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Smooth approximations for structural force in thin fluid films near the critical point are presented to facilitate the usage of formulas derived in [J. Colloid Interface Sci. 278 (2004) 173-183] in experimental studies.
We consider a general form of the local gradient theory for structural forces in thin fluid films near the critical point. A complete analytical solution of this problem at separation distances substantially larger than the molecular size is presented. That is, pi= -[330Psi(-4)H(8.8923-Psi) + 384exp(-Psi)H(Psi-8.8923)]H(-Gamma)+[1134.36Psi(-4)H(8.8923-Psi +… (More)
We consider the 1-D Cahn-Hilliard equation with the order parameter v and derive an equation for a modified order parameter g such that g''=v'. The new equation allows for separation of variables. This yields exact solutions for v expressed in terms of generalized hypergeometric functions. These solutions have an infinite gradient at their zeros and the… (More)
A new transformation termed the mu-derivative is introduced. Applying it to the Cahn-Hilliard equation yields dynamical exact solutions. It is shown that the mu-transformed Cahn-Hilliard equation can be presented in a separable form. This transformation also yields dynamical exact solutions and separable forms for other nonlinear models such as the modified… (More)
This paper presents a new form of the Cahn-Hilliard equation. The new equation is substantially more robust to simulating intrinsic instabilities of the spinodal dewetting process compared to the standard one.