Judging on the fact that there are certain non-Newtonian fluids, that behave in a way adverse to Newtonian Mechanics, such as oobleck, is there a way for the idea of centrifugal force to exist outside of just a reference frame in non-Newtonian mechanics? As I understand it, the only way for centrifugal forces to "exist" in normal Newtonian physics, is within a reference frame, and even then it's not really in existence anyways. Also what about in space, where micro-gravity is so small it's often negligible, and finally is there non-Newtonian mechanics that apply to non-Newtonian fluids. Just some queries, maybe I should have put this in multiple posts.
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2 Answers
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Oobleck is a non-Newtonian fluid but still obeys Newtonian mechanics (at least, to a very good approximation; let's ignore relativity and quantum mechanics since I don't think they are relevant for your question). If the oobleck is rotating, we can say that in its rest frame it experiences a centrifugal force. We could say the same thing about any other rotating object, there is nothing special about non-Newtonian fluids in this context. This is because everything in the Universe obeys Newtonian mechanics, in the limits of low velocities, weak gravitational fields, and large numbers of particles interacting at temperatures well above absolute zero where we can ignore relativity and quantum mechanics.
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It is important to clarify in which sense a non-Newtonian fluid does not obey the Newtonian mechanics.
The usual definition of non-Newtonian fluids is not coinciding with fluids that do not obey Newton's laws of motion. Rather, as you may find in Wikipedia, a non-Newtonian fluid does not follow Newton's law of viscosity. I.e., the momentum transfer in the fluid is not characterized by a viscosity constant independent of the stress. Therefore, the definition of non-Newtonian fluid specifies how the force depends on the system (the fluid particle) and its surroundings. It is not implying automatic violations of the assumptions behind Newton's laws of motion. In particular, the presence of inertial forces, like the centrifugal force, is the consequence of rewriting the Second Law in a non-inertial reference frame in a $\vec F=m \vec a$ form by introducing additional force-like terms depending on the body and the reference frame (but not on the forces in the inertial frame).
Therefore, non-Newtonian fluids in a rotating reference frame do experience centrifugal force. For the same reason, a different environment, like micro-gravity in space, does not introduce significant changes to the conceptual picture.
However, there is the possibility that real forces (as opposite to inertial forces) in a non-Newtonian fluid could behave differently from the force in Newton's Laws of motion. That's the case of non-Newtonian fluids with memory. The possibility that a force depends not only on the dynamical state of the system at time $t$ but also on the past history of the motion transcends the structure of Newton's theory in a significant way. For instance, the Second Law does not correspond anymore to an ordinary differential equation.
answered Sep 18, 2021 at 6:56
GiorgioP-DoomsdayClockIsAt-90GiorgioP-DoomsdayClockIsAt-90
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$\begingroup$ It might be useful to add a clarification differentiating between systems that aren't convenient to model using Newtonian kinematics and systems to which Newtonian kinematics are genuinely inapplicable. $\endgroup$– g sCommented Sep 18, 2021 at 8:10
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$\begingroup$ @gs Kinematic is not affected by the underlying dynamics. position, velocity, and acceleration of a fluid particle are described in the same way independently on the specific properties of forces. Their mutual relations aren't. However, elaborating on this last point, which is not directly related to the original question, was not the aim of my answer. $\endgroup$ Commented Sep 18, 2021 at 9:03