Influence of interface resistance on droplet growth.

(A) The sharp interface limit considers two spatial domains (volume fractions ϕin and ϕout, with diffusion coefficients Din and Dout) separated by a boundary, where the volume fraction jumps. In the spherically symmetric case considered here, the phase boundary moves until equilibrium is reached. (B) The chemical potential at the interface can be continuous (green) or discontinuous (blue, jump indicated by dashed line), resulting in different boundary kinetics (see panels (C) and (D)). (C) Snapshots of the volume fraction of condensate material at t = 2000s for different interface resistance. The droplet grows due to a diffusive flux from the right side. Systems size, 100 μm. We use λ = λs. For numerics see appendix B(D): Interface resistance plays a larger role in smaller droplets. In larger droplets diffusive flux dominates.

Influence of interface resistance on FRAP recovery.

(A): In a typical FRAP experiment, the droplet is close to equilibrium prior to the experiment. The fluorescent dye labeling the condensate material gets bleached, and is therefore not visible in fluorescence microscopy (unlabeled, white). Subsequently, the exchange of labeled and unlabeled material across the phase boundary can be observed. (B): The ratio between the concentrations right inside and outside (see panel (A), ϕin, ϕout) starts at zero (postbleach). Without interface resistance (grey dashed line), the ratio jumps immediately to the equilibrium partition coefficient Γ∗. For the case of interface resistance, the concentration ratio approaches the equilibrium value continuously. (C) Time course of FRAP recovery with and without interface resistance. Initial conditions and equilibrium values are identical, but with resistance recovery is slowed down.

Continuous models of interface resistance.

(A): Interface resistance in continuous models can arise through a minimum in particle mobility at the phase boundary. (B): If resistance is induced by a friction peak (orange, γM), there is a pronounced mobility minimum and therefore in (C) a strongly reduced diffusion coefficient at the phase boundary. In the case of interface resistance via a potential barrier (grey), friction and diffusion coefficient interpolate monotonously between the values inside and outside of the phase boundary. (C) The friction peak at the phase boundary induces a corresponding minimum in the diffusion coefficient (orange). For the potential barrier case, the diffusion coefficient interpolates monotonously between dense and dilute phases (grey). (D) Interface resistance in continuous models can also arise through a potential barrier at the phase boundary. (E) In the case of interface resistance via a potential barrier, the volume fraction displays a pronounced minimum at the phase boundary (blue, ϕB). (F) The minimum in (E) reflects a potential barrier at the phase boundary (blue). There is no potential barrier in the case of a mobility minimum (grey). (G) Time course of theoretical FRAP recovery for continuous boundary models. All models start with the same initial conditions. Away from the boundary, the concentration profiles of the mobility minimum and potential barrier cases are indistinguishable. (H) Zoom-in to the boundary region of panel (D). Note the distinct volume-fraction profiles within the boundary throughout recovery.

Quantification of interface resistance with different experimental techniques

(A): FRAP halftime depends sensitively on interface resistance, particularly for small droplets. For larger droplets, diffusive time scales become dominant (see discussion in [6]). (B): Given the current estimates of interfacial width, direct observation of phase boundary concentrations (orange and blue curves) via ensemble fluorescence microscopy (intensity I) is not possible due to the much larger PSF. (C) Suggested microfluidic assay to measure interface resistance. A capillary containing the dense and dilute phases is connected on the dilute side with a sub-saturated channel. All numerical solutions have λ = λs.