Liquid-Liquid Interface Deposition

• Liquid–Liquid Interface Deposition is a process class where material is organized or deposited at the mobile interface between two immiscible liquids, enabling film formation and crystallization.
• Different mechanisms—including bilayer entrainment, surfactant-stripping, thermal-shock crystallization, and evaporation-driven phase separation—demonstrate how interfacial stresses, surfactant partitioning, and thermal gradients dictate deposition outcomes.
• Key control parameters such as capillary number, viscosity and density ratios, surfactant behavior, and salt concentration critically influence film uniformity, microstructure, and the overall deposition process.

Searching arXiv for the cited LLID-related papers and closely related work to ground the article. {"query":"Liquid-Liquid Interface Deposition (Smith et al., 2024, Berry et al., 22 Aug 2025, Nasirimarekani, 2024, Champougny et al., 2020)", "max_results": 10} Liquid–Liquid Interface Deposition (LLID) denotes a class of deposition, assembly, entrainment, and crystallization processes in which material is generated, concentrated, or organized at the boundary between two immiscible liquids, and is either retained there as an interfacial film or transferred to a substrate. Across recent work, LLID encompasses at least four distinct physical realizations: bilayer entrainment during dip-coating of a plate withdrawn through two immiscible liquids; surfactant-stripping assembly of two-dimensional platelets at a water/dichloromethane interface; thermal-shock-driven crystal growth on a transient oil–brine interface created by drop impact; and evaporation-driven interfacial liquid-liquid phase separation whose physics has been proposed to translate from liquid–air to liquid–liquid systems (Champougny et al., 2020, Smith et al., 2024, Berry et al., 22 Aug 2025, Nasirimarekani, 2024). In all of these cases, the interface is not merely a geometric boundary: it acts as the locus where capillary stresses, surfactant partitioning, thermal gradients, phase separation, or shear transmission select the deposited thickness, coverage, or microstructure.

1. Interfacial basis and process classes

A unifying feature of LLID is that the liquid–liquid boundary is mobile and compliant rather than rigid. In the crystallization study of hexadecane on cold brine, the liquid–liquid interface is described as “defect-free,” lacking rigid surface defects and stress concentrators typical of solid substrates; this suppresses heterogeneous nucleation at fixed defects and contact-line pinning, and promotes uniform, stress-free crystal growth (Berry et al., 22 Aug 2025). In the 2D-material deposition method termed “Liquid Interface Deposition,” the interface between water and dichloromethane serves simultaneously as an assembly plane and as the region where surfactant is stripped from platelets, enabling their lateral consolidation into a film (Smith et al., 2024).

The underlying selection mechanisms differ markedly by modality. In two-liquid dip-coating, the decisive balance is between viscous entrainment and capillary suction, with the final film thicknesses set by peak shear stresses in a narrow coupling region (Champougny et al., 2020). In 2D-solid assembly, the decisive factor is preferential surfactant partitioning into the organic phase, which destabilizes aqueous colloidal stabilization and drives interfacial adsorption of platelets (Smith et al., 2024). In impact-triggered crystallization, thermal shock controls both nucleation and radial crystal growth while the available interfacial area evolves hydrodynamically (Berry et al., 22 Aug 2025). In evaporation-driven phase separation of Pluronic F-127, interfacial enrichment, salting-out, and evaporation-induced flow jointly determine whether the deposit is a coacervate cluster field, a lattice-like sheet, or a more continuous film; the paper explicitly suggests that the same physics can drive LLPS at oil–water interfaces (Nasirimarekani, 2024).

This diversity suggests that LLID is better understood as a process class than as a single mechanism. What is common is the use of an immiscible-liquid interface as the active site of thickness selection, lateral self-assembly, or pattern formation.

2. Bilayer entrainment in dip-coating with two immiscible liquids

A hydrodynamic foundation for LLID is provided by dip-coating from a bath containing two immiscible liquids, where a vertical plate withdrawn at speed $U$ entrains two thin films rather than one (Champougny et al., 2020). Liquid 1 is the denser lower bath, with viscosity $\mu_1$ and density $\rho_1$; liquid 2 is the lighter upper layer, with viscosity $\mu_2$, density $\rho_2$, and thickness $\Delta H$. The relevant interfaces are the liquid 1–liquid 2 interface with tension $\gamma_{12}$ and the liquid 2–gas interface with tension $\gamma_{2g}$. The reference capillary number is

$Ca \equiv \frac{\mu_1 U}{\gamma_{12}},$

with property ratios

$$M=\frac{\mu_2}{\mu_1}, \qquad R=\frac{\rho_2}{\rho_1}, \qquad \Sigma=\frac{\gamma_{2g}}{\gamma_{12}}.$$

The classical Landau–Levich–Derjaguin result for one liquid,

$\mu_1$0

extends to the two-liquid problem in a nontrivial way. The principal result is that the liquid–liquid and liquid–gas interfaces evolve essentially independently, as if each were a one-liquid dip-coating problem, except in a very narrow “virtual contact point” region at $\mu_1$1, where the interface separation falls sharply to its asymptotic value and shear stresses peak (Champougny et al., 2020). The dimensional vertical extent of this coupling region is of order $\mu_1$2; in rescaled coordinates, the zone where wall shear is significant spans $\mu_1$3. If the virtual contact point lies outside that window, no shear can be transmitted to the liquid–liquid interface, and the upper film cannot be entrained.

The final coated thicknesses are selected by the maxima of these shear stresses. For the lower film of liquid 1,

$\mu_1$4

while for the upper film of liquid 2,

$\mu_1$5

The prefactors $\mu_1$6 and $\mu_1$7 are explicitly reported as best linear fits to the numerical solutions. The lower film is therefore selected in an LLD-like manner by peak wall shear, whereas the upper film is selected by peak interfacial shear transmitted across the liquid–liquid boundary.

The upper film exists only within finite “islands” in $\mu_1$8 parameter space. The lower bound on upper-layer thickness is

$\mu_1$9

while the upper bound obeys approximately

$\rho_1$0

Within these islands, the lower film thickness is weakly dependent on $\rho_1$1 and increases monotonically with $\rho_1$2, whereas the upper film thickness is non-monotonic in both $\rho_1$3 and $\rho_1$4 and decreases toward the island edges, where it may vanish (Champougny et al., 2020).

The analysis assumes Newtonian fluids, laminar Stokes/lubrication flow, perfect wetting of the plate by both liquids, isothermal conditions, negligible evaporation, and no Marangoni effects. The explored regime uses $\rho_1$5, $\rho_1$6, $\rho_1$7, $\rho_1$8, and $\rho_1$9, with $\mu_2$0 so inertia is negligible (Champougny et al., 2020). The reported upper-film thicknesses are typically in the $\mu_2$1–$\mu_2$2 range in rescaled units, corresponding to dimensional values of about $\mu_2$3–$\mu_2$4 nm for $\mu_2$5 and $\mu_2$6 mm; the paper notes that van der Waals disjoining pressure may become relevant near the edges of the existence islands.

3. Surfactant-stripping assembly of two-dimensional solids

A distinct LLID implementation was introduced for the production of thin films and van der Waals heterostructures from aqueous surfactant-stabilized suspensions of 2D solids (Smith et al., 2024). In this method, aqueous suspensions of few-layer graphene, MoS$\mu_2$7, WS$\mu_2$8, or MoSe$\mu_2$9, stabilized by Triton X-100 or Tween 20, are brought into contact with dichloromethane (DCM). After emulsification, sonication, and centrifugation, platelets migrate to the water/DCM interface. Because the surfactant has a high partition coefficient into DCM, its concentration in the aqueous phase near the interface decreases, the surfactant desorbs from the platelet surfaces, and the “bare” platelets assemble laterally at the interface to lower the interfacial energy (Smith et al., 2024).

The reported solvent/surfactant criteria are precise: the phases must be immiscible; the separation solvent must be denser than water; the surfactant must have a high partition coefficient into the separation solvent; and the separation solvent must permit subsequent surfactant removal for recycling. For Triton X-100 between DCM and water, the measured partition coefficient is

$\rho_2$0

Under centrifugation, thicker platelets can be driven through the interface into the DCM and precipitate to the bottom, so the interfacial film becomes enriched in monolayer-to-few-layer platelets. Film formation also occurs without centrifugation under gravity, but more slowly, over about $\rho_2$1 h (Smith et al., 2024).

The workflow uses high-shear exfoliation in ultrapure water, with shear mixing at $\rho_2$2–$\rho_2$3 rpm, corresponding to shear rates of $\rho_2$4–$\rho_2$5 kHz, followed by pre-centrifugation to remove thicker and larger platelets. The assembly step employs a $\rho_2$6 ml centrifuge tube with about $\rho_2$7 ml DCM and about $\rho_2$8 ml aqueous suspension, vortex mixing, sonication to recover a clear interface, and centrifugation for $\rho_2$9 min at $\Delta H$0 rpm, corresponding to $\Delta H$1 (Smith et al., 2024). The authors report that the aqueous phase above the interface becomes optically clear and spectroscopically indistinguishable from pure water.

Transfer to substrates is achieved primarily by dipping. The tube is tilted to about $\Delta H$2 relative to vertical, the substrate is inserted into the DCM without breaking the interfacial film, the tube is returned to vertical, and DCM is added continuously so that the water/DCM interface rises along the substrate and deposits the film. Repeated dipping increases thickness or enables sequential deposition of different materials to form van der Waals heterostructures (Smith et al., 2024).

The demonstrated substrates include glass microscope slides, SiO$\Delta H$3/Si wafers, copper foil, aluminum foil, and plastics. For transparent few-layer graphene films, the reported transmittance range is $\Delta H$4–$\Delta H$5, with conductivities between $\Delta H$6 and $\Delta H$7 depending on transmittance and annealing. Conductivity is derived from sheet resistance using

$\Delta H$8

with $\Delta H$9 estimated from $\gamma_{12}$0 absorption per graphene layer and an interlayer spacing of about $\gamma_{12}$1 nm (Smith et al., 2024). Annealing under argon at $\gamma_{12}$2–$\gamma_{12}$3C for $\gamma_{12}$4 h increases $\gamma_{12}$5, which the paper attributes to improved inter-platelet contacts and removal of residual moisture or incidental contaminants rather than to surfactant removal.

The transport behavior is described as percolative-like rather than thin-metallic. The non-universal percolation exponent $\gamma_{12}$6 increases from $\gamma_{12}$7 in as-deposited films to $\gamma_{12}$8 after $\gamma_{12}$9C annealing, approaching the universal 2D value of about $\gamma_{2g}$0. The percolative figure-of-merit $\gamma_{2g}$1 spans $\gamma_{2g}$2–$\gamma_{2g}$3 (Smith et al., 2024). Sequential dipping was used to fabricate an FLG–MoS$\gamma_{2g}$4–WS$\gamma_{2g}$5 trilayer van der Waals heterostructure, with Raman spectra showing the expected layer-specific signatures and no detectable surfactant or solvent residues.

4. Thermal-shock-driven crystallization on a transient interface

Another LLID regime arises when a liquid drop impacts a colder immiscible liquid film and crystals appear and grow on the newly created interface (Berry et al., 22 Aug 2025). The reported system uses a hexadecane drop impacting a thin film of $\gamma_{2g}$6 wt% NaCl brine. The drop diameter is $\gamma_{2g}$7 mm, the film thickness is $\gamma_{2g}$8 mm, corresponding to $\gamma_{2g}$9, and the impact velocity is set by the release height, giving approximately $Ca \equiv \frac{\mu_1 U}{\gamma_{12}},$0, $Ca \equiv \frac{\mu_1 U}{\gamma_{12}},$1, and $Ca \equiv \frac{\mu_1 U}{\gamma_{12}},$2. The drop is at $Ca \equiv \frac{\mu_1 U}{\gamma_{12}},$3C, the film temperature ranges from $Ca \equiv \frac{\mu_1 U}{\gamma_{12}},$4C down to $Ca \equiv \frac{\mu_1 U}{\gamma_{12}},$5C, and the melting temperature of hexadecane is $Ca \equiv \frac{\mu_1 U}{\gamma_{12}},$6C (Berry et al., 22 Aug 2025).

Upon impact, the drop forms a radially expanding crown over the thin film. Within about $Ca \equiv \frac{\mu_1 U}{\gamma_{12}},$7–$Ca \equiv \frac{\mu_1 U}{\gamma_{12}},$8 ms, discrete crystals nucleate at the oil–brine interface as optically visible clusters, then grow radially in-plane at a roughly constant velocity set by the thermal shock. A cooler bath produces earlier nucleation and faster growth but fewer crystals overall, because rapid crystal growth consumes the available interfacial area before many additional nuclei can appear (Berry et al., 22 Aug 2025). Surface coverage grows monotonically, while the number of crystals follows an S-shaped time dependence.

The model couples thermal kinetics to impact hydrodynamics. Crystal growth is taken to be reaction-controlled at small undercooling, with

$Ca \equiv \frac{\mu_1 U}{\gamma_{12}},$9

where the measured $$M=\frac{\mu_2}{\mu_1}, \qquad R=\frac{\rho_2}{\rho_1}, \qquad \Sigma=\frac{\gamma_{2g}}{\gamma_{12}}.$$0 is $$M=\frac{\mu_2}{\mu_1}, \qquad R=\frac{\rho_2}{\rho_1}, \qquad \Sigma=\frac{\gamma_{2g}}{\gamma_{12}}.$$1 from direct tracking, and the fit-based value is about $$M=\frac{\mu_2}{\mu_1}, \qquad R=\frac{\rho_2}{\rho_1}, \qquad \Sigma=\frac{\gamma_{2g}}{\gamma_{12}}.$$2 (Berry et al., 22 Aug 2025). Nucleation is represented as a constant-rate appearance per unit area with an Arrhenius form depending on contact temperature. The area of a crystal nucleated at time $$M=\frac{\mu_2}{\mu_1}, \qquad R=\frac{\rho_2}{\rho_1}, \qquad \Sigma=\frac{\gamma_{2g}}{\gamma_{12}}.$$3 is

$$M=\frac{\mu_2}{\mu_1}, \qquad R=\frac{\rho_2}{\rho_1}, \qquad \Sigma=\frac{\gamma_{2g}}{\gamma_{12}}.$$4

The available interfacial area during the opening stage is modeled as

$$M=\frac{\mu_2}{\mu_1}, \qquad R=\frac{\rho_2}{\rho_1}, \qquad \Sigma=\frac{\gamma_{2g}}{\gamma_{12}}.$$5

and both crystal number and crystal-covered area are written as integral balances over the unoccupied area. After normalization by $$M=\frac{\mu_2}{\mu_1}, \qquad R=\frac{\rho_2}{\rho_1}, \qquad \Sigma=\frac{\gamma_{2g}}{\gamma_{12}}.$$6 and $$M=\frac{\mu_2}{\mu_1}, \qquad R=\frac{\rho_2}{\rho_1}, \qquad \Sigma=\frac{\gamma_{2g}}{\gamma_{12}}.$$7, the dynamics collapse onto master curves governed by a single control parameter,

$$M=\frac{\mu_2}{\mu_1}, \qquad R=\frac{\rho_2}{\rho_1}, \qquad \Sigma=\frac{\gamma_{2g}}{\gamma_{12}}.$$8

which combines nucleation activity, crystal growth, and the hydrodynamic time available during interface expansion (Berry et al., 22 Aug 2025). Larger $$M=\frac{\mu_2}{\mu_1}, \qquad R=\frac{\rho_2}{\rho_1}, \qquad \Sigma=\frac{\gamma_{2g}}{\gamma_{12}}.$$9 yields faster coverage and lower final normalized crystal count.

The impact hydrodynamics are expressed through thin-film scaling. With $\mu_1$00, the maximum contact area and time to maximum area scale as

$\mu_1$01

so $\mu_1$02 and $\mu_1$03 in the experimental range (Berry et al., 22 Aug 2025). The reported Reynolds and Weber numbers are approximately $\mu_1$04–$\mu_1$05 and $\mu_1$06–$\mu_1$07, respectively.

The practical control window is explicit. For uniform film deposition, the reported conditions are large $\mu_1$08 of about $\mu_1$09–$\mu_1$10C and moderate-to-high $\mu_1$11 of about $\mu_1$12–$\mu_1$13, so that $\mu_1$14 is large and full coverage occurs during the opening phase. For discrete crystallites, the reported conditions are smaller $\mu_1$15 of about $\mu_1$16–$\mu_1$17C and lower $\mu_1$18 of about $\mu_1$19–$\mu_1$20 (Berry et al., 22 Aug 2025). The authors note several limitations: the thermal model assumes semi-infinite media and constant contact temperature; nucleation is treated as spatially uniform; crystal overlap is neglected; and the hydrodynamic model is restricted to the opening phase $\mu_1$21.

5. Evaporation-driven phase separation and lattice formation

A related interfacial route to deposition is provided by liquid-liquid phase separation in an evaporating sessile droplet of Pluronic F-127 in salt-containing buffer (Nasirimarekani, 2024). The directly studied interface is liquid–air rather than liquid–liquid, but the paper explicitly proposes translation to LLID at oil–water interfaces through the same ingredients: interfacial enrichment of amphiphile, salt-driven salting-out, and evaporation-induced concentration gradients. The experimental system uses $\mu_1$22L droplets of Pluronic F-127 at $\mu_1$23, $\mu_1$24, and $\mu_1$25 w/w in M2B buffer on PLL-g-PEG-treated glass, at $\mu_1$26C and $\mu_1$27 relative humidity (Nasirimarekani, 2024).

The observations are concentration-dependent. At $\mu_1$28, below the cited CMC of about $\mu_1$29 w/w, the deposit consists of discrete polymeric coacervates at the contact line, with a thin deposited layer around clusters and irregular spatial distribution. At $\mu_1$30, a continuous sheet-like polymer network forms with a regular lattice pattern, periodic voids of initially circular geometry, pronounced radial rips, and a transition region of finger-like structures preceding the lattice. At $\mu_1$31, the result is a more continuous sheet with radially aligned finger-like defects and fewer pronounced rips (Nasirimarekani, 2024). In salt-free Milli-Q water, the $\mu_1$32 and $\mu_1$33 solutions do not undergo LLPS and do not form regular lattices.

The mechanism is described as interfacial enrichment of the surfactant-like polymer combined with salt–polymer interactions that reduce polymer–water affinity and promote LLPS. Two flow regimes are observed: an early outward, capillary-driven flow feeding a coffee ring, followed by inward contraction once LLPS and pattern formation begin. The inward contact-line speed increases markedly when lattice formation starts, and droplets forming lattices at $\mu_1$34 evaporate faster than those forming clusters at $\mu_1$35, with an overall drying time ratio about $\mu_1$36 shorter for $\mu_1$37 than for $\mu_1$38 at similar size (Nasirimarekani, 2024).

Several equations are introduced explicitly as interpretive rather than directly fitted descriptors. The paper invokes the Péclet number,

$\mu_1$39

Laplace pressure,

$\mu_1$40

Marangoni stress,

$\mu_1$41

and a Flory–Huggins free-energy form,

$\mu_1$42

It also notes that a Cahn–Hilliard-type coarsening picture with $\mu_1$43, $\mu_1$44, may be relevant, although no coarsening exponents are measured (Nasirimarekani, 2024).

The translation to LLID is proposed rather than demonstrated. The paper states that in an oil–water system containing an aqueous Pluronic/salt phase, interfacial accumulation plus salting-out could nucleate microphase-separated lattices at the liquid–liquid boundary, followed by interfacial gelation and transfer. At the same time, important quantities remain unmeasured in the reported experiments: lattice constants, pattern symmetry, film thickness and roughness, interfacial tension, and systematic salt-valency dependence (Nasirimarekani, 2024). The study therefore establishes an LLID-relevant mechanism rather than a complete liquid–liquid process map.

6. Control parameters, misconceptions, and unresolved issues

Across current LLID-related literature, the control variables are modality-specific but conceptually aligned. In two-liquid dip-coating, the decisive parameters are the capillary number $\mu_1$45, viscosity ratio $\mu_1$46, density ratio $\mu_1$47, surface-tension ratio $\mu_1$48, and floating-layer thickness $\mu_1$49; the operational window for upper-film entrainment is restricted to existence islands and to the $\mu_1$50 rescaled shear-transmission zone near the virtual contact point (Champougny et al., 2020). In surfactant-stripping deposition of 2D solids, the decisive requirements are immiscibility, an organic phase denser than water, strong surfactant partitioning into the organic phase, and sufficient platelet number density to cover the interface continuously (Smith et al., 2024). In impact-triggered crystallization, the principal levers are thermal shock $\mu_1$51 and impact velocity $\mu_1$52, which together determine $\mu_1$53, the competition between nucleation, growth, and expanding area (Berry et al., 22 Aug 2025). In evaporation-driven patterning, polymer concentration relative to the CMC, salt presence, humidity, and contact-line mobility govern whether the outcome is cluster formation, lattice formation, or a more continuous sheet (Nasirimarekani, 2024).

A common misconception is that a liquid–liquid interface is intrinsically passive or merely a transfer medium. The cited work shows the opposite. In bilayer dip-coating, local maxima of wall and interfacial shear set the final coated thicknesses (Champougny et al., 2020). In 2D-material deposition, surfactant partitioning into DCM drives in situ colloidal destabilization and interfacial assembly (Smith et al., 2024). In impact crystallization, interface mobility and thermal shock jointly determine whether the surface is covered by many small crystallites or by fewer larger crystals (Berry et al., 22 Aug 2025). In evaporation-driven LLPS, the interfacial region selects a regular lattice only within a narrow concentration and salt regime (Nasirimarekani, 2024).

A second misconception is that the “defect-free” character of liquid–liquid interfaces guarantees uniform deposition. The evidence is more limited. Two-liquid dip-coating exhibits finite existence islands, vanishing upper-film thickness at island edges, and possible disjoining-pressure effects for ultra-thin upper films (Champougny et al., 2020). Impact-triggered deposition can produce rapid full coverage, but the authors explicitly note that the minimal model neglects overlap, local thermal and solute gradients, and post-opening dynamics (Berry et al., 22 Aug 2025). Evaporation-driven sheet formation can generate radial rips and finger-like defects, and the film is described as delicate rather than mechanically resolved (Nasirimarekani, 2024). In 2D-material LID, discontinuities can arise when suspension concentration is too low, and successful transfer requires avoiding rupture of the interfacial film during insertion (Smith et al., 2024).

Several unresolved issues recur. Surfactants and contaminants alter $\mu_1$54, $\mu_1$55, spreading behavior, and stress transmission in dip-coating (Champougny et al., 2020); the same class of effects would plausibly perturb surfactant-stripping assembly and thermal-shock crystallization. Partial wetting and spreading constraints remain important for any LLID implementation that depends on floating-layer stability (Champougny et al., 2020). The impact-driven crystallization model assumes semi-infinite media and a thin-film opening law, so thicker baths, strong Marangoni flows, or very large $\mu_1$56 would require modification (Berry et al., 22 Aug 2025). The evaporation-driven LLPS study identifies the key role of salt but does not map lattice constant, film mechanics, or transfer protocols (Nasirimarekani, 2024). The 2D-material method demonstrates macroscopic films and heterostructures, but device-level transport or optoelectronic measurements on the van der Waals stacks are not reported (Smith et al., 2024).

Taken together, these studies indicate that LLID is a technically broad but physically coherent domain: material is deposited because an immiscible-liquid interface localizes an instability, a partitioning process, or a stress balance that does not exist in the same way on a rigid substrate. The resulting films range from nanometric bilayers and transparent graphene conductors to transient crystal carpets and regular polymeric lattices, but in each case the decisive event is interfacial selection rather than bulk deposition.