Slip boundary conditions liquid contact

Considering a surface temperature which is higher than the Leidenfrost temperature of the liquid in this study, it is assumed that there exists a microscale vapor layer which prevents a direct contact of the droplet and the surface. Similar to Fujimoto and Hatta (1996), the no-slip boundary condition is adopted at the solid surface during the droplet-spreading process and the free-slip... 

Liquid viscosities have been observed to increase, decrease, and remain constant in microfluidic devices as compared to viscosities in larger systems. ° Deviations from the no-slip boundary condition have been observed to occur at high shear rates. One important deviation from no-slip conditions occurs at moving contact lines, such as when capillary forces pull a liquid into a hydrophilic channel. The point at which the gas, liquid, and solid phases move along the channel wall is in violation of the no-slip boundary condition. Ho and Tai review discrepancies between classical Stokes flow theory and observations of flow in microchannels. No adequate theory is yet available to explain these deviations from classical behavior. ... 

The response of the QCM at the solid-liquid interface can be found by matching the stress and the velocity fields in the medium in contact. It is usually assumed that the relative velocity at the boundary between the liquid and the solid is zero. This corresponds to the non-slip boundary condition. Strong experimental evidence supports this assumption on the macroscopic scales [42,43]. hi this case the frequency shift, A, and the half-width of the... 

The no-slip condition at the substrate reflects the fact that liquid molecules at a solid substrate experience (significant) interactions responsible for adhesion. In contrast to liquid molecules in contact with other liquid molecules, they do not move easily on this substrate. As a consequence, the velocity of these molecules is approximately zero (hence, no-slip boundary condition). However, applying this boundary crmdition strictly would not allow for any displacement of a liquid on a... 

In any fluid continuum possessing a viscosity, however small, the velocity of the fluid adjacent to the solid boundary is the same as the boundary, there is no relative motion between fluid particles and solid boundaries with which they are in contact. Despite its apparent simplicity, the no-slip boundary condition leads to some physical inconsistencies that are not yet resolved completely. For example, the no-slip condition cannot explain the motion of a liquid interface in contact with a solid boundary according to this condition, the liquid interface in a partially filled glass must remain... 

Surface tension variations affect the mobility of the fluid-fluid interface and cause Marangoni flow instabilities. Surfactant-laden flows exhibit surface tension variations at the gas-liquid or liquid-liquid contact line due to surfactant accumulation close to stagnation points [2,53]. For gas-liquid systems, these Marangoni effects can often be accounted for by assuming hardening of the gas bubble, i.e. by replacing the no-shear boundary condition that is normally associated with a gas-liquid (free) boundary with a no-slip boundary condition. It should be noted that such effects can drastically alter pressure drop in microfluidic networks and theoretical predictions based on no-shear at free interfaces must be used with care in practical applications [54]. 

To determine the two integration constants Ci and C2, we apply the so-called no-slip boundary conditions. No-slip boundary conditions require that the liquid molecules directly in contact with the surfaces are stationary... 

The heat transfer across the vapor layer and the temperature distribution in the solid, liquid, and vapor phases are shown in Fig. 13. In the subcooled impact, especially for a droplet of water, which has a larger latent heat, it has been reported that the thickness of the vapor layer can be very small and in some cases, the transient direct contact of the liquid and the solid surface may occur (Chen and Hsu, 1995). When the length scale of the vapor gap is comparable with the free path of the gas molecules, the kinetic slip treatment of the boundary condition needs to be undertaken to modify the continuum system. Consider the Knudsen number defined as the ratio of the average mean free path of the vapor to the thickness of the vapor layer ... 

The nature of the liquid in contact with a surface is also very important, with respect to boundary conditions. Although slip has long been observed for highly non-Newtonian, viscoelastic liquids such as polymer flows and extrusions, many recent studies have reported slippage of Newtonian liquids under a variety of experimental conditions. This clearly indicates that care must be taken when modeling any type of micro- or nanofluidic system, no matter which liquid is employed. 

Lu et al. [7] extended the mass-spring model of the interface to include a dashpot, modeling the interface as viscoelastic, as shown in Fig. 3. The continuous boundary conditions for displacement and shear stress were replaced by the equations of motion of contacting molecules. The interaction forces between the contacting molecules are modeled as a viscoelastic fluid, which results in a complex shear modulus for the interface, G = G + mG", where G is the storage modulus and G" is the loss modulus. G is a continuum molecular interaction between liquid and surface particles, representing the force between particles for a unit shear displacement. The authors also determined a relationship for the slip parameter Eq. (18) in terms of bulk and molecular parameters [7, 43] ... 

Young equation. This has remained an unsolved theoretical problem for a long time because of the apparent contradiction between the advancing motion of the contact line and the no slip hydrodynamic boundary condition for the liquid at the solid surface this paradox is solved by a rolling motion of the spreading liquid on the solid surface. ... 

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