Capillary filtering of particles during dip coating

An object withdrawn from a liquid bath is coated with a thin layer of liquid. Along with the liquid, impurities such as particles present in the bath can be transferred to the withdrawn substrate. Entrained particles locally modify the thickness of the film, hence altering the quality and properties of the coating. In this study, we show that it is possible to entrain the liquid alone and avoid contamination of the substrate, at sufficiently low withdrawal velocity in diluted suspensions. Using a model system consisting of a plate exiting a liquid bath, we observe that particles can remain trapped in the meniscus which exerts a resistive capillary force to the entrainment. We characterize different entrainment regimes as the withdrawal velocity increases: from a pure liquid film, to a liquid film containing clusters of particles, and eventually individual particles. This capillary filtration is an effective barrier against the contamination of substrates withdrawn from a polluted bath and finds application against biocontamination.

Figure 1

(a) Schematic of the dip-coating experimental setup. Experimental visualizations of the three entrainment regimes during the withdrawal of the substrate from a suspension (2% of polystyrene particles of radius $a=125\mu \mathrm{m}$ in AP 100). (b) Liquid only, (c) entrainment of clusters, and (d) entrainment of individual particles. The time increases from left to right. Scale bars are $500\mu \mathrm{m}$.

Figure 2

(a) Evolution of the surface density of particles entrained ${\phi }_s$ (open blue rectangles) and individual particles entrained ${\phi }_{s,in}$ (blue solid circles) when increasing the withdrawal velocity $U$ for a suspension of polystyrene particles dispersed in silicone oil AP 100 ($\varphi =5\%$ and $a=70\mu \mathrm{m}$). The vertical dashed line and dashed-dotted line show the threshold velocities for cluster entrainment $U_{\text{cl}}^{*}$ and individual particle entrainment $U_{\text{in}}^{*}$, respectively. The insets illustrates the composition of the coated film in the different regimes. Scale bars are $500\mu \mathrm{m}$. (b) Threshold velocity $U_{\text{in}}^{*}$ for the entrainment of individual particles when varying the radius of the particles $a$ and the liquid phase: Silicone oil AP 100 (blue squares), AR 200 (red circles), and AP 1000 (green diamonds). The experiments are performed only for dilute suspensions, $\varphi <0.5\%$.

Figure 3

(a) Rescaled thickness of the liquid film $h/{\ell }_c$ without particles for varying capillary number Ca and silicone oil AP 100 (green symbols), AR 200 (blue symbols), and AP 1000 (green symbols). The dotted line is the theoretical prediction $h/{\ell }_c=0.94{\text{Ca}}^{2/3}$. (b) Thickness of the liquid film when varying the capillary number and withdrawing the glass plate from a suspension of polystyrene particles in silicone oil (AP 100) with $\varphi =0.28\%$ and $a=70\mu \mathrm{m}$ particles. The vertical lines indicate the three different regimes and the insets show typical film compositions on the plate.

Figure 4

(a) Schematic of the forces acting on a particle in the liquid meniscus. (b) Threshold capillary number ${\text{Ca}}_{\text{in}}^{*}$ for individual particle entrainment in the liquid film. The symbols are the experimental results for different silicone oils (blue squares: AP 100; red circles: AR 200; green diamonds: AP 1000) and the dotted line is the scaling ${\text{Ca}}_{\text{in}}^{*}=0.24{\mathrm{Bo}}^{3/4}$.

Figure 5

Evolution of the surface density of (a) the total particles entrained ${\phi }_s$ and (b) only the individual particles entrained ${\phi }_{s,\text{in}}$ when varying the capillary number Ca and for different volume fractions $\varphi =1\%$ (green diamonds), $\varphi =2\%$ (blue circles), and $\varphi =5\%$ (red squares). In (a) the colored dashed lines show the transition between the entrainment of liquid alone and the entrainment of particles in clusters. In (b) the vertical line shows the transition between the cluster regime and the individual particle regimes. (c) Mean size of the clusters entrained in the liquid film. The insets show different morphologies of clusters. (d) Diagram $(\varphi ,\text{Ca})$ reporting the existence of the three regimes, liquid alone, clusters, and individual particles, obtained for $\mathrm{\Delta }=33\mathrm{mm}$ and various volume fractions $\varphi$. The black lines are guides for the eye.

Figure 6

Velocity threshold leading to the contamination of a substrate withdrawn from contaminated water (white region). In the gray region, the substrate is expected to be withdrawn from the polluted water without contamination owing to the capillary filtering mechanism. The black corresponds to Eq. (3). The arrow indicates the range of size of different biological organisms [40, 41, 42, 43, 44, 45]. The solid symbols and the open symbols indicates contaminated and noncontaminated substrates, respectively. The blue circles are experiments with Synechocystis sp. PCC6803 and the red symbols are experiments with Chlamydomonas reinhardtii. The inset photographs are obtained from withdrawal experiments from suspensions of Chlamydomonas reinhardtii ($2a\sim 10\mu \mathrm{m})$ [(1a) and (1b)] and Synechocystis sp. PCC6803 ($2a\sim 3\mu \mathrm{m})$ [(2a) and (2b)]. At low withdrawal velocity, the microorganisms are not entrained: For (1a), $U=0.36\mathrm{mm}{\mathrm{s}}^{-1}$, and for (2a), $U=0.48\mathrm{mm}{\mathrm{s}}^{-1}$. At larger withdrawal velocity, the microorganisms contaminate the substrate: For (1b), $U=2.18\mathrm{mm}{\mathrm{s}}^{-1}$, and for (2b), $U=1.03\mathrm{mm}{\mathrm{s}}^{-1}$. The scale bars are $200\mu \mathrm{m}$.