No-slip Surface Research Articles

Spherical and sessile droplet dynamics by fluctuating hydrodynamics

We simulate the mesoscopic dynamics of droplets formed by phase-separated fluids at nanometer scales where thermal fluctuations are significant. Both spherical droplets fully immersed in a second fluid and sessile droplets which are also in contact with a solid surface are studied. Our model combines a Cahn–Hilliard formulation with incompressible fluctuating hydrodynamics; for sessile droplets, the fluid–solid contact angle is specified as a boundary condition. Deterministic simulations with an applied body force are used to measure the droplets' mobility from which a diffusion coefficient is obtained using the Einstein relation. Stochastic simulations are independently used to obtain a diffusion coefficient from a linear fit of the variance of a droplet's position with time. In some scenarios, these two measurements give the same value but not in the case of a spherical droplet initialized near a slip wall or in the case of sessile droplets with large contact angles (≥90°) on both slip and no-slip surfaces.

Biophysical fluid dynamics in a Petri dish

The humble Petri dish is perhaps the simplest setting in which to examine the locomotion of swimming organisms, particularly those whose body size is tens of microns to millimeters. The fluid layer in such a container has a bottom no-slip surface and a stress-free upper boundary. It is of fundamental interest to understand the flow fields produced by the elementary and composite singularities of Stokes flow in this geometry. Building on the few particular cases that have previously been considered in the literature, we study here the image systems for the primary singularities of Stokes flow subject to such boundary conditions—the Stokeslet, rotlet, source, rotlet dipole, source dipole, and stresslet—paying particular attention to the far-field behavior. In several key situations, the depth-averaged fluid flow is accurately captured by the solution of an associated Brinkman equation whose screening length is proportional to the depth of the fluid layer. The case of hydrodynamic bound states formed by spinning microswimmers near a no-slip surface, discovered first using the alga , is reconsidered in the geometry of a Petri dish, where the power-law attractive interaction between microswimmers acquires unusual exponentially screened oscillations. Published by the American Physical Society 2024

Numerical study on the forced convective flow and heat transfer mechanism with macro-patterned hydrophilic-hydrophobic hybrid surfaces

Hydrophilic-hydrophobic hybrid surfaces can be used to harmonize the drag and heat transfer. However, the hybrid surfaces are almost microscopic scale and hardly used for forced convection at present. In this study, six macro-patterned hydrophilic-hydrophobic hybrid surfaces (square, diamond, circle, ellipse, triangle, and sector) and a no-slip surface are built. The performances are studied with the k-ε turbulent model by COMSOL, and the mechanism of performance change is analyzed with large eddy simulation (LES). The results show that macro-patterned hybrid surfaces can all reduce the flow drag but have different influences on heat transfer. With the increasing Reynolds number, the drag reduction rate (DR) declines. The largest DRs are 14.57% with the ellipse-patterned at lower Reynolds numbers, and 13.18% with the triangle-patterned at higher Reynolds numbers. For heat transfer capability, although adding hydrophobic parts, the square-patterned and diamond-patterned hybrid surfaces can raise Nusselt numbers. Combined above, the largest goodness factor (φ) enlarged rates are 16.43% (square-patterned) and 16.35% (diamond-patterned). Meanwhile, the influencing mechanism with the macro-patterned hybrid surface concludes four factors: the velocity slip, thermal resistance increases of air cavities, eddies of hydrophilic-hydrophobic interfaces, and the guiding effect of hydrophobic patterns' edges.

Fabrication of a scalable slippery surface via novel sprayable breath figure technique for sustainable drag reduction and anti-biofouling in marine environments

The maritime industry has been seeking efficient solutions to combat hydrodynamic friction and biofouling, which increase operational costs and environmental issues. To address these concerns, we developed a novel sprayable breath figure (sBF) method to create a scalable and cost-effective lubricant-infused surface (LIS) for reducing frictional drag forces on marine vehicles. The proposed sBF method facilitated the rapid production of multilayered porous polymer films with micron-scale spherical cavities. It can be applied to large and curved surfaces, thus overcoming the limitations of traditional breath figure methods. Further surface treatment of oxygen plasma etching followed by polydimethylsiloxane (PDMS) brush grafting was employed to optimize the interfacial slip and lubricant retention of the slippery surface coating. The PDMS brush-grafted slippery surfaces demonstrated significant drag reduction under turbulent flow conditions. This was confirmed by direct velocity field measurements, showing nonzero slip velocity unlike conventional no-slip surfaces. The same surfaces also exhibited remarkable anti-biofouling performance, severely resisting marine biofouling in real-sea field tests over 50 days. The proposed sBF method was successfully applied to large-area and curved submerged bodies, and achieved a noticeable drag reduction under high-speed turbulent flows. This study is a critical step toward the practical implementation of this technology in the marine industry.

Control effect of superhydrophobic grooves on flow-induced noise generated by flow around cylindrical shell at large Reynolds number

Flow-induced noise is an important factor affecting the quiet performance of underwater vehicles. Superhydrophobic surfaces are an emerging technology for underwater vehicles. In this study, a superhydrophobic surface is innovatively applied to the flow-induced noise control of underwater cylindrical shells. Alternating no-slip and no-shear surfaces are used to simulate the superhydrophobic surface with spanwise superhydrophobic grooves so that the flow regime and flow-induced noise of a no-slip cylinder are compared with the superhydrophobic cylinder under a high Reynolds number. The results show that the superhydrophobic surface can effectively delay flow separation and control the size of the wake shedding vortex. The flow-shedding vortices mainly affect the flow-induced noise in the lower frequency range, which is consistent with the vortex shedding frequency. The radiation characteristics of the flow-induced noise generated by the fluctuation pressure are mainly influenced by the eigenfrequency of the model in the range of 100 Hz–5000 Hz. Moreover, the superhydrophobic surface can effectively reduce the flow-induced noise and change its radiation directivity at both high and low frequencies by controlling vortex shedding and reducing the fluctuation pressure, respectively. The findings reported here shed new light on the flow-induced noise control of underwater vehicles.

Determining The Role of Thermal Radiation on Hydromagnetic Flow in A Vertical Porous Superhydrophobic Microchannel

The focus of this article is to scrutinize the performances of thermal radiation and superhydrophobicity on a free convection of an electrically conducting fluid across an upstanding microchannel affected by a transverse magnetic field. The plates were alternatively heated and incorporated with suction/injection effect. The approximate expressions of the formulated differential equations have been calculated. It is interesting to report that the heat gradient and fluid motion are significantly propelled for mounting values of thermal radiation parameter in both case I: super-hydrophobic surface (SHS) is heated and case II: no slip surface (NSS) is heated. However, this effect brought down the fluid temperature at the NSS, which is attributable to the direction of the heat flow. On the other hand, the velocity deteriorates for mounting values of magnetic field factor by the Lorentz force attracting the molecules, consequently leading to the fluid deterioration.

Collective Flows Drive Cavitation in Spinner Monolayers.

Hydrodynamic interactions can give rise to a collective motion of rotating particles. This, in turn, can lead to coherent fluid flows. Using large scale hydrodynamic simulations, we study the coupling between these two in spinner monolayers at weakly inertial regime. We observe an instability, where the initially uniform particle layer separates into particle void and particle rich areas. The particle void region corresponds to a fluid vortex, and it is driven by a surrounding spinner edge current. We show that the instability originates from a hydrodynamic lift force between the particle and fluid flows. The cavitation can be tuned by the strength of the collective flows. It is suppressed when the spinners are confined by a no-slip surface, and multiple cavity and oscillating cavity states are observed when the particle concentration is reduced.

Superhydrophobic surfaces with recirculating interfacial flow due to surfactants are ‘effectively’ immobilized

At high surface Péclet numbers, it is common to associate the presence of surfactants with surface immobilization, where a free surface becomes indistinguishable from a no-slip surface. A different mechanism has recently been proposed for longitudinal shear flow along a unidirectional trench (Baier & Hardt, J. Fluid Mech., vol. 949, 2022, A34) wherein, at high Marangoni numbers, the meniscus spanning the finite-length trench becomes a constant-shear-stress surface due to contamination by incompressible surfactant. That model predicts recirculating interfacial flows on the meniscus, a phenomenon that has been observed experimentally (Song et al., Phys. Rev. Fluids, vol. 3, issue 3, 2018, 033303). By finding an explicit solution to the constant-shear-stress model at all protrusion angles and calculating the effective slip length for a dilute mattress of such surfactant-laden trenches, we show that those effective slip lengths are almost indistinguishable from those for a surface whose menisci have the same deflection but have been completely immobilized (i.e. they are no-slip surfaces). This means that, despite the presence of non-trivial recirculating vortical flows on the menisci, the aggregate slip characteristics of such surfaces are that they have been effectively immobilized. This surprising result underscores the need for caution in comparing theory with experiments based on effective slip properties alone.

Decomposition of Estuarine Circulation and Residual Stratification under Landfast Sea Ice

Abstract For Arctic estuaries that are characterized by landfast sea ice cover during the winter season, processes generating estuarine circulation and residual stratification have not yet been investigated, although some of the largest estuaries in the world belong to this class. Landfast sea ice provides a no-slip surface boundary condition in addition to the bottom boundary, such that frictional effects are expected to be increased. For this study of estuarine circulation and residual stratification under landfast sea ice, first, a simple linear analytical model is used. To include tidally varying scenarios, a water-column model is applied with a second-moment turbulence closure to juxtapose free-surface and ice-covered estuaries. Well-mixed and strongly stratified tidally periodic scenarios are analyzed by means of a decomposition of estuarine circulation into contributions from gravitational circulation, eddy viscosity–shear covariance (ESCO), surface stress, and river runoff. A new method is developed to also decompose tidal residual salinity anomaly profiles. Estuarine circulation intensity and tidally residual potential energy anomaly are studied for a parameter space spanned by the Simpson number and the unsteadiness number. These are the major results of this study that will support future scenario studies in Arctic estuaries under conditions of accelerated warming: (i) residual surface drag under ice opposes estuarine circulation; (ii) residual differential advection under ice destabilizes the near-surface flow; (iii) reversal of ESCO during strong stratification does not occur under landfast sea ice; (iv) tidal pumping (s-ESCO) contributes dominantly to residual stratification also with sea ice cover. Significance Statement Our work gives a first qualitative and quantitative understanding of how landfast sea ice cover on tidal estuaries impacts on the generation of estuarine circulation and residual stratification. Along the Arctic coasts, where some of the world’s largest estuaries are located, these processes play a significant role for the economy and ecology by means of transports of sediments, nutrients and pollutants. Due to Arctic amplification, the conditions for ice-covered estuaries are strongly changing in a way that the ice-covered periods may be shorter in the future. Our results intend to motivate field observations and realistic model studies to allow for better predicting the consequences of these changes.

Performance and near-wake analysis of a vertical-axis hydrokinetic turbine under a turbulent inflow

This study investigates the performance and near-wake characteristics of a full-scale vertical-axis hydrokinetic turbine under a uniform inflow and turbulent inflow with a 5% and 10% turbulence intensity. The governing equations of the flow field are the incompressible Navier–Stokes equations expressed within an arbitrary Lagrangian–Eulerian framework to account for mesh motion. To discretize the system of equations, the residual-based variational multiscale formulation, augmented with a weakly imposed Dirichlet boundary condition at no-slip surfaces, is used. Moreover, a turbulent inflow is prescribed using a synthetic turbulence generation method referred to as Smirnov’s random flow generation and the near-wake characteristics are studied using a multi-domain method. While the performance of the turbine slightly reduced under a turbulent inflow compared to a uniform inflow, there was a negligible difference in its performance between the two turbulent inflow conditions. A turbulent inflow also resulted in large fluctuations of the instantaneous power coefficient which has important implications for the fatigue life of certain components. Lastly, the wake recovery was notably improved under a turbulent inflow suggesting that a shorter streamwise inter-device spacing may be acceptable in highly turbulent tidal sites.

Microbial transport and dispersion in heterogeneous flows created by pillar arrays

Swimming microbes, such as bacteria and algae, live in diverse habitats including soil, seawater, and the human body. The habitats are characterized by structural boundaries and heterogeneous fluid flows. Although in recent decades much progress has been made in understanding the Brownian ratchet motion of microbes and their hydrodynamic interactions with the wall, the complex interplay between the structural and fluid environment with self-propelling microbial motion still remains elusive. Here, we developed a Langevin model to simulate and investigate the transport and dispersion of microbes in periodic pillar arrays. By tracing the spatiotemporal evolution of microbial trajectories, we show that a no-slip pillar surface induces local fluid shear, which redirects microbial movements. In the vicinity of pillars, looping trajectories and slow motion lead to a transient accumulation and sluggish transport of microbes. Several modes of microscopic motion, including swinging, zigzag, and adhesive motion, were observed. In an asymmetric pillar array, adjacent downstream pillars provide geometric guidance such that the microbial population has a deterministic shift perpendicular to the flow direction. Moreover, the effects of the topology of the pillar array, fluid flow properties, and microbial properties on microbial advection and dispersion in a pillar array were quantitatively analyzed. Our results highlight the importance of surrounding structures and flow on microbial transport and distribution, and these should be carefully considered in the study of microbial processes.

Numerical study on drag reduction and wake modification for the flows over a hydrofoil in presence of surface heterogeneity

In this article, direct numerical simulations of flow around NACA0012 hydrofoil with superhydrophobic surface (SHS) is presented. Surface heterogeneity takes into account by periodic no-slip and shear-free grates on the surface. The study is conducted for a range of [Formula: see text] degree angles of attack and at fixed Reynolds number ( Re) 1000. SHS leads to effective Navier slip on the hydrofoil surface and corresponding changes in velocity profile. Bubble separation delays for higher gas-fraction ( G.F), and minimizes the vortex shedding effects. As a result, flow remains two-dimensional (2D) for higher angles of attack as compared to flow over three-dimensional (3D) hydrofoil with no-slip boundary. Both the drag reduction and enhancement of lift force are observed. Maximum lift are observed at [Formula: see text], while the drag force continues to decrease with the gradual increase in angle of attack and patterned micro-grates fraction. Mode C with smaller wavelength is observed at [Formula: see text]. Furthermore, increase in gas-fraction leads to increase in slip length which thickens the boundary layer and mimics the vorticity implies drag reduction. Thus, replacement of the no-slip surfaces by superhydrophobic surfaces can be treated as a promising drag reduction technology.

Effect of magnetic field on the motion of two rigid spheres embedded in porous media with slip surfaces.

A semi-analytical study for the Stokes flow approximation caused by two solid spheres of different sizes with slip surfaces, immersed in a porous medium in the presence of a transverse magnetic field, is investigated. The two spheres are translating with different velocities along the line joining their centers. A general solution is developed from the superposition of the essential solutions in two spherical frameworks with origins located at the centers of the two spheres. Numerical results for the normalized hydrodynamic drag force acting on each sphere are obtained with good convergence for various values of the Hartmann number which characterizes the presence of magnetic field, the permeability parameter which characterizes the porous medium, separation parameter, and velocity and size ratios of the spheres. Our drag results are in good agreement with the available solutions in the literature in the cases of no-slip surfaces and when the porous medium turns into a pure fluid.

Energetics of synchronization for model flagella and cilia.

Synchronization is often observed in the swimming of flagellated cells, either for multiple appendages on the same organism or between the flagella of nearby cells. Beating cilia are also seen to synchronize their dynamics. In 1951, Taylor showed that the observed in-phase beating of the flagella of coswimming spermatozoa was consistent with minimization of the energy dissipated in the surrounding fluid. Here we revisit Taylor's hypothesis for three models of flagella and cilia: (1) Taylor's waving sheets with both longitudinal and transverse modes, as relevant for flexible flagella, (2) spheres orbiting above a no-slip surface to model interacting flexible cilia, and (3) whirling rods above a no-slip surface to address the interaction of nodal cilia. By calculating the flow fields explicitly, we show that the rate of working of the model flagella or cilia is minimized in our three models for (1) a phase difference depending on the separation of the sheets and precise waving kinematics, (2) in-phase or opposite-phase motion depending on the relative position and orientation of the spheres, and (3) in-phase whirling of the rods. These results will be useful in future models probing the dynamics of synchronization in these setups.

MHD free convection flow in a vertical porous super-hydrophobic micro-channel

A free convective flow of an incompressible and electrically conducting fluid through a vertical micro-channel of rectangular geometry was considered. Both plates were porous and heated alternately. A transverse magnetic field was applied across the channel. One channel wall surface was no slip and the other was super-hydrophobic. The purpose of the study is to examine the effects of super-hydrophobicity, magnetism and wall porosity on the main characteristics of the flow. The exact solutions of the formulated differential equations were provided. A few highlights of the results obtained include: (1) the magnetic parameter lowered the skin friction at both surfaces when either of them were heated, (2) the suction/injection parameter raised the fluid temperature when the super-hydrophobic surface (SHS) was heated and brought it down when the no slip surface (NSS) was heated, (3) a critical temperature jump coefficient was observed at which the flow rates in both cases (only SHS heated, and only NSS heated) were equal. A few application areas of the research include micro-fluidics and micro-electronics.

On the role of the Prandtl number in convection driven by heat sources and sinks

Abstract

Dynamics of a microswimmer–microplatelet composite

Guiding active microswimmers by external fields to requested target locations is a promising strategy to realize complex transport on the microscale. For this purpose, one possibility consists of attaching the microswimmers to orientable passive components. Accordingly, we analyze theoretically, using a minimal model, the dynamics of a microswimmer when rigidly attached to a (significantly larger) microplatelet, here represented by a thin circular disk. In this way, we first determine the flow field in the whole space induced by a Stokeslet that is located above the center of a spatially fixed rigid disk of no-slip surface conditions. Finally, we determine and analyze possible trajectories of the overall composite. To this end, the platelet is additionally endowed with a permanent magnetic moment, which allows us to steer the motion of the whole composite by a homogeneous external magnetic field. As previous experimental studies suggest, related setups may be helpful to guide sperm cells to requested targets or for the purpose of coordinated drug delivery.

Linear complementarity solution of 2D boundary slip EHL contact

Recent researches proved that bearing friction can be largely reduced with an oleophilic (no-slip) surface sliding against an oleophobic (slip) surface. The present work investigates the applicability of the slip/no-slip concept to 2D elastohydrodynamic lubrication (EHL) problems. Numerical analysis of isothermal EHL point contact is conducted under pure rolling conditions with the critical shear stress slip model. The challenge of determining the slip direction upon the attainment of the critical shear stress value in 2D problems is resolved by using a linear complementarity principle. The effect of boundary slip on bearing performance in terms of film thickness and friction is evaluated.

Translating and squirming cylinders in a viscoplastic fluid

Three related problems of viscoplastic flow around cylinders are considered. First, translating cylinders with no-slip surfaces appear to generate adjacent rotating plugs in the limit where the translation speed becomes vanishingly small. In this plastic limit, analytical results are available from plasticity theory (slipline theory) which indicate that no such plugs should exist. Using a combination of numerical computations and asymptotic analysis, we show that the plugs of the viscoplastic theory actually disappear in the plastic limit, albeit very slowly. Second, when the boundary condition on the cylinder is replaced by one that permits sliding, the plastic limit corresponds to a partially rough cylinder. In this case, no plasticity solution has been previously established; we provide evidence from numerical computations and slipline theory that a previously proposed upper bound (Martin & Randolph, Geotechnique, vol. 56, 2006, pp. 141–145) is actually the true plastic solution. Third, we consider how a prescribed surface velocity field can propel cylindrical squirmers through a viscoplastic fluid. We determine swimming speeds and contrast the results with those from the corresponding Newtonian problem.

The extrudate swell singularity of Phan-Thien–Tanner and Giesekus fluids

The stress singularity for Phan-Thien–Tanner (PTT) and Giesekus viscoelastic fluids is determined for extrudate swell (commonly termed die swell). In the presence of a Newtonian solvent viscosity, the solvent stress dominates the polymer stresses local to the contact point between the solid (no-slip) surface inside the die and the free (slip) surface outside the die. The velocity field thus vanishes like rλ0, where r is the radial distance from the contact point and λ0 is the smallest Newtonian eigenvalue (dependent upon the angle of separation between the solid and free surfaces). The solvent stress thus behaves like r−(1−λ0) and dominates the polymer stresses, which are like r−4(1−λ0)/(5+λ0) for PTT and r−(1−λ0)(3−λ0)/4 for Giesekus. The polymer stresses require boundary layers at both the solid and free surfaces, the thicknesses of which are derived. These results do not hold for the Oldroyd-B fluid.