Our recent work offers a solid understanding of the mechanics controlling consolidation and cracking of immobilized, i.e. close packed, colloidal dispersions that deform nonlinearly and viscoelastically due to contact or interfacial forces. Our model identifies, in terms of appropriate dimensionless groups, the conditions under which air-water, polymer-water, or polymer-air interfacial energies suffice to form homogeneous void-free or porous films as thin layers of aqueous dispersions dry on a rigid substrate. The model also predicts the capillary pressure above which cracking becomes favorable, when deformation is too slow to keep up with evaporation, as the elastic energy recovered when a crack opens exceeds the additional surface energy expended. Complementary experiments with polymer latices and inorganic oxide colloids in a pressure filtration cell permit direct measurement of the negative capillary pressures required for cracking, demonstrating that many packings do not crack until the capillary pressure exceeds significantly the minimum predicted for an infinite crack. Further experiments and theory establish the importance of flaws to nucleate cracks, as for linearly elastic solids under tension. This work provides a foundation for addressing a remaining puzzle and two related challenges. First, crack tips following a drying front in a thin film develop a characteristic spacing and often advance in the direction of the gradient in capillary pressure in a stick-slip fashion. This suggests an additional dynamical process, which some attribute to the flow of water driven through the particle packing by gradients in the capillary pressure. To elucidate the pattern selection process we propose two experimental geometries with controlled propagation of gradients, complemented with analysis of the dynamic process through an extension of the existing model. A thin rectangular channel confines evaporation to the open ends and allows cracks propagating in from the ends to be viewed through the flat faces via a microscope. Alternatively, the pressure filtration cell mentioned above can be tilted slightly to create a gradient in thickness of a thin layer with a free surface but without the lateral flows caused by nonuniform evaporation. Cracks nucleated by notches at the thick edge then should propagate toward the thin edge with increasing capillary pressure. Second, some technologies require highly porous films that cannot be dried at the desired thickness without cracking, raising the question of how to maintain capillary pressures for cracking above those attainable with menisci at the surface of the film. For this purpose we propose to study films formed with colloidal rods for which random packing creates pores larger than the rod diameter, thereby reducing the maximum capillary pressure relative to random close packing of spheres of the same diameter. Success will depend on whether the effective modulus of the packing, which controls cracking, does not fall enough to negate the benefit. Experiments with colloidal rods of boehmite, either bare or stabilized with a silica coating, in the pressure filtration cells will determine the critical capillary pressures as a function of film thickness to assess the potential. Third, we intend to explore film formation and cracking in the pressure filtration cell for binary mixtures of hard and soft spheres with interactions tuned to delay percolation of the hard phase to as high a volume fraction as possible. This effort, using the same experimental tools as above, will be guided by theory being developed to understand the recently discovered ?halo? effect due to electrostatic attractions between small highly charged polymer latices and larger electrically neutral inorganic spheres. The intellectual merit lies in the creation of a solid fundamental basis of understanding and using that to devise new avenues for the technology. Success in understanding these phenomena should benefit drying processes important to technologies ranging from conventional (but always improving) architectural coatings, through tape casting processes for fabricating ceramic substrates and multilayer devices, to carefully tailored particulate coatings for inkjet papers. The research provides broader impact by posing a stimulating vehicle for educating graduate students and undergraduates for careers in the chemical and related industries.
Drying colloidal dispersions by evaporating liquid creates coatings or films in important technologies, e.g. porous coatings on ink jet papers, sol-gel glass, and photographic film. The particles are polymer latices or inorganic oxides and the fluid is normally water. Processing of such films raises a number of interesting and difficult issues. As liquid evaporates particles are concentrated but the dispersion remains a fluid until a gelation, freezing, or glass transition is encountered. With slow evaporation particles reach random or ordered close packing. Further evaporation deforms the menisci between particles at the air-water interface, generating a negative capillary pressure that puts the dispersion in compression and produce close packing, i.e. a colloidal solid. Convection within the film during drying takes several forms, e.g. laterally in the plane of the film due to capillary pressure gradients and toward the air-water interface due to evaporation, and has several consequences, e.g. packing fronts that propagate horizontally and vertically, growth of colloidal crystals, and segregation of binary mixtures to create spatial patterns. Analysis by Routh and Russel1 coupled faster evaporation at the edges, capillary pressure gradients that drive lateral flows, and d'Arcy flows through the close-packed regions to predict the nonuniform film thickness. One important feature is the "open time" before the capillary pressure reaches the maximum sustainable and the air-water interface recedes into the packing, leaving a dry edge. If the particles deform and voids close as the water evaporates the result is a transparent film. With more elastic particles cracks can open to release tension in the plane of the film. In some situations, though, rapid evaporation produces close packing at the air-dispersion interface and "skinning". The ability to generate close packing of monodisperse colloids at a controlled rate has stimulated several creative initiatives. For example, in a mixture of large and small particles evaporation brings the large particles into close packing. Interstitial flows then convect smaller particles toward the free surface, creating a vertically segregated film.3 Many applications demand an impervious coating that requires viscous deformation to eliminate pores between close-packed latices at temperatures around the glass temperature. Qualitative understanding evolved through the invention of polymer latices in the 1950s, which spawned the latex paint technology. In the 1990s quantitative measurements appeared from both industrial and academic laboratories and theories eventually followed. The dominant driving force is usually a negative capillary pressure due to deflection of menisci at the air-water interface, which puts the packing in compression in the normal direction and in tension laterally. Our theory2 describing this process starts with Hertzian contact mechanics, augmented by a viscous analogue. Volume averaging over doublets yields a nonlinear time-dependent stress-strain relationship that determines the time required to close the pores and identifies whether capillary compression, wet sintering, or dry sintering controls the process. When evaporation is rapid and the particles deform easily, an impermeable skin can form at the air-water interface sealing off further evaporation. From this analysis a process map emerges depending on the rate of evaporation relative to viscous deformation.3,4 Wet sintering controls film formation when evaporation is slow relative to viscous deformation, while capillary compression provides the driving force intermediate evaporation rates. Only dry sintering can complete the process for very rapid evaporation. Skinning occurs for very rapid deformation and slow diffusion. Groups at Minnesota, Illinois, and Princeton have quantified the tensile stress associated with drying films with the classical cantilever technique.5 When particles do not deform viscously the capillary pressure produces elastic deformation that stores energy in the packing that is capable of generating cracks in the films.6 The elastic recovery upon the opening of an infinite crack can be derived by linearizing the general non-linear stress-strain relation and solving the governing equations via the lubrication analytically. Equating the total elastic energy recovered to the energy of the new air-water surface determines the minimum capillary pressure to open a crack. Measurements of the film thickness below which the air-water interface recedes into the packing without causing cracking,50 follow the theory (- - -) reasonably well. Direct measurements of the capillary pressure at the onset of cracking demonstrate independence of the particle size as expected by theory, but consistently lie above the prediction. Intentional introduction of microscopic flaws brought the data closer to the prediction,7 suggesting that imperfections in the packing are necessary to initiate cracking.
