Droplet motion on inclined heterogeneous substrates
نویسندگان
چکیده
We consider the static and dynamic behaviour of two-dimensional droplets on inclined heterogeneous substrates. We utilize an evolution equation for the droplet thickness based on the long-wave approximation of the Stokes equations in the presence of slip. Through a singular perturbation procedure, evolution equations for the location of the two moving fronts are obtained under the assumption of quasistatic dynamics. The deduced equations, which are verified by direct comparisons with numerical solutions to the governing equation, are scrutinized in a variety of dynamic and equilibrium settings. For example, we demonstrate the possibility for stick–slip dynamics, substrate-induced hysteresis, the uphill motion of the droplet for sufficiently strong chemical gradients and the existence of a critical inclination angle beyond which the droplet can no longer be supported at equilibrium. Where possible, analytical expressions are obtained for various quantities of interest, which are also verified by appropriate numerical experiments.
منابع مشابه
Hysteretic Effects in Droplet Motions on Heterogeneous Substrates: Direct Numerical Simulation
Amethodof calculation is introduced that allows the simulation of the time-dependent three-dimensional motion of liquid droplets on solid substrates for systems with finite equilibrium contact angles. The contact angle is a prescribed function of position on the substrate. An evolution equation is given, using the lubrication assumption, that includes viscous, capillary, and disjoining forces. ...
متن کاملRolling droplets
When a rigid circular cylinder or sphere is placed on a rough inclined plane it will roll down the plane. When the experiment is repeated with a rigid cube it will slide down the plane. If the object is deformable a variety of motions become possible; the motion of elastic bodies and fluid drops depends on the interfacial energies of the materials, the roughness of the interfaces, the size of t...
متن کاملDroplet spreading on chemically heterogeneous substrates.
Consider the spreading dynamics of a two-dimensional droplet over chemically heterogeneous substrates. Assuming small slopes and strong surface tension effects, a long-wave expansion of the Stokes equations yields a single evolution equation for the droplet thickness. The contact line singularity is removed by assuming slip at the liquid-solid interface. The chemical nature of the substrate is ...
متن کاملTowards Smart Substrates for Controlling Micrometric Droplet Motion
In this contribution, we describe a novel approach to the problem of setting micrometric droplets in motion. First, this paper reviews the state-of-the-art methods to enable millimetric droplet motion, and investigates the scalability of the most promising techniques on the basis of preliminary experiments. Then, we propose a novel approach based on substrates with radial 3D pattern. In the pos...
متن کاملDroplet shapes on structured substrates and conformal invariance
We consider the finite-size scaling of equilibrium droplet shapes for fluid adsorption (at bulk two-phase coexistence) on heterogeneous substrates and also in wedge geometries in which only a finite domain Λ A of the substrate is completely wet. For three-dimensional systems with short-ranged forces we use renormalization group ideas to establish that both the shape of the droplet height and th...
متن کامل