You should read about Maxwell's hypothesis for gas flows on specular reflection (as you call it, elastic) that can be seen as a non-transferring momentum collision; as opposed to "absorption followed by diffuse re-emission" with momentum transfer with the wall. This may help understanding liquids.

When you are close to the walls in liquid flows, the Knudsen number is much smaller than in gas flows and, therefore, the continuum approach must be seen as a possible approach and, except for vaporizing flows, I believe the no-slip boundary condition might be applicable. The thing for liquid is, as you said, that molecules are closer to each other (very dense fluid) and elastic collisions are unlikely to occur.

@Viriato

Can you elaborate a little more on " non-transferring momentum collision; as opposed to "absorption followed by diffuse re-emission" with momentum transfer with the wall".

Thanks

Also a a reference describing the above in brief will be really helpful.

Have a look into these books (particularly the second):

1 - GP Celata - heat transfer and fluid flow in microchannels

2 - SG Kandlikar et al. - heat transfer and fluid flow in minichannels and microchannels

By what I mean from theoretical was it is theoretical way of looking. What experimental should I look at to comment on the condition that continuum or slip flow holds.

Again, have a look into these books (particularly the second):

1 - GP Celata - heat transfer and fluid flow in microchannels

2 - SG Kandlikar et al. - heat transfer and fluid flow in minichannels and microchannels

I am positive they will help you to improve your knowledge on this issue. You do not need to go through the entire book - just 1 or 2 chapters.

Deweekar,

On the microscopic level the wall consists of billions of billions of interacting, vibrating atoms; their average speed is counted in hundreds of meters per second, and their vibration is pretty chaotic, though centered about some positions in space: that's why the walls appear to be "solid". Liquids and gases also consist of billions of billions of molecules whose average speed is rougly the same as that of the vibrating wall atoms (hundreds of meters per second), but their average position is free to change. That's why than can "flow". Thus, if a single fluid molecule hits the wall, it can be "reflected" in essentially any direction. What really matters is the AVERAGE fluid particle velocity near the wall. The collisions are always ellastic in that they conserve the total energy of the colliding molecules; however, this doeas not preclude energy transfer from one particle to the other. Sometimes the energy comes from the wall molecules, sometimes toward the wall molecules. The same concerns the momentum. The wall molecules can then immediatelly transmit this energy/momentum to other molecules that make up the wall. The point is that the mean position of each wall molecule is fixed in space. Hence, the mean position of the fluid particles near the wall should be also very close to zero, otherwise the friction forces ("viscosity") between the wall molecules and the fluid molecules would be immense. This, however, depends on the mean free path of the fluid molecules. For liquids the free mean path is of order of molecule diameter, i.e a fraction of nanometer. For rarified gases the free mean path can be larger than the channel diameter. In the formar case you can quite safely assume zero-velocity boundary conditions (at least for steady flows), unless you consider flows in microchanels, porous media etc. In the latter case the fluid particles that bounced off the wall are unlikely to hit other fluid particles and equilibrate - the notion of "friction" or "viscoisty" looses its usual meaning, you are in the Knudsen Regime, the fluid appers to slip along the walls (the mean fluid velocity at the wall is nonzero).

Anyway, there's no such a thing as a particle at rest. They're all in a rush. If the fluid velocity vanishes at some place, this means that the fluid molecules rush at essentially no preffered direction, colliding like they were all drunk. If the velocity is nonzero, the molecules also collide, at picosecond intervals (liquids), but on averege there is some order in their motion and local equilibrium. The local equilibrium. however, can be established only if the mean free path is much smaller than the container size, which is where the fluid density and the channel diameter may enter the game.

@Koza

Thanks for such a detailed explanation. If I got you correctly, then it means in case of liquids the mean position about which they vibrate or collide near the wall is very small and of the order nearly molecule dia, So we can assume they are relatively at rest w.r.t to wall. However, when mean free path increases then the same can not be assumed and we say they are relatively moving w.r.t to wall and hence slip flow or free molecular flow according to the Knudsen number.

Kindly correct me if I am wrong.

It would be helpful if you may also answer my anther query related to same.

https://www.researchgate.net/post/Can_anyone_advise_on_the_continuum_theory2

and secondly,

Then in case of micro channels, even though we may not consider slip flow condition, (and I suppose no slip means continuum and rest all don't) the only difference we have is that we need to consider effect of effects of forces such as surface tension. That is how we may differentiate between micro and macro ( I am talking about hydraulic dia of the range 200-600 micron)