Glossary

2.2 Slip boundary conditions and surface effects

5 min read•august 15, 2024

Slip boundary conditions challenge the traditional no-slip assumption in fluid dynamics at the nanoscale. They describe non-zero fluid velocity at solid-liquid interfaces, altering flow rates and energy dissipation in nanofluidic devices. This phenomenon is crucial for optimizing performance in applications like nanofiltration and lab-on-a-chip systems.

Surface properties, fluid characteristics, and external factors all influence slip length. , roughness, and surface charge play key roles in determining slip behavior. Understanding these effects is essential for designing efficient nanofluidic devices and harnessing unique phenomena like enhanced fluid transport and reduced friction.

Slip Boundary Conditions in Nanofluids

Concept and Significance

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  • Slip boundary conditions describe non-zero fluid velocity at solid-liquid interfaces in nanofluidic systems contradicting traditional no-slip assumption in macroscale fluid dynamics
  • Slip length defined as extrapolated distance beyond solid surface where fluid velocity becomes zero characterizing degree of slip at interface
  • Importance increases as system size decreases to nanoscale where surface effects dominate over bulk fluid behavior
  • Alters flow rates, pressure drops, and energy dissipation in nanofluidic devices leading to enhanced fluid transport and reduced friction
  • Influenced by surface chemistry, fluid properties, and operating conditions (temperature, pressure)
  • Crucial for optimizing performance of nanofluidic devices in applications (nanofiltration, energy harvesting, lab-on-a-chip systems)

Mathematical Representation and Measurement

  • Slip velocity mathematically expressed as vs=b∂v∂yv_s = b \frac{\partial v}{\partial y} where vsv_s slip velocity, bb slip length, ∂v∂y\frac{\partial v}{\partial y} velocity gradient at the wall
  • Slip length measured experimentally using techniques (atomic force microscopy, surface force apparatus, particle image velocimetry)
  • Typical slip lengths range from few nanometers to several micrometers depending on system properties
  • Navier slip condition commonly used to model slip boundary conditions vs=λτwv_s = \lambda \tau_w where λ\lambda slip coefficient, τw\tau_w wall shear stress

Impact on Nanofluidic Systems

  • Enhanced flow rates observed in nanochannels with slip compared to no-slip conditions leading to improved efficiency in nanofluidic devices
  • Reduced friction and energy dissipation in slip systems resulting in lower pumping power requirements for fluid transport
  • Slip phenomena can lead to apparent viscosity reduction in confined geometries affecting rheological measurements at nanoscale
  • Slip boundary conditions modify transport phenomena (heat transfer, mass transport) in nanofluidic systems impacting device performance
  • Slip-enhanced flows enable novel applications (high-efficiency nanofiltration membranes, energy harvesting from salinity gradients)

Factors Influencing Slip Length

Surface Properties

  • Surface plays critical role in determining slip length with hydrophobic surfaces generally exhibiting larger slip lengths compared to hydrophilic surfaces
  • Molecular structure and arrangement of solid surface including crystallinity and defects significantly impact slip length by altering fluid-solid interactions
  • Presence of dissolved gases or nanobubbles at solid-liquid interface enhances slip by creating gas layer between solid and liquid phases
  • Surface charge density influences formation and structure of electric double layer (EDL) affecting slip boundary conditions
  • Zeta potential characterizes electric potential at shear plane of EDL serving as important parameter in predicting and controlling slip behavior in charged systems

Fluid Characteristics

  • Fluid viscosity and shear rate key fluid characteristics influencing slip length with higher viscosities and shear rates typically leading to increased slip
  • Size and shape of fluid molecules relative to surface features impact slip length with smaller molecules generally exhibiting less slip than larger ones (water molecules vs. polymer chains)
  • Presence of dissolved ions in fluid and their distribution within EDL can lead to charge-induced slip where counterions near surface enhance fluid mobility
  • Non-Newtonian fluid behavior (shear-thinning, shear-thickening) can result in complex slip phenomena at nanoscale

External Factors

  • Temperature affects slip length through influence on fluid viscosity, surface tension, and molecular interactions at solid-liquid interface
  • External forces (electric, magnetic fields) modulate slip length by altering orientation and behavior of fluid molecules near surface
  • Pressure influences slip length by affecting fluid density and molecular packing at solid-liquid interface
  • Applied shear stress can induce slip transitions leading to non-linear relationships between slip velocity and shear rate

Surface Properties and Fluid Flow

Wettability and Contact Angle

  • Surface wettability characterized by contact angle between fluid and solid surface directly influences degree of slip and fluid flow behavior in nanochannels
  • Superhydrophobic surfaces combining high contact angles and nanoscale roughness create air pockets significantly enhancing slip and reducing flow resistance
  • Contact angle hysteresis affects dynamic wetting behavior in nanofluidic systems influencing fluid transport and stability
  • Wettability gradients can induce directional fluid transport in nanochannels enabling novel pumping mechanisms (capillary pumps)

Surface Roughness and Texture

  • Nanoscale leads to formation of composite interfaces where fluid partially penetrates surface features altering effective slip length
  • Interplay between surface roughness and wettability creates local variations in slip length along channel leading to complex flow patterns and enhanced mixing
  • Surface roughness induces local pressure gradients and vortices at nanoscale which may either enhance or impede fluid flow depending on specific geometry
  • Orientation and periodicity of surface roughness features relative to flow direction significantly impact overall slip behavior and flow characteristics
  • Tailoring surface wettability and roughness through nanofabrication techniques (lithography, self-assembly) allows precise control of fluid flow in nanofluidic devices enabling novel applications in separation and analysis

Surface Charge and Slip Boundary Conditions

Electric Double Layer (EDL) Effects

  • Thickness of EDL characterized by Debye length determines extent of electrostatic interactions between charged surface and fluid impacting slip behavior
  • EDL structure influenced by ionic strength of fluid with thinner EDLs observed in high ionic strength solutions affecting slip length
  • Overlap of EDLs in narrow nanochannels leads to unique electrokinetic phenomena modifying slip conditions and fluid transport

Electrokinetic Phenomena

  • Electrokinetic phenomena (electro-osmosis, streaming potential) arise from interaction between surface charge, EDL, and applied electric fields modifying slip conditions
  • Electro-osmotic flow velocity in presence of slip boundary conditions given by veo=−ϵζηE(1+bλD)v_{eo} = -\frac{\epsilon \zeta}{\eta}E(1 + \frac{b}{\lambda_D}) where ϵ\epsilon permittivity, ζ\zeta zeta potential, η\eta viscosity, EE electric field, bb slip length, λD\lambda_D Debye length
  • Streaming potential generated by pressure-driven flow in charged nanochannels affected by slip boundary conditions influencing energy harvesting applications

Charge Distribution and Heterogeneity

  • Surface charge heterogeneity and patchiness create local variations in slip length leading to complex flow patterns and enhanced mixing in nanofluidic channels
  • Charge regulation at solid-liquid interface affects local surface charge density and slip behavior in response to changes in solution pH and ionic composition
  • External electric fields used to manipulate EDL structure and surface charge distribution providing means to dynamically control slip boundary conditions in nanofluidic devices

Key Terms to Review (18)

Atomic Force Microscopy (AFM): Atomic Force Microscopy (AFM) is a powerful imaging technique that allows researchers to visualize and manipulate surfaces at the nanoscale by measuring the forces between a sharp probe and the sample surface. This technique is critical in various fields as it provides detailed information about surface topography, mechanical properties, and intermolecular interactions. AFM operates by scanning a cantilever with a sharp tip over the surface of a sample, detecting changes in forces that occur at the atomic level.
Bioassays: Bioassays are experimental procedures used to measure the effects of a substance on living organisms, often to determine the potency or concentration of a biological agent. These assays are crucial in evaluating the biological activity of drugs, toxins, or other chemicals and can involve various organisms or cell types. The design of bioassays can be influenced by factors such as the properties of the substance being tested and the environment, including surface interactions and fluid dynamics.
Brownian motion: Brownian motion refers to the random movement of particles suspended in a fluid, resulting from their collisions with fast-moving molecules in the fluid. This phenomenon is crucial for understanding behaviors at the nanoscale, impacting various applications from flow sensors to quantum effects in nanofluidics.
Capillarity: Capillarity is the ability of a liquid to flow in narrow spaces without the assistance of external forces, often observed in thin tubes or porous materials. This phenomenon is crucial in various applications, as it allows for the movement of fluids in small-scale environments, playing a vital role in how substances interact with surfaces and the transport of fluids in biological systems.
Cauchy Momentum Equation: The Cauchy Momentum Equation describes the motion of fluid substances and is derived from Newton's second law. It relates the rate of change of momentum within a control volume to the forces acting on it, including pressure gradients and viscous stresses. This equation is critical in understanding how fluids behave under various conditions, particularly when examining slip boundary conditions and surface effects in nanoscale systems.
Coulombic interactions: Coulombic interactions refer to the electrostatic forces that occur between charged particles, described by Coulomb's law. These interactions play a crucial role in determining how particles behave at the nanoscale, especially in the presence of surfaces, as they influence phenomena like adhesion, aggregation, and the movement of particles in nanofluidic systems.
Diffusion: Diffusion is the process by which particles spread from an area of higher concentration to an area of lower concentration, driven by the random motion of molecules. In the context of nanoscale systems, diffusion is crucial for understanding how substances move within confined spaces, affecting various applications like drug delivery and single-cell manipulation.
Dynamic Light Scattering (DLS): Dynamic Light Scattering (DLS) is a technique used to measure the size of small particles in suspension or within a medium by analyzing the scattering of light caused by these particles. This method is particularly useful in nanofluidics and lab-on-a-chip devices because it provides insights into particle dynamics and interactions at the nanoscale, which are heavily influenced by slip boundary conditions and surface effects.
Hydrophobicity: Hydrophobicity refers to the property of a surface or material that repels water, leading to minimal interaction with water molecules. This characteristic is crucial in understanding how fluids behave at the nanoscale, influencing phenomena such as diffusion rates and transport processes in nanochannels, as well as affecting slip boundary conditions and the behavior of molecules at surfaces. The interplay between hydrophobicity and the scaling laws of nanofluidics underpins many applications in lab-on-a-chip devices.
Knudsen number: The Knudsen number (Kn) is a dimensionless quantity that represents the ratio of the molecular mean free path length to a characteristic length scale of a system, often used to assess the flow regime in a fluid. It is crucial for understanding how fluid dynamics behave at the nanoscale, where traditional continuum assumptions may break down and molecular effects become significant.
Microfluidic mixers: Microfluidic mixers are devices designed to mix small volumes of fluids at the microscale, typically utilizing geometrical and flow dynamics to achieve efficient mixing in Lab-on-a-Chip applications. These mixers exploit various principles such as laminar flow, diffusion, and chaotic advection to ensure that even the smallest quantities of liquids are thoroughly combined. The design of these mixers can significantly influence the performance of chemical reactions and biological assays within microfluidic systems.
Navier Slip Model: The Navier Slip Model is a mathematical description of fluid flow near solid boundaries, which allows for a finite slip between the fluid and the surface. This model addresses how real fluids behave at nanoscales, where traditional no-slip boundary conditions may not apply, providing insights into the effects of surface properties on fluid dynamics.
No-slip condition: The no-slip condition is a fundamental principle in fluid dynamics that states that a fluid in contact with a solid surface will have zero velocity relative to that surface. This means that at the boundary layer, the velocity of the fluid matches the velocity of the surface it is in contact with, creating a layer where fluid velocity transitions from the surface to the free stream flow. This concept is crucial for understanding flow behavior at micro and nanoscale levels, influencing both slip boundary conditions and computational modeling of fluid dynamics.
Slip Flow: Slip flow refers to a flow regime where the velocity of a fluid at a solid boundary differs from that of the fluid itself, resulting in a slip at the boundary. This phenomenon is particularly significant at the nanoscale, where the effects of molecular interactions and surface properties become pronounced, affecting transport processes and sensor behavior.
Surface Energy: Surface energy is the excess energy at the surface of a material compared to its bulk, arising from the disruption of intermolecular bonds at the surface. This property plays a crucial role in various phenomena, including wetting, adhesion, and the behavior of liquids at interfaces, which are particularly important in applications involving micro and nanoscale systems.
Surface roughness: Surface roughness refers to the texture of a surface characterized by its irregularities and deviations from a perfectly flat plane. This property is crucial as it affects various physical phenomena such as fluid flow, adhesion, and light scattering, which are particularly significant in nanoscale applications like etching, deposition, and fluid transport in nanochannels.
Surface-to-volume ratio: The surface-to-volume ratio is a measure that compares the surface area of an object to its volume, which becomes significantly important as the size of the object decreases to the nanoscale. In nanofluidics, this ratio affects various physical phenomena, including transport properties, heat transfer, and reaction kinetics, since smaller structures tend to have a higher surface area relative to their volume, leading to enhanced surface interactions and unique behaviors.
Wettability: Wettability refers to the ability of a liquid to maintain contact with a solid surface, influenced by the adhesive and cohesive forces at play. It plays a crucial role in determining how fluids interact with surfaces in various applications, such as lab-on-a-chip devices, where precise fluid management is essential for functionality. The wettability of materials can affect bonding techniques, surface modifications, and the overall efficiency of nanofluidic systems.
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