Plateau-Rayleigh instability in a soft viscoelastic material

Plateau-Rayleigh instability of a soft layer coated on a rigid cylinder

We study the Plateau-Rayleigh instability of a soft viscoelastic solid layer coated on a rigid cylinder i.e., a soft fibre with a rigid core. The onset of instability is examined using a linear stability analysis. We find that increasing the rigid cylinder radius or the stiffness of the layer reduces the growth rate of the fastest growing mode. For each rigid cylinder radius, a critical elastocapillary number is found below which all wavelengths of disturbances are stable. The critical value for a soft fibre with a thick rigid cylindrical core can be several orders of magnitudes larger than that for a totally soft fibre (no rigid core). This highlights the strong stabilizing effect of the rigid core on the system. Increasing the relaxation timescale of the viscoelastic material also slows down the growth of disturbances, but has no effect on the critical elastocapillary number. Interestingly, the wavelength of the fastest growing mode is independent of the rigid cylinder radius for the purely elastic case.

Thermally-modulated shape transition at the interface of soft gel filament and hydrophobic substrate

A liquid filament may pinch off into different shapes on interacting with a soft surface, as modulated by the interplay of inertial, capillary, and viscous forces. While similar shape transitions may intuitively be realized for more complex materials such as soft gel filaments as well, their intricate controllability towards deriving precise and stable morphological features remains challenging, as attributed to the complexities stemming from the underlying interfacial interactions over the relevant length and time scales during the sol-gel transition process. Circumventing these deficits in the reported literature, here we report a new means of precisely-controlled fabrication of gel microbeads via exploiting thermally-modulated instabilities of a soft filament atop a hydrophobic substrate. Our experiments reveal that abrupt morphological transitions of the gel material set in at a threshold temperature, resulting in spontaneous capillary thinning and filament breakup. We show that this phenomenon may be precisely modulated by an alteration in the hydration state of the gel material that may be preferentially dictated by its intrinsic glycerol content. Our results demonstrate that the consequent morphological transitions give rise to topologically-selective microbeads as an exclusive signature of the interfacial interactions of the gel material with the deformable hydrophobic interface underneath. Thus, intricate control may be imposed on the spatio-temporal evolution of the deforming gel, facilitating the inception of highly ordered structures of specific shapes and dimensionalities on demand. This is likely to advance the strategies of long shelf-life analytical biomaterial encapsulations via realizing one-step physical immobilization of bio-analytes on the bead surfaces as a new route to controlled materials processing, without demanding any resourced microfabrication facility or delicate consumable materials.

Oscillations of a soft viscoelastic drop

A soft viscoelastic drop has dynamics governed by the balance between surface tension, viscosity, and elasticity, with the material rheology often being frequency dependent, which are utilized in bioprinting technologies for tissue engineering and drop-deposition processes for splash suppression. We study the free and forced oscillations of a soft viscoelastic drop deriving (1) the dispersion relationship for free oscillations, and (2) the frequency response for forced oscillations, of a soft material with arbitrary rheology. We then restrict our analysis to the classical cases of a Kelvin-Voigt and Maxwell model, which are relevant to soft gels and polymer fluids, respectively. We compute the complex frequencies, which are characterized by an oscillation frequency and decay rate, as they depend upon the dimensionless elastocapillary and Deborah numbers and map the boundary between regions of underdamped and overdamped motions. We conclude by illustrating how our theoretical predictions for the frequency-response diagram could be used in conjunction with drop-oscillation experiments as a "drop vibration rheometer", suggesting future experiments using either ultrasonic levitation or a microgravity environment.

Model of spontaneous droplet transport on a soft viscoelastic substrate with nonuniform thickness

Dynamic wetting of droplets on soft solids has many industrial and biological applications which require an understanding of the underlying fluid transport mechanism. Here we study the case of a droplet on a viscoelastic substrate of variable thickness which is known to give rise to a spontaneous droplet transport. This phenomenon is known as droplet durotaxis and has been observed experimentally. Here we develop a model assuming a small linear gradient in substrate thickness to reveal the physical mechanism behind this transport phenomena. We show the variable thickness causes an asymmetric deformation along the drop contact line, which causes a variation in the contact angle. This generates a net driving force on the drop, causing it to move in the direction of higher thickness. The resulting drop velocity is determined by balancing the work done by the moving drop with the viscoelastic dissipation of the substrate (viscoelastic braking) and computed from a self-consistent model. We find our results to be in qualitative agreement to previously reported experimental findings.