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"LIQUIDS AS QUASI-SOLIDS . . . COULD MAKE A NICE TOPIC FOR YOUR DOCTORAL THESIS" (SCIENTISTS.) EINSTEIN, ALBERT. Autograph Letter Signed, "A.E.," to aspiring Romanian physicist Melanie Serbu ("Dear Miss Serbu"), in German, sketching a suggestion for her doctoral thesis involving the mathematical similarity of waves in solids and liquids. 2 pages, 4to, written on two sheets; faint scattered staining, paper clip stain at upper edge, horizontal folds. Huntington, 15 July 1937
"I am glad that you agree with me on the concept of liquids as quasi-solids. Don't talk much about this matter with others; I believe that this could make a nice topic for your doctoral thesis later, and I am thinking primarily of the theoretical implementation of the idea. It probably won't be entirely new. For example, the term 'relaxation time' (Boltzmann) is common in gas theory and has something to do with this. "I'll sketch you the thing for pure shear deformation. "[xy coordinate system diagram] "p = shear force in the y direction, acting on a surface element parallel to the y-z plane "n = elongation in the y direction "For an ideal solid body one would have "p=kdn/dx [equation] "In the liquid, given a lack of movement and initial p, the magnitude will decrease according to [equation] or [equation]. "If at the same time there is a transverse movement dependent on x, the consideration is as follows. "At time t, the shear force is in x = p "In the time t there are two additional changes. "1) by increasing the deformation during dt [equation] "2) by relaxation [equation] "So overall it is [equation I] "On the other hand, the equation of motion is (mass • acceleration = force) [equation II] "I and II together determine the movement. Of course, this can easily be transferred or generalized to the case of any movements. "But what about the viscosity? Consider the motion [equation] where a is the time-constant deformation rate. "Equation (I) then simply returns [equation] "From this follows for the viscosity coefficient b simply [equation] "Only now b is known for a liquid and if K is set equal to the value for the frozen liquid, then the relaxation rate T is obtained. "You can now amuse yourself by integrating Equations I and II for time-sinusoidal waves. One can thus predict how high frequencies are necessary so that the behavior of the liquid in relation to waves is noticeably different than according to the usual viscosity theory. "According to this, the left side in I can be neglected compared to the second member of the right side. Conversely: if the processes are fast enough, the left term is large compared to [ratio], and I can be replaced by the equation [equation] (integrated after t). One has in fact all the transitions between a solid body and an ideal viscous liquid."
