Liquid-Assisted Rolling Mechanisms

• Liquid-assisted rolling is a spectrum of phenomena where a liquid phase modulates rolling through lubrication, capillarity, chemo-mechanical effects, and altered contact mechanics.
• The topic covers diverse applications, from motile vesicle design and self-cleaning surfaces to electrospun yarn consolidation and soft robotic actuation.
• Quantitative studies employ metrics like rolling parameters, isoperimetric quotients, and friction coefficients to elucidate transitions between sliding, rolling, and jamming.

Searching arXiv for the cited papers and closely related work on rolling in wet or liquid-mediated systems. Liquid-assisted rolling can be understood as an umbrella description for rolling phenomena in which a liquid phase, a thin liquid film, solvent uptake and evaporation, capillary bridges, or liquid-mediated contact laws determine the onset, kinematics, stability, or material consequences of rolling. In the recent literature, this umbrella spans motile vesicles that exploit lubrication forces to roll on substrates, soft elastomeric cylinders that roll through asymmetric swelling and deswelling, electrospun yarns densified by wet rolling and drying, and dense suspensions in which resistance to gear-like rolling shifts discontinuous shear thickening and shear jamming (Magrinya et al., 2024, Mondal et al., 2015, Mandal et al., 28 Sep 2025, Singh et al., 2020).

1. Mechanistic classes of liquid-assisted rolling

The principal mechanisms reported in the literature are distinct. In lubrication-dominated systems, thin liquid films between moving bodies and nearby boundaries generate the hydrodynamic coupling needed for rolling or rolling-like translation. Synthetic vesicles with an encapsulated rotating particle are designed specifically so that lubrication forces drive vesicle rolling, while colloidal “surface rollers” translate parallel to a wall because the boundary couples externally imposed rotation to translation (Magrinya et al., 2024, Chamolly et al., 2020).

A second class is capillarity-driven or wetting-mediated rolling. In electrospun yarns, brief wetting followed by rolling and controlled drying generates meniscus forces that compact loosely packed nanofiber assemblies into tightly bound bundles; dry rolling controls show negligible change, indicating that capillarity-driven consolidation dominates over mechanical pressing (Mandal et al., 28 Sep 2025). In wet granular beds, capillary bridges introduce cohesion that changes the rolling and cascading regimes by narrowing the fast flowing layer, broadening the creeping region, and increasing the dynamic angle of repose (Jarray et al., 2018).

A third class is solvent-driven chemo-mechanical rolling. Soft PDMS cylinders roll when a small quantity of solvent produces localized swelling on one side and evaporation from exposed regions. The resulting asymmetric swelling gradient bends the cylinder, shifts its center of mass, and generates a torque through the substrate contact; rolling begins only above a threshold curvature (Mondal et al., 2015). Closely related experiments show that the same mechanism can drive uphill motion and the transport of dead loads significantly larger than the cylinder’s own weight (Hore et al., 2015).

A fourth class concerns liquid-modified contact mechanics. In dense suspensions and pore-scale particle-laden flows, rolling resistance is treated as a contact-level constraint or coefficient that lumps particle rigidity, particle shape, lubrication, and fluid-mediated resistance. In this setting, the liquid phase does not simply reduce friction; it also enters the constitutive description of rolling resistance, jamming, bridge stability, and clogging (Singh et al., 2020, Nayak et al., 16 Jan 2026).

2. Lubrication-mediated rolling at interfaces

In active vesicles, the canonical system consists of PEG-PLA vesicles of radius $R_v = 10 - 40$ $\mu$m encapsulating a ferromagnetic particle of radius $R_p = 4$ $\mu$m. An external rotating magnetic field at $1$–$10$ Hz drives the internal particle around the vesicle equator, generating confined rotational flows. The rolling dynamics are then governed by membrane mechanics and membrane–substrate tribology rather than by dry contact alone. Two regimes are reported: at low rotation rates, membrane tethers have time to interact and “stick,” yielding nearly perfect rolling with $\xi_v \approx 1$; at higher rates, tethers align under shear and a thin fluid layer dominates friction, yielding mostly sliding with $\xi_v \ll 1$. The transition matches a rheological crossover of the PEG-PLA membrane and is reported to be independent of substrate chemistry, implicating intrinsic membrane mechanics as dominant (Magrinya et al., 2024).

Externally actuated colloidal rollers near a rigid boundary exhibit a related but analytically distinct mechanism. The wall breaks the symmetry of the Stokes flow, so an imposed rotation produces translation parallel to the surface. In the comoving frame, the roller generates a local vortex of closed streamlines. Cargo trapping occurs not by reversible advection alone, but through time-irreversible interactions between finite-size cargo and the wall: if the cargo cannot pass through the bottleneck beneath the roller, steric interaction forces it across the separatrix into the vortex. Thin, disc-like rollers are predicted to provide the most favorable trapping conditions, whereas spherical rollers do not trap cargo (Chamolly et al., 2020).

For droplets on inclined substrates, rolling is not identified from raw vorticity alone. A diffuse-interface study decomposes the internal velocity gradient into strain, shear, and residual rigid-body rotation, and defines a rolling percentage $\%R$. For fixed viscosity ratio and slip length, $\%R$ is reported to depend only on the drop shape through the isoperimetric quotient $\mu$0. More circular drops roll more; highly non-circular drops slide more; and for small $\mu$1, the scaling $\mu$2 is reported. High viscosity contrast also increases the rolling fraction, whereas larger slip length increases speed but decreases the rolling fraction (Thampi et al., 2011).

Internal liquid can also alter rolling dynamics even when the rolling body is macroscopically solid. For a fluid-filled hollow cylindrical shell rolling on an incline, an analytical treatment based on Duhamel’s theorem yields the unsteady internal velocity field and the shell motion. The long-time state is not a terminal velocity but a constant acceleration, and that acceleration depends only on the shell-to-fluid mass ratio, not on the fluid viscosity. Stability analysis in a frozen-time framework predicts instability to long wavelength axial waves, with a critical Reynolds number based on shell angular velocity at neutral stability of approximately $\mu$3, corresponding to a Taylor number of approximately $\mu$4 (Supekar et al., 2014).

3. Capillary and solvent-driven rolling of solids and fiber assemblies

In solvent-actuated elastomeric rolling, the characteristic physical sequence is localized solvent uptake, asymmetric swelling, evaporation-driven deswelling, bending, and then rolling. One formulation emphasizes that the solvent spreads along the cylinder length but does not completely immerse it, so the swelling is shallow relative to the cylinder diameter. The curvature $\mu$5 increases after solvent addition, reaches a maximum, decreases slightly as rolling starts, and then plateaus while rolling continues. Rolling initiates only above a threshold curvature $\mu$6, and the threshold scales as $\mu$7. The rolling velocity increases linearly with curvature and with substrate or ambient temperature, but locomotion ceases below the threshold curvature (Mondal et al., 2015).

A companion study extends the same mechanism to incline climbing and load carrying. Small quantities of solvents such as chloroform, toluene, hexane, and heptane generate a persistent swelling zone at the rear of a PDMS cylinder, with evaporation from the exposed part sustaining the asymmetry. The driving torque is strong enough that the cylinder can roll up an inclined plane within a range of inclination, and its velocity can even increase over that range. The cylinder can also drag a dead weight approximately $\mu$8–$\mu$9 times its own weight. A scaling relation for the rolling velocity is reported as

$R_p = 4$0

so the velocity increases with cylinder diameter, modulus, and solvent vapor pressure, and decreases with solvent surface tension and density (Hore et al., 2015).

Liquid-assisted rolling in electrospun yarns is mechanically different but still capillarity-driven. PAN nanofiber yarns are placed on PTFE-lined glass, wetted with either deionized water or ethanol, stroked perpendicularly to distribute the liquid and remove excess, then rolled parallel to the yarn axis with intermittent $R_p = 4$1 rotations to maintain circularity, and finally dried in a vacuum desiccator for $R_p = 4$2 hours; some samples are annealed at $R_p = 4$3 for $R_p = 4$4 hours after drying. The central result is that wet rolling yields large gains in tensile strength and modulus, whereas dry rolling yields negligible changes compared with as-spun yarns. Water consistently outperforms ethanol because its elastocapillary driving term on PAN is larger, and heat treatment further increases stiffness at the expense of ductility. Quantitatively, alignment rises from approximately $R_p = 4$5 in as-spun yarns to $R_p = 4$6 in water plus heat-treated yarns, water-rolled and heat-treated yarns show up to $R_p = 4$7 increase in peak load versus as-spun, and for yarn diameters below $R_p = 4$8 $R_p = 4$9m the modulus and strength approach single-nanofiber limits of $\mu$0 GPa and $\mu$1 MPa (Mandal et al., 28 Sep 2025).

4. Liquid-modified friction, jamming, and rolling resistance

Dense suspensions provide a prominent counterexample to the common intuition that a liquid environment mainly lubricates away contact constraints. Particle-based simulations of non-Brownian suspensions under shear show that adding rolling friction, in addition to sliding friction, lowers the volume fraction required for discontinuous shear thickening and shear jamming. The reported jamming points shift from $\mu$2 for frictionless contacts to $\mu$3 with sliding friction only and to $\mu$4 when both sliding and rolling friction are large. Rolling friction also generates thicker, more robust, and more anisotropic force chains, increases the velocity correlation length, and is associated with a more elastic-like response, including positive normal stress differences $\mu$5 (Singh et al., 2020).

At the pore scale, direct numerical simulations with DEM-IBM coupling treat the coefficient of rolling friction $\mu$6 as a lumped parameter for particle rigidity, particle shape, lubrication, and fluid-mediated resistance. The reported trend is monotonic: at $\mu$7, bridges are rare and typically unstable; as $\mu$8 increases to $\mu$9, bridges form more frequently, remain stable for longer periods, and produce more pronounced pressure build-up behind the clog. Increased rolling friction suppresses the ability of particles to roll off each other or around walls, stabilizing chains at the pore throat and reducing the mean number of particles that pass before clogging (Nayak et al., 16 Jan 2026).

In rotating drums, wet granular assemblies show an additional liquid-assisted modification of rolling behavior through capillary cohesion. Liquid-induced cohesion decreases the width of the flowing region and the particle velocity at the free surface, while increasing the width of the creeping region and the dynamic angle of repose. It also reduces the local granular temperature, indicating more coherent cluster motion and fewer random collisions. By chemically silanizing glass beads, the contact angle is increased and the capillary force reduced, and the flow reverts toward dry-like behavior (Jarray et al., 2018).

Liquid marbles demonstrate a different interfacial limit. Their granular shell prevents capillary adhesion to the substrate, making them highly mobile, but the shell also resists rolling until it yields. The departing angle $1$0 increases exponentially with grain surface fraction $1$1, with a reported fit $1$2 and $1$3. Measured values range from $1$4 at $1$5 to $1$6 at $1$7. The shell is modeled with a Mohr-Coulomb criterion $1$8, with an effective friction coefficient of $1$9, and the pressure function follows a logistic dependence on surface coverage (Takai et al., 25 Jun 2025).

5. Quantitative descriptors and constitutive frameworks

Several quantitative descriptors recur across the literature. For vesicles and particles, a rolling parameter compares translational speed with the speed of perfect rolling: $10$0 A free rotating particle near a solid substrate has a low rolling parameter, $10$1, indicating mostly slip rather than rolling, whereas low-frequency vesicle motion can approach $10$2 (Magrinya et al., 2024).

For droplets, the distinction between rolling and sliding is formalized by residual vorticity,

$10$3

with the rolling velocity extracted from the average residual vorticity. The resulting rolling fraction collapses onto a universal curve when plotted against the isoperimetric quotient $10$4 for fixed viscosity ratio and slip length (Thampi et al., 2011).

Capillary consolidation in fiber assemblies is described with the elastocapillary driving term $10$5 and the elastocapillary number

$10$6

For PAN yarns, water gives $10$7 mN/m, while ethanol gives $10$8 mN/m, consistent with stronger capillary compaction for water. Structure–property relations are then captured by a regression of the form

$10$9

where alignment and packing density are independent, synergistic predictors of peak load, with an adjusted $\xi_v \approx 1$0 for the combined model (Mandal et al., 28 Sep 2025).

Wet granular flow control is framed through the granular Weber number

$\xi_v \approx 1$1

and the dynamic angle of repose is collapsed onto logarithmic functions of $\xi_v \approx 1$2, including

$\xi_v \approx 1$3

In dense suspensions, by contrast, the relevant diagnostics are the frictional jamming point and the non-affine velocity correlation function

$\xi_v \approx 1$4

with rolling friction increasing the correlation length $\xi_v \approx 1$5 and thereby contributing to the viscosity increase (Jarray et al., 2018, Singh et al., 2020).

6. Applications, design principles, and recurring misconceptions

The application space is correspondingly broad. Lubrication-driven vesicle rolling provides design principles for motile vesicles intended to navigate complex environments and is directly relevant to cell biomechanics and microrobotics (Magrinya et al., 2024). Hydrodynamic surface rollers provide a route to size-selective cargo trapping and transport analogous to deterministic lateral displacement (Chamolly et al., 2020). Droplet rolling criteria support rational design of self-cleaning hydrophobic surfaces when rolling is desirable and of sprays or coatings when rolling must be suppressed (Thampi et al., 2011).

Capillarity-driven wet rolling is a processing method rather than a locomotion mechanism in electrospun yarns, but it establishes a practical route for improving mechanical performance without twisting. Because water-based treatment is reported to be operationally straightforward and environmentally benign, the method is positioned for composites, technical textiles, and biomedical scaffolds (Mandal et al., 28 Sep 2025). Solvent-driven elastomeric rolling has obvious implications for soft robotics and micro-actuation, especially because the cylinders can climb inclines and transport dead loads (Hore et al., 2015, Mondal et al., 2015).

Two recurring misconceptions are explicitly contradicted by the cited work. First, rolling in a wet environment is not equivalent to frictionless motion. Liquid marbles exhibit static friction because their granular shell must yield before rolling begins, and wet granular beds can become more cohesive and less agitated as capillary forces increase (Takai et al., 25 Jun 2025, Jarray et al., 2018). Second, lubrication does not eliminate the need to model rolling resistance. In dense suspensions, sliding-only models fail to account for discontinuous shear thickening at low volume fractions, while in pore-scale clogging the effective rolling-friction coefficient governs whether bridges are rare and unstable or frequent and persistent (Singh et al., 2020, Nayak et al., 16 Jan 2026).

Taken together, these studies indicate that liquid-assisted rolling is not a single mechanism but a family of interfacial and bulk phenomena linked by a common structural fact: a liquid phase alters the translation–rotation balance, the accessible contact modes, or the energy pathway by which rolling is initiated and sustained. A plausible implication is that future unification will depend less on a universal equation of motion than on a shared constitutive language for lubrication, capillarity, adhesion, and rolling resistance across scales.