fields, have been presented to demonstrate the validity and applicability of the model, and a few salient features of the two-phase immiscible electroosmotic flows at solid surface. The wall slip in the vicinity of moving contact line and the Smoluchowski slip in the electric double layer are both investigated. © 2012 Global-Science Press.

We develop a continuum hydrodynamic model for two-phase immiscible flows that involve electroosmotic effect in an electrolyte and moving contact line at solid surfaces. The model is derived through a variational approach based on the Onsager principle of minimum energy dissipation. This approach was first presented in the derivation of a continuum hydrodynamic model for moving contact line in neutral two-phase immiscible flows (Qian, Wang, and Sheng, J. Fluid Mech. 564, 333-360 (2006)). Physically, the electroosmotic effect can be formulated by the Onsager principle as well in the linear response regime. Therefore, the same variational approach is applied here to the derivation of the continuum hydrodynamic model for charged two-phase immiscible flows where one fluid component is an electrolyte exhibiting electroosmotic effect on a charged surface. A phase field is employed to model the diffuse interface between two immiscible fluid components, one being the electrolyte and the other a nonconductive fluid, both allowed to slip at solid surfaces. Our model consists of the incompressible Navier-Stokes equation for momentum transport, the Nernst-Planck equation for ion transport, the Cahn-Hilliard phase-field equation for interface motion, and the Poisson equation for electric potential, along with all the necessary boundary conditions. In particular, all the dynamic boundary conditions at solid surfaces, including the generalized Navier boundary condition for slip, are derived together with the equations of motion in the bulk region. Numerical examples in two-dimensional space, which involve overlapped electric double layer fields, have been presented to demonstrate the validity and applicability of the model, and a few salient features of the two-phase immiscible electroosmotic flows at solid surface. The wall slip in the vicinity of moving contact line and the Smoluchowski slip in the electric double layer are both investigated. © 2012 Global-Science Press.

Based on our continuum hydrodynamic model for immiscible two-phase flows at solid surfaces, the stick-slip motion has been predicted for moving contact line at chemically patterned surfaces [Wang et al., J. Fluid Mech., 605 (2008), pp. 59-78]. In this paper we show that the continuum predictions can be quantitatively verified by molecular dynamics (MD) simulations. Our MD simulations are carried out for two immiscible Lennard-Jones fluids confined by two planar solid walls in Poiseuille flow geometry. In particular, one solid surface is chemically patterned with alternating stripes. For comparison, the continuum model is numerically solved using material parameters directly measured in MD simulations. From oscillatory fluid-fluid interface to intermittent stick-slip motion of moving contact line, we have quantitative agreement between the continuum and MD results. This agreement is attributed to the accurate description down to molecular scale by the generalized Navier boundary condition in our continuum model. Numerical results are also presented for the relaxational dynamics of fluid-fluid interface, in agreement with a theoretical analysis based on the Onsager principle of minimum energy dissipation.

Based on our continuum hydrodynamic model for immiscible two-phase flows at solid surfaces, the stick-slip motion has been predicted for moving contact line at chemically patterned surfaces [Wang et al., J. Fluid Mech., 605 (2008), pp. 59-78]. In this paper we show that the continuum predictions can be quantitatively verified by molecular dynamics (MD) simulations. Our MD simulations are carried out for two immiscible Lennard-Jones fluids confined by two planar solid walls in Poiseuille flow geometry. In particular, one solid surface is chemically patterned with alternating stripes. For comparison, the continuum model is numerically solved using material parameters directly measured in MD simulations. From oscillatory fluid-fluid interface to intermittent stick-slip motion of moving contact line, we have quantitative agreement between the continuum and MD results. This agreement is attributed to the accurate description down to molecular scale by the generalized Navier boundary condition in our continuum model. Numerical results are also presented for the relaxational dynamics of fluid-fluid interface, in agreement with a theoretical analysis based on the Onsager principle of minimum energy dissipation.

Based on our continuum hydrodynamic model for immiscible two-phase flows at solid surfaces, the stick-slip motion has been predicted for moving contact line at chemically patterned surfaces [Wang et al., J. Fluid Mech., 605 (2008), pp. 59-78]. In this paper we show that the continuum predictions can be quantitatively verified by molecular dynamics (MD) simulations. Our MD simulations are carried out for two immiscible Lennard-Jones fluids confined by two planar solid walls in Poiseuille flow geometry. In particular, one solid surface is chemically patterned with alternating stripes. For comparison, the continuum model is numerically solved using material parameters directly measured in MD simulations. From oscillatory fluid-fluid interface to intermittent stick-slip motion of moving contact line, we have quantitative agreement between the continuum and MD results. This agreement is attributed to the accurate description down to molecular scale by the generalized Navier boundary condition in our continuum model. Numerical results are also presented for the relaxational dynamics of fluid-fluid interface, in agreement with a theoretical analysis based on the Onsager principle of minimum energy dissipation.

By using the recently discovered generalized Navier boundary condition, we numerically evaluate the Poiseuille flow of two immiscible fluids between parallel plates with undulating solid surfaces (modeled by a sinusoidal function). The purpose of the simulation is to study the effect of the surface roughness on the motion of the two-phase flow. It is shown that when the magnitude of the undulation (with period fixed) is increased, there is a critical value above which the contact line “jumps” over the valleys of the undulations, leaving behind isolated pockets of the pushed fluid. Moreover, the contact line exhibits pinning behavior, i.e., the contact lines moves much more slowly than the tip of the front of the fluid–fluid interface, leading to fingering of the pushing fluid.

The no-slip boundary condition, i.e., zero fluid velocity relative to the solid at the fluid-solid interface, has been very successful in describing many macroscopic flows. A problem of principle arises when the no-slip boundary condition is used to model the hydrodynamics of immiscible-fluid displacement in the vicinity of the moving contact line, where the interface separating two immiscible fluids intersects the solid wall. Decades ago it was already known that the moving contact line is incompatible with the no-slip boundary condition, since the latter would imply infinite dissipation due to a non-integrable singularity in the stress near the contact line. In this paper we first present an introductory review of the problem. We then present a detailed review of our recent results on the contact-line motion in immiscible two-phase flow, from molecular dynamics (MD) simulations to continuum hydrodynarnics calculations. Through extensive XID studies and detailed analysis, we have uncovered the slip boundary condition governing the moving contact line, denoted the generalized Navier boundary condition. We have used this discovery to formulate a continuum hydrodynamic model whose predictions are in remarkable quantitative agreement with the MD simulation results down to the molecular scale. These results serve to affirm the validity of the generalized Navier boundary condition, as well as to open up the possibility of continuum hydrodynamic calculations of immiscible flows that are physically meaningful at the molecular level.

By using the recently discovered generalized Navier boundary condition, we numerically evaluate the Poiseuille flow of two immiscible fluids between parallel plates with undulating solid surfaces (modeled by a sinusoidal function). The purpose of the simulation is to study the effect of the surface roughness on the motion of the two-phase flow. It is shown that when the magnitude of the undulation (with period fixed) is increased, there is a critical value above which the contact line “jumps” over the valleys of the undulations, leaving behind isolated pockets of the pushed fluid. Moreover, the contact line exhibits pinning behavior, i.e., the contact lines moves much more slowly than the tip of the front of the fluid–fluid interface, leading to fingering of the pushing fluid.

The no-slip boundary condition, i.e., zero fluid velocity relative to the solid at the fluid-solid interface, has been very successful in describing many macroscopic flows. A problem of principle arises when the no-slip boundary condition is used to model the hydrodynamics of immiscible-fluid displacement in the vicinity of the moving contact line, where the interface separating two immiscible fluids intersects the solid wall. Decades ago it was already known that the moving contact line is incompatible with the no-slip boundary condition, since the latter would imply infinite dissipation due to a non-integrable singularity in the stress near the contact line. In this paper we first present an introductory review of the problem. We then present a detailed review of our recent results on the contact-line motion in immiscible two-phase flow, from molecular dynamics (MD) simulations to continuum hydrodynarnics calculations. Through extensive XID studies and detailed analysis, we have uncovered the slip boundary condition governing the moving contact line, denoted the generalized Navier boundary condition. We have used this discovery to formulate a continuum hydrodynamic model whose predictions are in remarkable quantitative agreement with the MD simulation results down to the molecular scale. These results serve to affirm the validity of the generalized Navier boundary condition, as well as to open up the possibility of continuum hydrodynamic calculations of immiscible flows that are physically meaningful at the molecular level.

By using the recently discovered generalized Navier boundary condition, we numerically evaluate the Poiseuille flow of two immiscible fluids between parallel plates with undulating solid surfaces (modeled by a sinusoidal function). The purpose of the simulation is to study the effect of the surface roughness on the motion of the two-phase flow. It is shown that when the magnitude of the undulation (with period fixed) is increased, there is a critical value above which the contact line “jumps” over the valleys of the undulations, leaving behind isolated pockets of the pushed fluid. Moreover, the contact line exhibits pinning behavior, i.e., the contact lines moves much more slowly than the tip of the front of the fluid–fluid interface, leading to fingering of the pushing fluid.

The no-slip boundary condition, i.e., zero fluid velocity relative to the solid at the fluid-solid interface, has been very successful in describing many macroscopic flows. A problem of principle arises when the no-slip boundary condition is used to model the hydrodynamics of immiscible-fluid displacement in the vicinity of the moving contact line, where the interface separating two immiscible fluids intersects the solid wall. Decades ago it was already known that the moving contact line is incompatible with the no-slip boundary condition, since the latter would imply infinite dissipation due to a non-integrable singularity in the stress near the contact line. In this paper we first present an introductory review of the problem. We then present a detailed review of our recent results on the contact-line motion in immiscible two-phase flow, from molecular dynamics (MD) simulations to continuum hydrodynarnics calculations. Through extensive XID studies and detailed analysis, we have uncovered the slip boundary condition governing the moving contact line, denoted the generalized Navier boundary condition. We have used this discovery to formulate a continuum hydrodynamic model whose predictions are in remarkable quantitative agreement with the MD simulation results down to the molecular scale. These results serve to affirm the validity of the generalized Navier boundary condition, as well as to open up the possibility of continuum hydrodynamic calculations of immiscible flows that are physically meaningful at the molecular level.

Molecular dynamics (MD) simulations have been carried out to investigate the slip of fluid in the lid driven cavity flow where the no-slip boundary condition causes unphysical stress divergence. The MD results not only show the existence of fluid slip but also verify the validity of the Navier slip boundary condition. To better understand the fluid slip in this problem, a continuum hydrodynamic model has been formulated based upon the MD verification of the Navier boundary condition (NBC) and the Newtonian stress. Our model has no adjustable parameter because all the material parameters (density, viscosity, and slip length) are directly determined from MD simulations. Steady-state velocity fields from continuum calculations are in quantitative agreement with those from MD simulations, from the molecular-scale structure to the global flow. The main discovery is as follows. In the immediate vicinity of the corners where moving and fixed solid surfaces intersect, there is a core partial-slip region where the slippage is large at the moving solid surface and decays away from the intersection quickly. In particular, the structure of this core region is nearly independent of the system size. On the other hand, for a sufficiently large system, an additional partial-slip region appears where the slippage varies as 1/r, with r denoting the distance from the corner along the moving solid surface. The existence of this wide power-law region is in accordance with the asymptotic 1/r variation of stress and the NBC.

Molecular dynamics (MD) simulations have been carried out to investigate the slip of fluid in the lid driven cavity flow where the no-slip boundary condition causes unphysical stress divergence. The MD results not only show the existence of fluid slip but also verify the validity of the Navier slip boundary condition. To better understand the fluid slip in this problem, a continuum hydrodynamic model has been formulated based upon the MD verification of the Navier boundary condition (NBC) and the Newtonian stress. Our model has no adjustable parameter because all the material parameters (density, viscosity, and slip length) are directly determined from MD simulations. Steady-state velocity fields from continuum calculations are in quantitative agreement with those from MD simulations, from the molecular-scale structure to the global flow. The main discovery is as follows. In the immediate vicinity of the corners where moving and fixed solid surfaces intersect, there is a core partial-slip region where the slippage is large at the moving solid surface and decays away from the intersection quickly. In particular, the structure of this core region is nearly independent of the system size. On the other hand, for a sufficiently large system, an additional partial-slip region appears where the slippage varies as 1/r, with r denoting the distance from the corner along the moving solid surface. The existence of this wide power-law region is in accordance with the asymptotic 1/r variation of stress and the NBC.

Molecular dynamics (MD) simulations have been carried out to investigate the slip of fluid in the lid driven cavity flow where the no-slip boundary condition causes unphysical stress divergence. The MD results not only show the existence of fluid slip but also verify the validity of the Navier slip boundary condition. To better understand the fluid slip in this problem, a continuum hydrodynamic model has been formulated based upon the MD verification of the Navier boundary condition (NBC) and the Newtonian stress. Our model has no adjustable parameter because all the material parameters (density, viscosity, and slip length) are directly determined from MD simulations. Steady-state velocity fields from continuum calculations are in quantitative agreement with those from MD simulations, from the molecular-scale structure to the global flow. The main discovery is as follows. In the immediate vicinity of the corners where moving and fixed solid surfaces intersect, there is a core partial-slip region where the slippage is large at the moving solid surface and decays away from the intersection quickly. In particular, the structure of this core region is nearly independent of the system size. On the other hand, for a sufficiently large system, an additional partial-slip region appears where the slippage varies as 1/r, with r denoting the distance from the corner along the moving solid surface. The existence of this wide power-law region is in accordance with the asymptotic 1/r variation of stress and the NBC.