The rapid covering of a solid surface by a liquid is an event common to diverse processes in nature, science, engineering, and medicine. Some examples from manufacturing include processes such as investment casting, electroplating, cleaning, dip coating, spin coating, painting, screen printing, and production of powder slurries. In the field of medicine, examples include the flow of liquids into syringes and through intravenous feeding tubes. By any of these processes, gas may become trapped as isolated pockets, or voids, at liquid-solid surfaces. The number and size of the voids that form depend both on the details of the liquid flow and on the properties of the solid surface, such as its roughness and its tendency to be wet by the liquid. In coating or casting applications, voids that are not removed can result in defects that compromise the adhesion, electrical properties, surface finish, and durability of the product.
Conditions for the initial formation of a void are especially favorable at reentrant features of a rough surface, such as pinhole defects in films, pits and scratches formed by grinding, and even intentional cavities formed by a prior photolithographic or stamping procedure. Flow of liquid can cover such features before the gas can escape, especially if the solid surface is lyophobic. This phenomenon is particularly prevalent, for example, when electrolytically depositing metals into small cavities (≈50 µm diameter) like those formed in photoresist masks for patterning electrical circuits. For such geometries a commonly observed defect is a lens-shaped depression in the deposited metal, as illustrated in Fig. 1. These depressions indicate regions of low current where a bubble prevented adequate liquid contact.
Fig. 1. Illustration of electroplating defect caused by gas-filled voids trapped in recessed cavities.
Given the negative impact that gas-filled voids have on many processes, it is desirable to find ways either to prevent their formation or to expedite their removal from the system once they have formed. In situations where it is not feasible either to modify the way in which liquid is introduced at the surface or to chemically modify the surfaces, the formation of surface voids may be unavoidable. In many of these systems, voids persist because they are thermodynamically stable. For such systems, voids can be removed only by supplying work, such as mechanical vibration or impact in their vicinity.
This paper analyzes systems in which voids may be trapped in low-energy configurations. A thermodynamic model is presented of a gas-filled void at an idealized reentrant surface feature, and the model is used to calculate the most stable void configuration (including the possibility of the void being liberated from the surface). The approach is similar to that used by Chatain et al. [1] to analyze the thermodynamically stable shapes of two-phase systems enclosed within a cubic cavity. By calculating the free energy of the stable configuration relative to that of a liberated void of the same size, the minimum work required to release the void is predicted. The idealized model has the benefits of being analytically tractable and of leading to insights that should be qualitatively valid for real systems. In fact, as shown in Section 3, even the quantitative predictions of the work required to remove a void are expected to be good approximations that can be used to help design procedures for removing these types of defects.