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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)
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.
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.
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)
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)