Plenary talk given at the 90th Annual Meeting of Argentine Physical Society September '05 (PDF)

Presentation at DFD APS meeting  '07 (powerpoint)

[See below for recent publications]

The flow of thin films is relevant in a number of different fields, such as engineering (microchip production), biology (lining of mammalian lungs), and chemistry (flow of surface active materials). The dynamics of the fronts of these films is not very well understood. In many situations, the fronts become unstable, leading to the formation of finger-like rivulets, saw-tooth patterns, or, in the case of surfactant flow, dendritic tip-splitting petals.

Figure shows an example of our computational results modeling the flow of thin fluid film down a vertical surface (such as paint flowing down a wall). This figure shows the height of the fluid (h) at four different times (T), starting from random initial conditions (see here for the details). We observe the development of instability (rivulets). I am interested in understanding the processes leading to the instability, as well as in developing computational methods allowing for simulating the physical systems where this type of instability is present. For the time being, the research concentrates on the relatively simple problem of the instability in the gravity driven flow down an inclined plane (shown in the figure). Consequently, the analysis will be extended to other related flows.

Here are postscript files of two talks given at NJIT June '00: Part I, Part II)

Animation of the flow down a vertical plane: 2D (Quicktime , Avi ), or 3D Avi .

Thin films related teaching:

Selected recent publications on thin liquid films:

(see here for the complete list).

On the breakup of fluid films of finite and infinite extent, , with J. Diez, Phys. Fluids, 19, 072107 (2007).

Long-wave linear stability theory for two-fluid channel flow including compressibility effects, , with T. Segin and B. S. Tilley, IMA J. Appl. Math., 71, 715 (2006).

On flooding and undercompressive shocks in countercurrent two-layer flow, , with T. Segin and B. S. Tilley, J. Fluid Mech., 532, 217 (2005).

On nontrivial traveling waves in thin film flows including contact lines, , with J. Diez, Physica D, 209, 135 (2005)

Instabilities in the flow of thin films on inhomogeneous surfaces, with J. Diez, Phys. Fluids 16, 3341 (2004)

Spreading of a thin two-dimensional strip of fluid on a vertical plane: Experiments and modeling, with A.G. Gonzalez, J. Diez, J. Gomba, R. Gratton, Phys. Rev. E 70, 026309 (2004)

Instabilities in the flow of thin liquid films, SIAM Review 45, 95 (2003)

Simulations of thin liquid films and drops in higher dimensions, with J. Diez, J. Comp. Phys. 173, 274 (2002)

Flow of thin films on patterned surfaces: Controlling the instability, with J. Diez, Phys. Rev. E 65, 045301 (2002)

Pattern formation in gravity driven flow of thin films: Constant flux flow, with J. Diez, Phys. Fluids. 13, 3168 (2001)

Contact line instabilities of thin liquid films, with J. Diez, Phys. Rev. Lett. 86, 632 (2001)

Global models for moving contact lines, with J. Diez and A. L. Bertozzi, Phys. Rev. E 63, 011208 (2001)

Nonlinear dynamics and transient growth of driven contact lines, with A. L. Bertozzi, Phys. Fluids 11, 3560 (1999)