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Cato edited Payam.tex
almost 11 years ago
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\item Dimensional analysis argument not fully understood: I think $t_{\rm h}\sim \ell/c_{\rm s}$ on physical grounds, but Payam says $t_{\rm h}\sim \ell^2\rho/\eta$ from dimensional analysis. What is the interpretation of Payam's $t_{\rm h}$? Are the two compatible?
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\begin{itemize}
\item The two $t_{\rm h}$s are measuring different things. Payam's $t_{\rm h}$ is considering the {\it diffusion }of a particle's momentum: the characteristic time in the velocity autocorrelation. My $t_{\rm h}$ is about information flow via
sound waves. sonic waves: this is much smaller than the vorticity time-scale.
\item
Why does {\it What should the time-scale be from physical reasoning? What is the physics behind setting up the flow profile $\vec{v}(\vec{x})$ in the
hydrodynamic disturbance travel diffusively rather fluid around the DNA? And which process (sound or vorticity) carries more momentum?}
\item Another thing to consider: {\it does it even matter?} The time-scale they use is larger than
at the
sound speed? sound-time, and places a more stringent test on the steady-state assumption. So my objection would only strengthen the conclusion. The vorticity moves slowest, and the fluid velocity profile might only assume the anticipated form once this final piece has arrived to distance $\ell$ from the DNA.
\item Could the problems in Payam's other paper conceivably be explained by this phenomenon?
\item Some reading about propagation of hydrodynamic information:\\
\citet{Hinch_1975} application of Langevin equation to fluid suspensions; includes fluid inertia and interaction with suspension.\\