Drying and deposition of poly(ethylene oxide) droplets determined by Péclet number

Abstract

By varying many experimental parameters (temperature, pressure, humidity, contact angle, concentration and volume) we discover that whether evaporating droplets of PEO polymer solution deposit tall solid pillars or flat puddles is controlled by the dimensionless Péclet number, relating flux to diffusion.This article will appear in issue 17 of Soft Matter, a themed issue on Dynamics and Rheology of Fluid Interfaces. AbstractWe report results of a detailed experimental investigation into the drying of sessile droplets of aqueous poly(ethylene oxide) (PEO) polymer solutions under various experimental conditions. Samples are prepared with a range of initial concentrations c 0 and are filtered to remove traces of undissolved PEO clusters. In typical experiments, droplets with initial volumes between 5 L and 50 L are left to evaporate while temperature and relative humidity are monitored. Droplets either form a disk-like solid "puddle" or a tall conical "pillar". The droplet mass is monitored using a microbalance and the droplet profile is recorded regularly using a digital camera. Subsequent processing of the data allows values of droplet volume V, surface area A, base radius R, contact angle θ and height h to be determined throughout drying. From this data we identify four stages during pillar formation: pinned drying; pseudo-dewetting; bootstrap building; solid contraction and propose physical models to explain key aspects of each stage and to predict the transition from each stage to the next. The experimental parameters of relative humidity, temperature, pressure, droplet volume and initial contact angle are all systematically varied and observed to influence the drying process and consequently whether the droplet forms a pillar or a puddle. We combine these parameters into a dimensionless Péclet number Pe, which compares the relative effects of evaporation and diffusion, and show that the drying behaviour is only dependent on c 0 and Pe.

The effects of molecular weight, evaporation rate and polymer concentration on pillar formation in drying poly(ethylene oxide) droplets

“…This aspect of the results is in agreement with the Péclet model, which argues that increasing the relative effect of evaporation rate against polymer diffusion causes earlier polymer build up at the contact line, leading to taller fully dried pillar structures. While we have not increased atmospheric pressure in this study, we would predict that, much as with the high humidity results published previously [21], a significantly reduced evaporation rate would lead to a Péclet number less than unity and flat uniform deposits. Interestingly, So, although the Péclet argument captures some of the pillar-formation behaviour, the dependence on molecular weight is not as expected: samples with high M w do not easily form pillars.…”

“…The cloudiness of higher molecular weight solutions is due to non-dissolving micron-sized aggregates of PEO formed during mixing, the origin of which is still under contention [25]. In previous experiments [21] these aggregates were removed by passing the solution through a 0.45µm filter, and through careful density and viscosity measurements of the solutions after filtration, they have been shown to account for a very small percentage (< 5%) of the total PEO in solution. Furthermore these aggregates seem to have little effect on the final morphology, and so were not removed here.…”

“…Droplets drying at atmospheric pressure were prepared and recorded as described by Baldwin et al [21]. The rate of change of volumeV was determined both by gravimetric means to an accuracy of ±1mg and by extracting the two dimensional droplet profile (h(r)) from the digital side-on images using ImageJ software (US National Institutes of Health).…”

“…In a 1 dimensional model [21,22] pillar formation was shown to be controlled by a Péclet type ratio of the evaporation rate, −V (where V is droplet volume), which drives the polymer to the contact line during pinned drying, and the gradient diffusion coefficient of the polymer, D G , which in the absence of evaporation would homogenize the solution, along with initial droplet parameters of mass concentration c 0 , droplet base radius R, contact angle θ. In this work, as supported by various theoretical modelling approaches to particle dynamics during sessile droplet drying [1,10,23], we assume that the majority of evaporation over the surface of a droplet occurs in a narrow wedge very close to the contact line.…”

Monolith formation and ring-stain suppression in low-pressure evaporation of poly(ethylene oxide) droplets

“…It dissolves in water, although at high concentrations or molecular weights solutions can appear cloudy due to micron-sized clusters of undissolved polymer (Hammouda et al 2004). Recent experimental work on the evaporation of PEO droplets (Willmer et al 2010;Baldwin et al 2011) proposed a four-stage drying mechanism including a 'bootstrap' stage in which the liquid droplet is lifted above the surface by the freshly formed solid deposit, resulting in solid monoliths. These structures, which can be taller than the initial droplet, clearly defy the typical ring-stain effect, as nearly all the dried material ends up in the centre, rather than distributed around the edge of the initial triple line (where the three materials, liquid droplet, vapour and solid substrate all meet).…”