BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Talks.cam//talks.cam.ac.uk// X-WR-CALNAME:Talks.cam BEGIN:VEVENT SUMMARY:Osmotic Self-Propulsion - Ehud Yariv\, Israel Institute of Technol ogy DTSTART:20150420T123000Z DTEND:20150420T133000Z UID:TALK59072@talks.cam.ac.uk CONTACT:Julius Bier Kirkegaard DESCRIPTION:Osmotic self-propulsion of micron-size particles is a vibrant research area which has attracted significant attention in the physics\, c hemistry\, and engineering communities. The underlying mechanism is a cata lytic reaction at the particle boundary\, converting chemical energy into mechanical motion in a viscous liquid solution. When the chemical reaction is nonuniform\, this may result in particle motion. Practically\, the des ired non-uniformity is accomplished by employing inhomogeneous surfaces\; thus\, typical experiments make use of nano-rods composed of platinum-gold segments. Golestanian et al. [1] presented an idealized continuum descrip tion\, where the chemical catalysis is modelled by a prescribed distributi on of solute flux and the interaction of solute molecules with that bounda ry is represented by diffusio-osmotic slip. Neglecting solute advection\, Golestanian et al. [1] obtained a linear model which they employed to calc ulate the swimming velocity of a spherical particle and a slender rod.\n\n I will discuss two problems. The first [2] is motivated by the desire to p roperly model the nano-rod swimmers prevailing in experiments. We consider self-diffusiophoresis of an axisymmetric particle whose boundary is speci fied by an arbitrary axial distribution of cross-sectional radius. Focusin g upon slender particle shapes and making use of matched asymptotic expans ions we obtain a remarkably simple approximation for the particle velocity . This approximation can accommodate discontinuous flux distributions\, wh ich are commonly used for describing bimetallic particles\; it agrees stri kingly well with the numerical calculations of Popescu et al. [3]\, perfor med for spheroidal particles. Our approximation differs from that derived by Golestanian et al. [1]\; their erroneous formula appears to be the cons equence of an attempt to apply an intuitive approach in a delicate situati on where the diffusio-osmotic slip and self-propulsion speed are not of th e same asymptotic order.\n\nThe continuum model of Golestanian et al. [1] was recently extended by Michelin & Lauga [4]\, who incorporated solute ad vection and modeled the chemical reaction using both the prescribed-flux c ondition and a more realistic kinetic description\, where the kinetic-rate coefficient itself is prescribed. The second problem I will discuss [5] i s motivated by numerical solutions [4] of the resulting nonlinear model\, performed for various values of the Péclet (Pe) and Damköhler (Da) numbe rs\; in particular\, simulations performed at large values of Pe indicate that the swimming velocity scales inversely with the 1/3 power of that num ber. We have analyzed this problem using a boundary-layer approximation. T he scaling pertinent to that limit allows to decouple the problem governin g the solute concentration from the flow field. The resulting nonlinear bo undary-layer problem is handled using a transformation to stream-function coordinates and a subsequent application of Fourier transforms\, and is th ereby reduced to a nonlinear integral equation governing the interfacial c oncentration. Its solution provides the requisite approximation for the pa rticle velocity\, which indeed scales as the Pe-1/3. In the fixed-rate mod el\, large Péclet numbers may be realized in different limit processes. W e consider the case of large swimmers or strong reaction\, where Da is lar ge as well\, scaling as Pe. In that double limit\, where no boundary layer is formed\, we obtain a closed-form approximation for the particle veloci ty\, expressed as a nonlinear functional of the rate-constant distribution \; this velocity scales as Pe-2. Both the fixed-flux and fixed-rate asympt otic predictions agree with the numerical values provided by computational solutions of the nonlinear transport problem. \n\nJoint work with Ory Sch nitzer and Sébastien Michelin.\n\n[1] R. Golestanian\, T. B. Liverpool & A. Ajdari\, Designing phoretic micro-and nano-swimmers\, New J. Phys. 9\, 126 (2007). \n\n[2] O. Schnitzer & E. Yariv\, Osmotic self-propulsion of s lender particles\, Phys. Fluids 27\, 031701 (2015). \n\n[3] M. N. Popescu\ , S. Dietrich\, M. Tasinkevych & J. Ralston\, Phoretic motion of spheroida l particles due to self-generated solute gradients\, Eur. Phys. J. E Soft Matter 31\, 351–367 (2010). \n\n[4] S. Michelin & E. Lauga\, Phoretic se lf-propulsion at finite Péclet numbers\, J. Fluid Mech. 747\, 572-604 (20 14). \n\n[5] E. Yariv & S. Michelin\, Phoretic self-propulsion at large P éclet numbers\, J. Fluid Mech. 768\, R1 (2015). LOCATION:MR11\, Centre for Mathematical Sciences\, Wilberforce Road\, Cam bridge END:VEVENT END:VCALENDAR