A surfactant is an interfacially active substance that changes surface tension. A concentration gradient therefore generates tangential Marangoni stress.
A cationic surfactant with a sixteen-carbon hydrocarbon tail and a positively charged trimethylammonium head group, accompanied by a counterion. It is an amphiphile that can form aqueous micelles. Its head-group charge has the opposite sign to that of sodium dodecyl sulfate.
An anionic surfactant with a twelve-carbon hydrocarbon tail and a negatively charged sulfate head group, accompanied by a sodium counterion. This separation of hydrophobic and hydrophilic regions makes it an amphiphile. It forms aqueous micelles under suitable concentration and temperature conditions and is used in sodium dodecyl sulfate polyacrylamide gel electrophoresis.
The material derivative of surface concentration combines tangential and normal area change, surface diffusion, and relaxation towards a reservoir concentration . The rate represents exchange; setting recovers transport without exchange. The concentration is measured per interfacial area, so stretching dilutes it.
A spherical inviscid bubble moving slowly through a viscous liquid has a dipolar surfactant perturbation. The associated Marangoni stress reduces the tangential velocity from its clean-bubble value towards zero. In the linear regime, with , the consistent Newtonian fluid stress tensor gives .
The dipolar normal traction is balanced by buoyant hydrostatic pressure and the concentration-dependent normal capillary stress, in addition to the constant gas pressure and equilibrium Laplace pressure. A degree-one shape perturbation translates a sphere rather than deforming it; the balance fixes the terminal speed. A uniform gas pressure alone cannot balance this mode.
Linear steady transport on a translating sphere gives . The components of its unit normal vector are degree-one spherical harmonics. The condition ensures the concentration perturbation is small relative to .
Outward interfacial flow from a thinning region dilutes surfactant there and raises its surface tension. The resulting Marangoni stress pulls fluid back toward the thinning region, opposes further stretching, and slows rupture.
For strong Marangoni stress and large , the unstable band has . Its rate is asymptotically . Maximizing this quadratic in gives the displayed finite-wavelength maximum. The growth timescale is not alone a bubble lifetime: initial disturbance size and thickness evolution also enter.
An insoluble surfactant remains on an interface. Without surface diffusion, its material concentration changes only through the local surface-area dilation rate.
Surface diffusion transports particles along an interface down a concentration gradient. On an isotropic smooth interface with constant diffusivity , its flux is and its concentration source is , using the surface gradient and surface Laplacian.
For concentration per unit surface area, conservation on a moving material interface givesThe material derivative follows the surface particles. The two dilution terms are tangential expansion and curvature-induced area change from normal velocity ; the last term is surface diffusion.
For radius and tangential velocity with symmetric traceless , the surface divergence is . At small surface Péclet number , neglecting advection of the concentration perturbation givesThe result follows because this quadratic is a degree-two spherical harmonic with surface Laplacian times itself and zero spherical mean.
Soap consists of sodium or potassium salts of long-chain fatty acids. Its hydrophilic carboxylate head and hydrophobic hydrocarbon tail make it an amphiphile; saponification of triglycerides produces these salts.
A detergent can disrupt a lipid bilayer; in a protease protection assay, removing the membrane barrier tests the cause of apparent protection.
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Surfactant, short for surface-active agent, is a substance that reduces surface tension in liquids. Surfactants are typically amphiphilic molecules, meaning they have both hydrophilic (water-attracting) and hydrophobic (water-repelling) parts. This unique structure allows them to accumulate at interfaces, such as between air and water or oil and water, altering the properties of the surface.