Shapes of Nonsymmetric Capillary Bridges.

L R Pratt,N Pesika,D T Gomez,A Muralidharan

doi:10.1021/acs.jpcb.1c07448

L R Pratt, N Pesika + Show 2 more

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https://doi.org/10.1021/acs.jpcb.1c07448

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Here we study the shapes of droplets captured between chemically distinct parallel plates. This work is a preliminary step toward characterizing the influence of second-phase bridging between biomolecular surfaces on their solution contacts, i.e., capillary attraction or repulsion. We obtain a simple, variable-separated quadrature formula for the bridge shape. The technical complication of double-ended boundary conditions on the shapes of nonsymmetric bridges is addressed by studying waists in the bridge shape, i.e., points where the bridge silhouette has zero derivative. Waists are generally expected with symmetric bridges, but waist points can serve to characterize shape segments in general cases. We study how waist possibilities depend on the physical input to these problems, noting that these formulas change with the sign of the inside–outside pressure difference of the bridge. These results permit a variety of different interesting shapes, and the development below is accompanied by several examples.

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We study the shapes of nonsymmetric capillary bridges between planar contacts (Figure 1), laying a basis for studying the forces that result from the bridging
A background aspect of our curiosity in these problems is the possibility of evaporative bridging between ideal hydrophobic surfaces, influencing the solution contacts between biomolecules.[4−10] Assessment of critical evaporative lengths in standard aqueous circumstances on the basis of explicit thermophysical properties[8] sets those lengths near 1 μm
Simple, variable-separated quadrature formulas for the shapes of capillary bridges, not necessarily symmetric

Summary

■ INTRODUCTION

We study the shapes of nonsymmetric capillary bridges between planar contacts (Figure 1), laying a basis for studying the forces that result from the bridging. We will consider (Figure 2) intermediate positions where r(̇ z) = 0 and sin θ(z) = 1. A contact angle near π/2 will correspond to a lower level for the horizontal line and be less restrictive of the possible values of a common waist radius R. To achieve Δp/γ = 1/R − r < 0 for a bridge with wiast radius R, clearly the curvature rat that waist should be substantially positive to ensure that the negative second contribution dominates. The radius at the waist should be fairly large, thereby reducing the contribution of the positive first term These points combined suggest that to achieve adhesion the contact areas should be larger than the waist area, which itself should be substantial. The aspect ratio of the bridge is vastly changed, as was true in the discussion of capillary adhesion of ref 2; capillary adhesion would be expected for this shape

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■ CONCLUSIONS

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