Fluid deformable surfaces

Abstract

Lipid membranes are examples of fluid deformable surfaces, which can be viewed as two-dimensional viscous fluids with bending elasticity. With this solid–fluid duality any shape change contributes to tangential flow and vice versa any tangential flow on a curved surface induces shape deformations. This tight coupling between shape and flow makes curvature a natural element of the governing equations. The modelling and numerical tools outlined in Torres-Sánchez et al. (J. Fluid Mech., vol. 872, 2019, pp. 218–271) open a new field of study by enabling the exploration of the role of curvature in this context.

Axisymmetric flows on the torus geometry

“…In recent years there has been a growing interest in studying and understanding hydrodynamic flows on curved surfaces, supported by increasing evidence for their relevance in a wide range of problems in nature and engineering. Examples include phenomena in materials science, such as the motion of electrons in graphene (Giordanelli, Mendoza & Herrmann 2018), interface rheology in foams (Cox, Weaire & Glazier 2004) and the dynamics of confined active matter (Keber et al 2014; Janssen, Kaiser & Löwen 2017; Henkes, Marchetti & Sknepnek 2018; Pearce et al 2019); in biophysics, such as flows on curved biomembranes (Arroyo & Desimone 2009; Henle & Levine 2010; Al-Izzi, Sens & Turner 2018; Fonda et al 2018) or fluid deformable surfaces (Torres-Sánchez, Millán & Arroyo 2019; Voigt 2019); in fusion technology, such as plasma motion under toroidal confinement (Boozer 2005); and in geophysics, such as zonal flows on planets and the Sun (Sasaki, Takehiro & Yamada 2015).…”

Evolution dynamics of thin liquid structures investigated using a phase-field model

“…Droplets of various shapes either floating in a surrounding fluid or sitting on a solid substrate are ubiquitous in life science from the subcellular to the tissue scale, where cell organelle, cells, tissues, and membranes are shaped to execute specific functions. 1 A comprehensive understanding of the dynamic interactions of liquid–fluid and liquid–solid is of fundamental importance for exploring the rich phenomena appearing in the life science and colloidal systems. The precise control of droplet production, droplet shaping, droplet dynamics, and bubble dynamics is critical in applications such as inkjet printing, drug delivery, drag reduction, microfluidics, and lab-on-a-chip systems, among others.…”

Stability of rotating equilibrium states of fluid deformable surfaces

“…Such surfaces play an essential role in biology, see for example, refs. [1][2][3][4]. The mathematical description of fluid deformable surfaces has been introduced in refs.…”