We analyse the effect of surface viscoelasticity on the temporal stability of a free cylindrical liquid jet coated with insoluble surfactant, extending the results of Timmermans & Lister (2002). Our development requires, in particular, deriving the correct expressions for the normal and tangential stress boundary conditions at a general axisymmetric interface when surface viscosity is modelled with the Boussinesq-Scriven constitutive equation. These stress conditions are applied to obtain a new dispersion relation for the liquid thread, which is solved to describe its temporal stability as a function of four governing parameters, namely the capillary Reynolds number, the elasticity parameter, and the shear and dilatational Boussinesq numbers. It is shown that both surface viscosities have a stabilising influence for all values of the capillary Reynolds number and elasticity parameter, the effect being more pronounced at low capillary Reynolds numbers. The wavenumber of maximum amplification depends non-monotonically on the Boussinesq numbers, especially for very viscous threads at low values of the elasticity parameter. Finally, two different lubrication approximations of the equations of motion are derived. While the validity of the leading-order model is limited to small enough values of the elasticity parameter and of the Boussinesq numbers, a higher-order parabolic model is able to accurately capture the linearised behaviour for the whole range of values of the four control parameters.

We report a numerical analysis of the unforced break-up of free cylindrical threads of viscous Newtonian liquid whose interface is coated with insoluble surfactants, focusing on the formation of satellite droplets. The initial conditions are harmonic disturbances of the cylindrical shape with a small amplitude , and whose wavelength is the most unstable one deduced from linear stability theory. We demonstrate that, in the limit → 0, the problem depends on two dimensionless parameters, namely the Laplace number, La = ρσ 0R /µ 2 , and the elasticity parameter, β = E/σ 0 , where ρ, µ and σ 0 are the liquid density, viscosity and initial surface tension, respectively, E is the Gibbs elasticity andR is the unperturbed thread radius. A parametric study is presented to quantify the influence of La and β on two key quantities: the satellite droplet volume and the mass of surfactant trapped at the satellite's surface just prior to pinch-off, V sat and Σ sat , respectively. We identify a weak-elasticity regime, β 0.05, in which the satellite volume and the associated mass of surfactant obey the scaling law V sat = Σ sat = 0.0042La 1.64 for La 2. For La 10, V sat and Σ sat reach a plateau of about 3% and 2.9% respectively, V sat being in close agreement with previous experiments of low-viscosity threads with clean interfaces. For La < 7.5, we reveal the existence of a discontinuous transition in V sat and Σ sat at a critical elasticity, β c (La), with β c → 0.98 for La 0.2, such that V sat and Σ sat abruptly increase at β = β c for increasing β. The jumps experienced by both quantities reach a plateau when La 0.2, while they decrease monotonically as La increases up to La = 7.5, where both become zero.

Microfluidic systems are usually fabricated with soft materials that deform due to the fluid stresses. Recent experimental and theoretical studies on the steady flow in shallow deformable microchannels have shown that the flow rate is a nonlinear function of the pressure drop due to the deformation of the upper soft wall. Here, we extend the steady theory of Christov et al. (2018) by considering the start-up flow from rest, both in pressure-controlled and in flow-rate-controlled configurations. The characteristic scales and relevant parameters governing the transient flow are first identified, followed by the development of an unsteady lubrication theory assuming that the inertia of the fluid is negligible, and that the upper wall can be modeled as an elastic plate under pure bending satisfying the Kirchhoff-Love equation. The model is governed by two non-geometrical dimensionless numbers: a compliance parameter β, which compares the characteristic displacement of the upper wall with the undeformed channel height, and a parameter γ that compares the inertia of the solid with its flexural rigidity. In the limit of negligible solid inertia, γ → 0, a quasi-steady model is developed, whereby the fluid pressure satisfies a nonlinear diffusion equation, with β as the only parameter, which admits a self-similar solution under pressure-controlled conditions. This simplified lubrication description is validated with coupled three-dimensional numerical simulations of the Navier equations for the elastic solid and the Navier-Stokes equations for the fluid. The agreement is very good when the hypotheses behind the model are satisfied. Unexpectedly, we find fair agreement even in cases where the solid and liquid inertia cannot be neglected.

The structure of the flow induced by the van der Waals destabilization of a non-wetting liquid film placed on a solid substrate is unraveled by means of theory and numerical simulations of the Stokes equations. Our analysis reveals that lubrication theory, which yields h min ∝ τ 1/5 where h min is the minimum film thickness and τ is the time until breakup, cannot be used to describe the local flow close to rupture. Instead, the slender lubrication solution is shown to experience a crossover to a universal self-similar solution of the Stokes equations that yields h min ∝ τ 1/3 , with an opening angle of 37 • off the solid.A non-wetting liquid film placed on a solid substrate becomes unstable to infinitesimal surface waves when its thickness becomes smaller than about 100 nm, leading to a spinodal dewetting pathway coexistent with hole nucleation [1][2][3][4][5][6][7][8][9]. Spontaneous growth of perturbations takes place when the destabilizing van der Waals (vdW) forces exceed the stabilizing surface tension force, provided that the disturbance wavenumber is below a certain cut-off [10][11][12]. Previous theoretical efforts to describe the nonlinear dynamics leading to film rupture were based on lubrication theory [9,13,14], which assumes that the longitudinal length scale is much larger than the film thickness, and provides models with simpler mathematical structure than the Navier-Stokes equations.

Little is known about mechanisms of membrane fission in bacteria despite their requirement for cytokinesis. The only known dedicated membrane fission machinery in bacteria, FisB, is expressed during sporulation in Bacillus subtilis and is required to release the developing spore into the mother cell cytoplasm. Here we characterized the requirements for FisB-mediated membrane fission. FisB forms mobile clusters of ~12 molecules that give way to an immobile cluster at the engulfment pole containing ~40 proteins at the time of membrane fission. Function mutants revealed that binding to acidic lipids and homo-oligomerization are both critical for targeting FisB to the engulfment pole and membrane fission. Our results suggest that FisB is a robust and unusual membrane fission protein that relies on homo-oligomerization, lipid-binding and likely the unique membrane topology generated during engulfment for localization and membrane scission, but surprisingly, not on lipid microdomains or negative-curvature lipids.

The ability of many living systems to actively self-propel underlies critical biomedical, environmental, and industrial processes. While such active transport is well-studied in uniform settings, environmental complexities such as geometric constraints, mechanical cues, and external stimuli such as chemical gradients and fluid flow can strongly influence transport. In this chapter, we describe recent progress in the study of active transport in such complex environments, focusing on two prominent biological systems-bacteria and eukaryotic cells-as archetypes of active matter. We review research findings highlighting how environmental factors can fundamentally alter cellular motility, hindering or promoting active transport in unexpected ways, and giving rise to fascinating behaviors such as directed migration and large-scale clustering. In parallel, we describe specific open questions and promising avenues for future research. Furthermore, given the diverse forms of active matterranging from enzymes and driven biopolymer assemblies, to microorganisms and synthetic microswimmers, to larger animals and even robots-we also describe connections to other active systems as well as more general theoretical/computational models of transport processes in complex environments. * Preprint of a chapter in the book Out-of-Equilibrium Soft Matter: Active Fluids, to be published by the Royal Society of Chemistry.

How do growing bacterial colonies get their shapes? While colony morphogenesis is well studied in two dimensions, many bacteria grow as large colonies in three-dimensional (3D) environments, such as gels and tissues in the body or subsurface soils and sediments. Here, we describe the morphodynamics of large colonies of bacteria growing in three dimensions. Using experiments in transparent 3D granular hydrogel matrices, we show that dense colonies of four different species of bacteria generically become morphologically unstable and roughen as they consume nutrients and grow beyond a critical size—eventually adopting a characteristic branched, broccoli-like morphology independent of variations in the cell type and environmental conditions. This behavior reflects a key difference between two-dimensional (2D) and 3D colonies; while a 2D colony may access the nutrients needed for growth from the third dimension, a 3D colony inevitably becomes nutrient limited in its interior, driving a transition to unstable growth at its surface. We elucidate the onset of the instability using linear stability analysis and numerical simulations of a continuum model that treats the colony as an “active fluid” whose dynamics are driven by nutrient-dependent cellular growth. We find that when all dimensions of the colony substantially exceed the nutrient penetration length, nutrient-limited growth drives a 3D morphological instability that recapitulates essential features of the experimental observations. Our work thus provides a framework to predict and control the organization of growing colonies—as well as other forms of growing active matter, such as tumors and engineered living materials—in 3D environments.

Theory and numerical simulations of the thinning of liquid threads at high superficial concentration of surfactants suggest the existence of an asymptotic regime where surface tension balances surface viscous stresses, leading to an exponential thinning with an e-fold time FðΘÞð3μ s þ κ s Þ=σ, where μ s and κ s are the surface shear and dilatational viscosity coefficients, σ is the interfacial tension, Θ ¼ κ s =μ s , and FðΘÞ is a universal function. The potential use of this phenomenon to measure the surface viscosity coefficients is discussed.