On the validity of the no slip condition

On the Validity of the No-Slip Condition
Slip or No-Slip?

1. On the Validity of the No-Slip Condition Slip or No-Slip ?  Presented by Daryoosh Borzuei Boundary Layer Theory Course Professor F.Bazdidi Tehrani January 2021

2. Contents Introduction Navier B.C. No-Slip Condition Slip Condition Conclusions

3. Introduction The “ no-slip ” boundary condition → zero fluid velocity relative to the solid at the fluid-solid interface. The no-slip boundary condition at a solid–liquid interface is at the center of our understanding of fluid mechanics. T his condition is an assumption that cannot be derived from first principles and could, in theory, be violated . Successful in describing many macroscopic flows how about microscopic flows? Is “ no-slip ” condition always valid ? Comparison of Continuum and Molecular Dynamics (MD)

4. Introduction Comparison of continuum and Molecular Dynamics (MD) ? No-Slip Boundary Condition → A Paradigm Paradigms , whether right or wrong, are the basis of many judgments.

5. Navier B.C. History of the No-Slip Condition Navier introduced the linear boundary condition (also proposed later by Maxwell ). The component of the fluid velocity tangent to the surface, , is proportional to the rate of strain , (or shear rate) at the surface , Introduces a slip length and assumes that the amount of slip is proportional to the shear rate in the fluid at the solid surface.   The strain rate tensor  

6. Navier B.C. λ has the unit of a length , and is referred to as the slip length . λ → slip length → distance from the fluid-solid interface to where the linearly extrapolated tangential velocity vanishes . For a pure shear flow, λ can be interpreted as the fictitious distance below the surface where the no-slip boundary condition would be satisfied. Interpretation of the (Maxwell–Navier) slip length λ

7. No-Slip Condition Using the Scale Analysis Method    

8. No-Slip Condition Typically, λ ranges from a few angstroms to a few nanometers . The Knudsen number is a dimensionless parameter defined as: Maxwell theory predicts that the slip length is related to the mean free path as:       No-Slip Boundary Condition      

9. Slip Condition No-slip condition is believed to be valid as far as the characteristic length of the flow is much greater than the mean length of the path of the fluid molecular between collisions . If the length scale of the fluidic system is in the same range as the mean free path, i.e., Kn = 1, the fluid cannot be treated as a continuum . The next question → Traditional Situations,Where Slip Occurs . The phenomenon of slip has already been encountered in three different contexts.   Slip Length  

10. Slip Condition Gas Flow → Gas flow, in devices with dimensions that are on the order of the mean free path of the gas molecules shows significant slip. For e.x, air under standard conditions of temperature and pressure , and , in general, depends strongly on pressure and temperature . Non-Newtonian Fluids → The flows of Non-Newtonian fluids such as polymer solutions show significant apparent slip in a variety of situations, some of which can lead to slip-induced instabilities. Contact Line Motion → The no-slip boundary condition is not applicable to the moving contact line ( MCL) where the fluid-fluid interface intersects the solid wall.   (for ideal gas)  

11. Slip Condition The static and moving contact lines: The distance over which the fluid velocity changes from U to zero tends to vanish as the contact line is approached. In particular, this stress divergence is non-integrable . Cause to Singularities  

12. Conclusions The no-slip boundary condition at a solid–liquid interface is at the center of our understanding of fluid mechanics . However, this condition is an assumption that cannot be derived from first principles and could, in theory, be violated . Navier B.C.→ no-slip boundary condition in macroscopic flows Traditional Situations,Where Slip Occurs → The phenomenon of slip has already been encountered in three different contexts Gas Flow , Non-Newtonian Fluids and Contact Line Motion Moving contact lines → Cause to Singularities  

13. Special Thanks For Your Listening In contrast with the usual picture where the velocity of a liquid or gas flow on a solid wall is zero, recent experiments have shown that simple liquids and gases may significantly slip on solid surfaces and , consequently, the no-slip condition should be replaced by a more general relation [email protected] www.linkedin.com/in/da-borzuei

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