So, for water compressed under a piston at a constant temperature, the total observed pressure increases the thermal pressure caused by water molecules bouncing off the surface does not change in this process but the intermolecular forces respond to the compression changing the total pressure. If water is compressed (at a constant temperature) the resulting pressure increase is due to the change of $P_f$. So the total pressure in a liquid is $P = P_k + P_f$, where $P_f$ (negative at normal conditions) is the component of the pressure due to intermolecular forces, strongly dependent on the density. We don't see this huge pressure because it is largely compensated by intermolecular attraction forces. If the pressure is due to particle collisions then why does it increase without any increase of temperature and density? Furthermore, using the numbers for water at normal conditions, $n=33e27 m^$, T=300 K, we'd get the kinetic pressure $P_k$ at about 10 million atmospheres, but we don’t see it! First of all, we know that we can put water under a piston and increase the pressure isothermically at nearly constant density. However, it would not be right to say that for liquids (e.g., consider water for concreteness) the pressure is the kinetic pressure $P_k=nkT$. The quoted paragraph from the textbook talks about fluids which usually includes gases, liquids, and plasmas. Is this model - the one that talks about pressure arising due to collisions, sufficient to explain pressure related phenomena in all possible situations or is it a mere approximation? How can we explain that using this collision model? I'm confused because, the nature of collisions should be a property of the fluid, and should not vary with depth. It is also a well known fact that pressure in a static fluid increases with depth. If, they wish to tell us that the collision is elastic (as in the case of kinetic theory of gases), why is this a valid assumption? Maybe, the right question to ask is, to what extent is it a valid assumption?Īccording to the aforementioned extract, pressure arises due to collisions between molecules and the surface. I've a few questions, conceptual in nature, which stemmed from the above paragraph -Īll that is mentioned is that the component of molecule's momentum perpendicular to surface is reversed nothing is mentioned about its magnitude. The above is an extract from Physics by Resnick, Halliday & Krane. The net result of reaction force exerted by many molecules on the surface gives rise to the pressure on the surface. The surface must exert an impulsive force on the molecule, and by Newton's Third Law the molecule exerts an equal force perpendicular to the surface. As a result of a collision, the component of a molecule's momentum perpendicular to the surface is reversed. We present simulation tests involving complex solid-fluid interactions, including solid fractures generated by fluid interactions.Microscopically, the pressure exerted by a fluid on a surface in contact with it is caused by collisions of molecules of fluid with the surface. We also show how our merging-and-splitting approach can be used for coupling different simulation systems using different and otherwise incompatible integrators. We show that our merging-and-splitting method is effective in robustly handling collisions and avoiding penetrations in particle-based simulations. Thus, collisions last for the duration of a time-step, allowing neighboring particles of the colliding particles to influence each other. This scheme merges colliding particles at the beginning of the time-step and then splits them at the end of the time-step. We introduce particle merging-and-splitting, a simple scheme for robustly handling collisions between particles that prevents inter-penetrations of separate objects without introducing numerical instabilities. Robustly handling collisions between individual particles in a large particle-based simulation has been a challenging problem.
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