The translational and rotational drag on a cylinder moving in a membrane

Abstract

The translational and rotational drag coefficients for a cylinder undergoing uniform translational and rotational motion in a model lipid bilayer membrane is calculated from the appropriate linearized Navier–Stokes equations. The calculation serves as a model for the lateral and rotational diffusion of membrane-bound particles and can be used to infer the ‘microviscosity’ of the membrane from the measured diffusion coefficients. The drag coefficients are obtained exactly using dual integral equation techniques. The region of validity of an earlier asymptotic solution obtained by Saffman (1976) is elucidated.

Toward Hydrodynamics with Solvent Free Lipid Models: STRD Martini

“…To achieve this last point, a modeling approach must account properly for the hydrodynamics of the solvent adjacent to the membrane. This is clear from continuum arguments originally proposed by Saffman and Delbruck (13), and later extended by Hughes, Palinthorpe, and White (14).…”

“…Saffman-Delbruck (SD) theory (13,14) (referred to in the following as SDHPW to acknowledge the extension by Hughes, Palinthorpe, and White) predicts that the mobility of a membrane-spanning cylinder increases logarithmically with the ratio of the SD length to the radius of the cylinder. The SD length, in turn, is the ratio of the surface viscosity of the membrane to the shear viscosity of the solvent in the bulk.…”

Surface viscosity and Marangoni stresses at surfactant laden interfaces

“…Because a bilayer membrane is densely packed it is very nearly incompressible and hence variations in surfactant concentration are reasonably ignored; additionally, several authors have argued that Langmuir monolayers can be effectively incompressible even in the liquid expanded state Barentin et al (2000), Fischer (2004a), Sickert, Rondelez & Stone (2007). Many other works have extended the mathematical description of probes translating within viscous, incompressible interfaces (Hughes, Pailthorpe & White 1981;Evans & Sackmann 1988;Lubensky & Goldstein 1996;Stone & Ajdari 1998;Levine & MacKintosh 2002;Fischer 2004b;Camley et al 2010;Shlomovitz et al 2013); in particular, Evans & Sackmann (1988) and Barentin et al (1999) computed the force on a probe within a membrane over a thin subphase. To provide a point of comparison (particularly for compressible interfaces with large dilatational viscosity), we sketch the result of Barentin et al (1999) here.…”

Drag Coefficient of a Raftlike Domain Embedded in a Fluid Membrane Being a Near-Critical Binary Mixture

“…The membrane viscosity in C is also assumed to be this constant . The fluid membrane is surrounded on both sides by 3D incompressible fluids sharing the same viscosity 3 . In calculating the drag coefficient of a liquid domain, we can neglect its deformation during its translational motion because the deformation contributes to the drag force beyond the linear regime.…”

“…The biomembrane can be regarded as a two-dimensional (2D) fluid surrounded by three-dimensional (3D) fluids. Modeling a membrane protein as a rigid disk embedded in a flat fluid membrane, some researchers calculated its drag coefficient, [1][2][3][4] which is related to its diffusion coefficient, accessible more readily in experiments. [5][6][7] In the biomembrane, some minor lipid constituents are thought to be concentrated at domains called lipid rafts.…”