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Generalizing results of Chou and Wang \cite{1} we study the flows of theleaves $(M_{\Theta})_{\Theta>0}$ of a foliation of $\mathbb{R}^{n+1}\setminus\{0\}$ consisting of uniformly convex hypersurfaces in the direction of theirouter normals with speeds $-\log(F/f)$. For quite general functions $F$ of theprincipal curvatures of the flow hypersurfaces and $f$ a smooth and positivefunction on $S^n$ (considered as a function of the normal) we show that thereis a distinct leaf $M_{\Theta_{*}}$ in this foliation with the property thatthe flow starting from $M_{\Theta_{*}}$ converges to a translating solution ofthe flow equation. Furthermore, when starting the flow from a leave inside$M_{\Theta_{*}}$ it shrinks to a point and when starting the flow from a leaveoutside $M_{\Theta_{*}}$ it expands to infinity. While \cite{1} considered thismechanism with $F$ equal to the Gauss curvature we allow $F$ to be among othersthe elementary symmetric polynomials $H_k$. We, furthermore, show that suchkind of behavior is robust with respect to relaxing certain assumptions atleast in the rotationally symmetric and homogeneous degree one curvaturefunction case.

Flowing the leaves of a foliation with normal speed given by the logarithm of general curvature functions