EngArc - L - No-Slip Condition

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No-Slip Condition

Quick

Experimental observations indicate that a fluid in motion comes to a complete stop at a solid surface and assumes a zero velocity relative to the surface. A fluid in direct contact with a solid "sticks" to the surface due to viscous effects, and there is no slip. This is the no-slip condition.

When a fluid is forced to flow over a curved surface, such as the back side of a cylinder at sufficiently high velocity, the boundary layer can no longer remain attached to the surface, and at some point it separates from the surface—a process called flow separation. The no-slip condition applies everywhere along the surface, even downstream of the separation point.

Equation

u_fluid ≡ u_wall

boundary condition for velocity of fluid at a solid surface

Nomenclature

u_fluid	velocity of fluid at solid surface
u_wall	velocity of solid surface

Details

Velocity Profile

The no-slip condition for a viscous fluid:

As a fluid flows along a solid surface, it tends to "stick" to the surface. That is, the velocity of the fluid that is at the solid surface matches the velocity of the solid surface. So, for water in a pipe, the velocity of the water at the surface of the wall of the pipe will be equal to the velocity of the pipe wall surface. This is the "no-slip" condition and is a very important condition that must be satisfied in any accurate analysis of fluid flow phenomena. At a solid boundary, the fluid will have zero velocity relative to the boundary. In other words, the fluid velocity at all fluid–solid boundaries is equal to that of the solid boundary.

The no-slip condition does not always hold in reality. For example, at very low pressure such as at high altitude, even when the continuum approximation still holds there may be so few molecules near the surface that they "bounce along" down the surface.

While the no-slip condition is used almost universally in modeling of viscous flows, it is sometimes neglected in favor of the 'no-penetration condition' (where the fluid velocity normal to the wall is set to the wall velocity in this direction, but the fluid velocity parallel to the wall is unrestricted) in elementary analyses of inviscid flow, where the effect of boundary layers is neglected.

The no-slip condition poses a problem in viscous flow theory at contact lines: places where an interface between two fluids meets a solid boundary. Here, the no-slip boundary condition implies that the position of the contact line does not move, which is not observed in reality. Analysis of a moving contact line with the no slip condition results in infinite stresses that can't be integrated over. The rate of movement of the contact line is believed to be dependent on the angle the contact line makes with the solid boundary, but the mechanism behind this is not yet fully understood.

Water in a river flows around large rocks. The water velocity normal to the rock surface is zero and water approaching the solid surface at any angle comes to a complete stop at the surface. The tangential velocity of water at the surface is also zero.

The layer that sticks to the surface slows down the fluid around it, and is therefore reponsible for the shape of the velocity profile. The interface between the fluid and solid is called the boundary layer.

The fluid property responsible for the no-slip condition and the development of the boundary layer is viscosity.

The layer of fluid at a moving surface has the same velocity as the surface itself. A consequence of the no-slip condition is that all velocity profiles must have zero values with respect to the surface at the points of contact between a fluid and a solid surface. Another consequence of the no-slip condition is the surface drag, which is the force a fluid exerts on a surface in the flow direction.

Fluid flow is often confined by solid surfaces, and it is important to understand how the presence of solid surfaces affects fluid flow. Water in a river cannot flow through large rocks, and goes around them. That is, the water velocity normal to the rock surface must be zero, and water approaching the surface normally comes to a complete stop at the surface. What is not so obvious is that water approaching the rock at any angle also comes to a complete stop at the rock surface, and thus the tangential velocity of water at the surface is also zero.

Consider the flow of a fluid in a stationary pipe or over a solid surface that is nonporous (i.e., impermeable to the fluid). All experimental observations indicate that a fluid in motion comes to a complete stop at the surface and assumes a zero velocity relative to the surface. that is, a fluid in direct contact with a solid "sticks" to the surface due to viscous effects, and there is no slip. This is known as the no-slip condition.

The layer that sticks to the surface slows the adjacent fluid layer because of viscous forces between the fluid layers, which slows the next layer, and so on. Therefore, the no-slip condition is responsible for the development of the velocity profile. The flow region adjacent to the wall in which the viscous effects (and thus the velocity gradients) are significant is called the boundary layer.

A fluid layer adjacent to a moving surface has the same velocity as the surface. A consequence of the no-slip condition is that all velocity profiles must have zero values with respect to the surface at the points of ocntact between a fluid and a solid surface. Another consequence of the no-slip condition is the surface drag, which is the force a fluid exerts on a surface in the flow direction.

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