Abstract
The effect of thixotropy on the two-dimensional spreading of a sessile drop is modelled using lubrication theory. Thixotropy is incorporated by the inclusion of a structure parameter, λ, measuring structure build-up governed by an evolution equation linked to the droplet micromechanics. A number of models are derived for λ coupled to the interface dynamics; these range from models that account for the cross-stream dependence of λ to simpler ones in which this dependence is prescribed through appropriate closures. Numerical solution of the governing equations show that thixotropy has a profound effect on the spreading characteristics; the long-time spreading dynamics, however, are shown to be independent of the initial structural state of the droplet. We also compare the predictions of the various models and determine the range of system parameters over which the simple models provide sufficiently good approximations of the full, two-dimensional spreading dynamics.
Highlights
Thixotropy is of central importance in a variety of applications, due to its presence in a wide range of fluids, which include natural muds, slurries, clay suspensions, greases, paints, gels and adhesives [1]
We will model thixotropy by the direct inclusion of a structure parameter, it has been shown that thixotropy and yield stress behaviour can be the natural limit of viscoelastic behaviour, when the relaxation time is large, [3,4,5]
Thixotropy can have a dramatic effect upon the flow behaviour as exemplified by the chaotic regimes observed in numerical studies of a highly thixotropic fluid displaced by a Newtonian fluid [6]
Summary
Thixotropy is of central importance in a variety of applications, due to its presence in a wide range of fluids, which include natural muds, slurries, clay suspensions, greases, paints, gels and adhesives [1]. We will model thixotropy by the direct inclusion of a structure parameter, it has been shown that thixotropy and yield stress behaviour can be the natural limit of viscoelastic behaviour, when the relaxation time is large, [3,4,5]. Structure parameter models can be seen to be a natural extension of viscoelastic thixotropy models when you take the structure parameter to be the trace of the conformation tensor. Thixotropy can have a dramatic effect upon the flow behaviour as exemplified by the chaotic regimes observed in numerical studies of a highly thixotropic fluid displaced by a Newtonian fluid [6]. We will restrict our analysis to capillary-driven flows where inertia is negligible
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