Characterization of Particle Transport and Deposition Due to Heterogeneous Dewetting on Low-Cost Inkjet-Printed Devices.

This work investigates the deposition patterns left by evaporating particle-laden droplets on heterogeneous surfaces with spatially varying wettability. Spatial differences in receding contact angles give rise to scalloped-shaped contact lines. During evaporation, the contact line recedes in one location and remains pinned in another. This nonuniform contact line recession results in particle self-assembly above areas where the contact line remains pinned but not where it recedes. This behavior is fairly robust across a variety of particle sizes, concentrations, and device geometries. We hypothesize that particle self-assembly in these cases is due to the competition between particle diffusion and evaporative-driven advective flow. Diffusion appears to be more pronounced in regions where the contact line recedes, while advection appears to be more pronounced near the pinned portion of the contact line. As such, particles appear to diffuse away from receding areas and toward pinned areas, where advection transports them to the contact line. The distribution of particle deposition above the pinned regions was influenced by the particle size and the concentration of particles in the droplet. Similar to homogeneous surfaces, deposition was more prevalent at the pinned portion of the contact line for smaller particles and lower concentrations and more uniformly distributed across the entire pinned region for larger particles and higher concentrations. A better understanding of this process may be beneficial in a wide variety of particle separation applications, such as printing, cell patterning, biosensing, and anti-icing.

Coplanar Electrowetting-Induced Droplet Detachment from Radially Symmetric Electrodes.

This work demonstrates electrowetting-induced droplet detachment in air from coplanar electrodes using a single voltage pulse. It also presents two models to predict when this detachment will occur. Previous works approximated the minimum energy for detachment based on (i) adhesion work at the solid-liquid interface and (ii) interfacial energy changes along all three interfaces in the system. This investigation updates those models to include changes in gravitational potential energy during detachment and provides validation by testing predicted detachment thresholds against experimental observations. Droplets of varying volume were ejected from electrowetting devices with (i) radially symmetric four-part coplanar electrodes and (ii) single electrodes with a ground wire inserted directly into the droplet. All experiments were performed in air. Incorporation of gravitational potential energy improves predictions for critical electrowetting number and captures the observed increase in applied voltage required with increased droplet volume. These new models will be of particular benefit in three-dimensional digital microfluidics applications that manipulate droplets in air.

Thermal analysis of dry eye subjects and the thermal impulse perturbation model of ocular surface.

In this study, we explore the usage of ocular surface temperature (OST) decay patterns to distinguished between dry eye patients with aqueous deficient dry eye (ADDE) and meibomian gland dysfunction (MGD). The OST profiles of 20 dry eye subjects were measured by a long-wave infrared thermal camera in a standardized environment (24 °C, and relative humidity (RH) 40%). The subjects were instructed to blink every 5 s after 20 âˆ¼ 25 min acclimation. Exponential decay curves were fit to the average temperature within a region of the central cornea. We find the MGD subjects have both a higher initial temperature (p < 0.022) and a higher asymptotic temperature (p < 0.007) than the ADDE subjects. We hypothesize the temperature difference among the subpopulations is due to tear volume and heat transfer mechanisms. To study the validity of our claim, we develop a mathematical model, referred to as the thermal impulse perturbation (TIP) model. We conclude that long-wave-infrared thermal imaging is a plausible tool in assisting with the classification of dry eye patient.

Phantom study of tear film dynamics with optical coherence tomography and maximum-likelihood estimation.

In this Letter, we implement a maximum-likelihood estimator to interpret optical coherence tomography (OCT) data for the first time, based on Fourier-domain OCT and a two-interface tear film model. We use the root mean square error as a figure of merit to quantify the system performance of estimating the tear film thickness. With the methodology of task-based assessment, we study the trade-off between system imaging speed (temporal resolution of the dynamics) and the precision of the estimation. Finally, the estimator is validated with a digital tear-film dynamics phantom.

Fast evaporation of spreading droplets of colloidal suspensions.

When a coffee droplet dries on a countertop, a dark ring of coffee solute is left behind, a phenomenon often referred to as the coffee-ring effect. A closely related yet less-well-explored phenomenon is the formation of a layer of particles, or skin, at the surface of the droplet during drying. In this work, we explore the behavior of a mathematical model that can qualitatively describe both phenomena. We consider a thin axisymmetric droplet of a colloidal suspension on a horizontal substrate undergoing spreading and evaporation. In contrast to prior work, precursor films (rather than pinned contact lines) are present at the droplet edge, and evaporation is assumed to be limited by how quickly molecules can transfer out of the liquid phase (rather than by how quickly they can diffuse through the gas phase). The lubrication approximation is applied to simplify the mass and momentum conservation equations, and the colloidal particles are allowed to influence the droplet rheology through their effect on the viscosity. By describing the transport of the colloidal particles with the full convection-diffusion equation, we are able to capture depthwise gradients in particle concentration and thus describe skin formation, a feature neglected in prior models of droplet evaporation. The highly coupled model equations are solved for a range of problem parameters using a finite-difference scheme based on a moving overset grid. The presence of evaporation and a large particle Peclet number leads to the accumulation of particles at the liquid-air interface. Whereas capillarity creates a flow that drives particles to the droplet edge to produce a coffee ring, Marangoni flows can compete with this and promote skin formation. Increases in viscosity due to particle concentration slow down droplet dynamics and can lead to a reduction in the spreading rate.

The influence of a lipid reservoir on the tear film formation.

We present a mathematical model to study the influence of a lipid reservoir, seen experimentally, at the lid margin on the formation and relaxation of the tear film during a partial blink. Applying the lubrication limit, we derive two coupled non-linear partial differential equations characterizing the evolution of the aqueous tear fluid and the covering insoluble lipid concentration. Departing from prior works, we explore a new set of boundary conditions (BCs) enforcing hypothesized lipid concentration dynamics at the lid margins. Using both numerical and analytical approaches, we find that the lipid-focused BCs strongly impact tear film formation and thinning rates. Specifically, during the upstroke of the eyelid, we find specifying the lipid concentration at the lid margin accelerates thinning. Parameter regimes that cause tear film formation success or failure are identified. More importantly, this work expands our understanding of the consequences of lipid dynamics near the lid margins for tear film formation.

Exchange of tears under a contact lens is driven by distortions of the contact lens.

We studied the flow of the post-lens tear film under a soft contact lens to understand how the design parameters of contact lenses can affect ocular health. When a soft contact lens is inserted, the blinking eyelid causes the lens to stretch in order to conform to the shape of the eye. The deformed contact lens acts to assume its un-deformed shape and thus generates a suction pressure in the post-lens tear film. In consequence, the post-lens tear fluid moves; it responds to the suction pressure. The suction pressure may draw in fresh fluid from the edge of the lens, or it may eject fluid there, as the lens reassumes its un-deformed shape. In this article, we develop a mathematical model of the flow of the post-lens tear fluid in response to the mechanical suction pressure of a deformed contact lens. We predict the amount of exchange of fluid exchange under a contact lens and we explore the influence of the eye's shape on the rate of exchange of fluid.

Maximum-likelihood estimation in Optical Coherence Tomography in the context of the tear film dynamics.

Understanding tear film dynamics is a prerequisite for advancing the management of Dry Eye Disease (DED). In this paper, we discuss the use of optical coherence tomography (OCT) and statistical decision theory to analyze the tear film dynamics of a digital phantom. We implement a maximum-likelihood (ML) estimator to interpret OCT data based on mathematical models of Fourier-Domain OCT and the tear film. With the methodology of task-based assessment, we quantify the tradeoffs among key imaging system parameters. We find, on the assumption that the broadband light source is characterized by circular Gaussian statistics, ML estimates of 40 nm +/- 4 nm for an axial resolution of 1 µm and an integration time of 5 µs. Finally, the estimator is validated with a digital phantom of tear film dynamics, which reveals estimates of nanometer precision.

Tear film dynamics on an eye-shaped domain I: pressure boundary conditions.

We study the relaxation of a model for the human tear film after a blink on a stationary eye-shaped domain corresponding to a fully open eye using lubrication theory and explore the effects of viscosity, surface tension, gravity and boundary conditions that specify the pressure. The governing non-linear partial differential equation is solved on an overset grid by a method of lines using a finite-difference discretization in space and an adaptive second-order backward-difference formula solver in time. Our 2D simulations are calculated in the Overture computational framework. The computed flows show sensitivity to both our choices between two different pressure boundary conditions and the presence of gravity; this is particularly true around the boundary. The simulations recover features seen in 1D simulations and capture some experimental observations including hydraulic connectivity around the lid margins.