Heterogeneous drying and nonmonotonic contact angle dynamics in concentrated film-forming latex drops

The dynamic drying process is studied in spatially heterogeneous film-forming latex suspensions across a wide range of dispersion concentrations using optical imaging techniques. Systematic changes in latex suspension concentration are found to affect lateral drying heterogeneity and surface topology. A nonmonotonic decay in contact angle is observed at the edges of drying droplets by continuously monitoring evaporation dynamics, which is quantitatively characterized by the peak strain and peak formation time. An analytical model is developed to explain the nonmonotonic contact-angle decay by considering a transient dilational stress imposed on a viscoelastic solid model for the particle network. Importantly, the latex concentration dependence of this phenomenon provides evidence for a smooth transition from fluid-line pinning to fluid-line recession behavior during drying, leading to ringlike to volcanolike deposition patterns, respectively. Using experimental data for drying heterogeneity, we quantitatively explore the influence of Marangoni flow and capillary pressure on drying behavior. Moreover, our results show that latex concentration and particle packing can also be strategically used to reduce contact-line friction, thereby affecting fluid-line recession. Taken together, these results show that studying latex suspensions in seemingly simple droplet geometries provides insight into the emergent spatially heterogeneous viscoelastic properties during film formation.

Figure 1

Drying mechanisms in dilute, concentrated, and film-forming suspensions. (a) Dilute dispersion: drying in ultradilute suspensions showing a pinned contact line (left) and receding contact line (right). Time progression is denoted by dotted lines. The contact angle either decreases monotonically for the first case or remains constant at equilibrium values in the latter case. (b) Concentrated film-forming dispersion: emergent heterogeneity in concentrated latex suspensions. A radially outward capillary flow (green arrow) causes particles to partition preferentially at the drop edge. This leads to two effects: First, an interfacial gradient in surface active agents causes a counter Marangoni flow (red arrow) and second, a reduction of pressure at the drop edge due to particle close packing leads to fluid-line recession. Regions within the same drop include a dry region beyond the fluid line with particles in random close packing, a drying front of close-packed particles saturated with water at the receding fluid line, a packing front of concentrated particles with volume fraction below close packing, and the fluidic center. (c) Stages of film formation. Latex particles in an initially stable aqueous dispersion closely pack at the drop edge, which increases resistance to fluid flow in the particle interstices and causes the fluid line to recede. As evaporation continues, interparticle voids are lost and particles deform from their spherical shape while initially maintaining their individual particle identities. Continued evaporation causes the particle layer to turn transparent due to homogenization of the refractive index, which often signals film formation. Further macromolecular interdiffusion and coalescence between boundaries at $T>T_g$ causes formation of a homogeneous, continuous, and transparent polymer film with increased mechanical strength.

Figure 2

Nondimensional dynamic contact angle at the drop edge for a drying latex suspension as a function of dispersion volume fraction. Contact-angle data are shown for latex suspensions that exhibit two distinct peaks in contact angles $\left(\varphi \ge 0.025\right)$. The graph is nondimensionalized for ease of visualization only and does not affect data analysis. The inset shows contact-angle data for dilute latex suspensions $[\varphi =(1.25\times {10}^{-5})–(1.25\times {10}^{-2})]$ exhibiting only a simple decay in contact angle as a function of time, with the case of $\varphi =0.025$ from the main plot repeated here for reference. This gives a common framework to understand the transition from monotonic to nonmonotonic contact-angle decays as concentration is increased. For all samples, error bars are reported as the standard deviation from at least three independent experiments. Labels I–IX denote the nonmonotonic features in contact-angle decay (shown here for the $\varphi =0.4$ case) and correspond to stages in deposit peak formation, as explained in Fig. 3.

Figure 3

Schematic of three distinct stages during drying for dispersions with high latex concentration. In stage 1, the fluid line recedes and the contact angle monotonically decays. In stage 2, formation of the dry outer edge leads to expansion and contraction of the outer interface, causing a peak in contact angle at time ${\tau }_{P1}$. In stage 3, the inner crater of a volcanolike topology forms and depletion of water here expands and contracts the inner interface, subsequently resulting in a secondary peak in contact angle at time ${\tau }_{P2}$. In optical micrographs, the dashed red line indicates the fluid-line position. In schematic images, the solid blue line represents the responsive particle-rich interface (open arrows) that introduces contact angle-peaks and the dashed blue line represents the fluid interface shown to constantly recede (filled arrows). Roman numerals I–IX correspond to stages in two-peaked contact-angle decay curves common to all high concentrations, shown in Fig. 2 for the case of $\varphi =0.4$.

Figure 4

Quantitative analysis of absolute time scales and receding fluid-line position during latex droplet drying. (a) Average time scales associated with contact angle are plotted as a function of dispersion volume fraction $\varphi$, including final drying time ${\tau }_F$, primary peak time ${\tau }_{P1}$, relative secondary peak time ${\tau }_{P2}/{\tau }_{P1}$, and final drying time relative to water volume in the droplet ${\tau }_F^{\prime }={\tau }_F/V_w$. The dashed vertical line shows the transition from the dilute regime to the concentrated regime. (b) Quantitative analysis of receding fluid-line position during droplet drying. Initial contact-line position (black squares) and receding fluid-line position (black circles) are plotted normalized to the drop radius (1.51 mm) for a $\varphi =0.1$ latex dispersion. Here the time axis is normalized to the final drying time ${\tau }_F$ because peak formation time is not evident from (purely) optical imaging experiments. The position of the receding fluid line is further plotted with a time delay of 10% of the total drying time (red circles), which leads to good correspondence with the different stages in contact-angle decay (black line), as described in the text. Time points shown with roman numerals correspond to stages of deposit evolution shown in Fig. 3.

Figure 5

Dependence of latex concentration on deposition patterns. (a) Optical micrographs (top-down view) of dry-film patterns for latex dispersions with varying $\varphi$: (i) $1.25\times {10}^{-5}$, (ii) $1.25\times {10}^{-4}$, (iii) $1.25\times {10}^{-3}$, (iv) $1.25\times {10}^{-2}$, (v) 0.025, (vi) 0.05, (vii) 0.1, (viii) 0.2, and (ix) 0.4. The scale bar is 1.5 mm. (b) Surface profilometry data showing radial dependence of film height. Truncated peaks for the $\varphi =0.4$ sample arise due to instrument range limitations. (c) Deposit peak position and height as a function of latex volume fraction. The ratio of peak position of deposit maximum $r_p$ relative to drop radius $R$ (half filled circles) shows an exponential decay (red line, exponential fit). Open triangles show peak height of the dry film pattern $h_p$, which obeys a power-law relationship with volume fraction $\varphi$ such that $h_p\propto {\varphi }^{0.65}$. (d) Relative crater size in volcanolike deposits and receding fluid-line velocity as a function of $\varphi$. The ratio of crater size to deposit diameter ${\mathrm{\Delta }}_{\text{FWHM}}/2R$ (open circles) shows single-exponential decay (red line, exponential fit). Vertical dashed lines in (c) and (d) demarcate the dilute and concentrated regimes.

Figure 6

Analytical model for nonmonotonic contact-angle decay. (a) Geometry and height profile of a drying droplet with packing front located at $r_f$, with a fluidic region to the left and a compacted region to the right. (b) Pressure in the compacted region at the instant the fluid line begins to recede. The dotted line shows a qualitative sketch of the pressure distribution from Eq. (6) and $\overline{p}$ is the average pressure. The solid line shows the approximation of capillary pressure sustained by the particle network. (c) Strain response plotted for three cases of continued evaporation of the dilute limit (top panel), viscoelastic solid creep-recovery response upon application of a transient step stress from $t_1$ to $t_{\max }$ (middle panel), and a linear superposition of the continued evaporation and creep response (bottom panel).

Figure 7

Results from the analytical model for drying latex suspensions. (a) Strain $\gamma =\theta \left(t\right)/{\theta }_0$ as a function of time for the latex suspension with volume fraction $\varphi =0.40$. The gray dashed line represents the initial rate of evaporation in the continual evaporation (low latex concentration) limit. The experimental strain curve is used to estimate system parameters, as explained in the text. (b) Average strain rate $d\gamma /dt$ for the latex suspension with volume fraction $\varphi =0.40$. (c) System parameters obtained for different latex volume fraction samples, including modulus $E$, viscosity $\eta$, and retardation time $\tau$ for the compacted particle region. Error bars arise from statistical differences in averaged strain responses. (d) Peak strain ${\gamma }_{P1}$ determined from the analytical model and experiments.

Figure 8

Factors affecting fluid-line recession and onset of lateral drying heterogeneity, including scaled Marangoni number ${\text{Ma}}^{\prime }$ (circles), reduced capillary pressure (squares), and contact-line friction coefficient (triangles) as a function of dispersion volume fraction $\varphi$. The contact-line friction constant $k_{cl}$ is calculated from Fig. S9 in [21] as a function of $\varphi$ based on the theory described in Ref. [4] and is found to have a simple power-law dependence on latex volume fraction $\varphi$ such that $k_{\text{cl}}\propto {\varphi }^{-0.7}$. The vertical dashed line denotes the transition between the dilute and concentrated regimes.

Figure 9

Factors affecting fluid-line recession and onset of lateral drying heterogeneity. Experimental dependence of the dimensionless primary peak time ${\tau }_{P1}/{\tau }_F$ on scaled Marangoni number ${\text{Ma}}^{\prime }$, reduced capillary pressure $P_{\text{cap}}$, and contact-line friction $k_{\text{cl}}$. The dashed line represents the dilute limit data where no drying heterogeneity and thus no peak is observed before final drying of the film; in this regime, ${\tau }_{P1}/{\tau }_F\approx 1$. The vertical dashed line in all panels shows the transition from fluid-line pinning to fluid-line recession. The dotted line in the middle panel shows results from simulations based on the Routh-Russel model [11, 12]. A detailed comparison of data and simulation results can be found in Fig. S8 in [21].