I.V. Vodolazskaya, Yu.Yu. Tarasevich, O.P. Isakova

Understanding the process of drying of protein solution drop is important for scientific and medical applications. In the drying sessile drops of bioliquids many appearances can be observed: the ringlike deposit, sol-gel transition, complex drop profile behavior, deformations of the gel-air interface, stik-slip motion of the contact line, crystallization. In this paper we proposed the model of round drying drop based on conservation equations, phase boundary condition and assumption that maximal drop height decreases with approximate constant velocity. Experimentally, the drying drop is bounded by the contact line in the plane of the substrate, the contact line remains pinned during most of the drying process, one is forced to fluid flow generation toward contact line. This flow is capable of transferring all of the solute to the contact line and thus accounts for the ringlike deposit. Our model is two-component (the fluid and the solute) system with two phases: sol in the middle of the drop and gel near the contact line. The volume fraction of the solute in gel phase is high and fixed. In sol phase space averaged volume fraction of the solute changes with time. Our assumptions are: into the low concentrate solution small drops gravitational effects can be neglected, so the boundary between the phases is vertical; diffusion effects for solute can be neglected (the diffusion coefficient of protein molecules is small); the fluid density is constant; the evaporation rate is small and constant in the sol phase, the drying of the drop occurs under constant temperature condition; the liquid-air interface is spherical surface (for slow flows we can consider the surface shape as equilibrium shape); the gel phase obstructs the liquid flow (such is the case albumin gel); the gelation process near the liquid-air interface is neglected; the maximal drop height velocity is proportional to averaged volume fraction of the solute; the contact angle between the liquid-air interface and gel-air interface on the phase boundary is proportional to averaged volume fraction of the solute. The model involves a set of nonlinear partial differential equations and requires numerical calculation for the analysis. We investigated parameter dependence of the drop shape, the same as: initial volume fraction of the solute, drop dimensions, the ratio of the maximal drop height velocity to the evaporation rate. Simulation data allow a good description of the protein solution drop shape with small initial solute concentration.