Evidence for the Existence of an Effective Interfacial Tension between Miscible Fluids. 2. Dodecyl Acrylate−Poly(dodecyl acrylate) in a Spinning Drop Tensiometer

Abstract

We studied drops of dodecyl acrylate in poly(dodecyl acrylate) (molecular weight of 25,000) in a spinning drop tensiometer to determine whether an effective interfacial tension (EIT) existed between these two miscible fluids. We found convincing evidence. We estimated the mechanical relaxation time from an immiscible analogue (1-propanol and poly(dodecyl acrylate)) and showed that the dodecyl acrylate drops maintained quasi-steady diameters long after this relaxation period. Drops continuously grew in length and became more diffuse, but the width of the transition zone did not grow with t(1/2) as expected from Fick's law although this system had been shown to follow Fick's law in a static configuration (Antrim, D.; Bunton, P.; Lewis, L. L.; Zoltowski, B. D.; Pojman, J. A. J. Phys. Chem. B 2005, 109, 11842-11849). The EIT was determined from Vonnegut's equation, EIT = (Deltarho)omega(2)r(3)/4; both the inner and outer diameters were measured, yielding values of 0.002 and 0.02 mN m(-1), respectively. The EIT was found to be independent of the rotation rate above 6000 rpm and independent of the initial drop volume. The EIT was found to decrease with temperature and increase with the difference in concentration between the monomer drop and polymer-monomer fluid. The square gradient parameter, k, was determined from EIT = k(Deltac(2)/delta), where Deltac is the difference in mole fraction and delta is the width of the transition zone. The square gradient parameter was on the order of 10(-9) N. The square gradient parameter was found to decrease with temperature, to be independent of concentration, and to increase with the molecular weight of the polymer.

Nonequilibrium Interfacial Tension in Simple and Complex Fluids

“…In addition to our data, we also analyze literature data obtained by spinning drop tensiometry for dodecyl acrylate-poly(dodecyl acrylate) mixtures [17] (DA-PDA, the solvent is pure DA) and water-glycerol mixtures [13] (the solvent is pure water). The relevant parameters for these systems are summarized in Table II.…”

“…For consistency with the other sets of data, we express concentration as the volume fraction φ of PDA and of glycerol, for the data of Refs. [17] and [13], respectively.…”

“…Here, κ is the Korteweg or square gradient parameter, δ the thickness of the interface, and Δφ is expressed in terms of a difference in volume fraction, e.g., between a solute and the solvent for molecular fluid [13][14][15][16], or between polymer or colloidal suspensions and their solvent for complex fluids [17,18]. Clearly, the interfacial tension described by Eq.…”

“…Simulations [33] and experiments [34,35] probing the Saffman-Taylor instability led to the conclusions that no interfacial tension exists between miscible fluids; in particular, the observation of a fractal-like interface between two miscible fluids was attributed to a vanishing interfacial energy cost, i.e., to Γ e ¼ 0 [34,35]. This has to be contrasted with experiments and simulations on miscible fluids probing capillary waves [14,15,36], the shape of drops and menisci [13,16,17,37,38], and that of patterns in hydrodynamic instabilities [18,[27][28][29][39][40][41], which all claimed the existence of an effective interfacial tension. The sign of Γ e is also debated.…”

Instabilities of Diffuse Interfaces

“…Pojman et al supervised an experiment on the International Space Station to study the behavior of honey and water and were able to put an upper bound on the value of the Korteweg stress parameter for that system [35]. Zoltowski et al studied a monomer that is miscible in its polymer [49]. This system relates to simulations performed on a polymer system showing how convection could be caused by gradients in the effective tension between a monomer and its miscible polymer [7].…”