Effective Interaction between Active Colloids and Fluid Interfaces Induced by Marangoni Flows

Effective Interaction between Active Colloids and Fluid Interfaces Induced by Marangoni Flows Alvaro Domínguez,1,* P. Malgaretti,2,3,†M. N. Popescu,2,3 and S. Dietrich2,3 1Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, 41080 Sevilla, Spain 2Max-Planck-Institut für Intelligente Systeme, Heisenbergstraße 3, 70569 Stuttgart, Germany 3IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany (Received 18 September 2015; published 18 February 2016) We show theoretically that near a fluid-fluid interface a single active colloidal particle generating, e.g., chemicals or a temperature gradient experiences an effective force of hydrodynamic origin. This force is due to the fluid flow driven by Marangoni stresses induced by the activity of the particle; it decays very slowly with the distance from the interface, and can be attractive or repulsive depending on how the activity modifies the surface tension. We show that, for typical systems, this interaction can dominate the dynamics of the particle as compared to Brownian motion, dispersion forces, or self-phoretic effects. In the attractive case, the interaction promotes the self-assembly of particles into a crystal-like monolayer at the interface. DOI: 10.1103/PhysRevLett.116.078301 Significant attention has been paid lately to micrometer sized particles capable of self-induced motility [1–3]. They are seen as promising candidates for novel techniques in chemical sensing [4] or water treatment [5]. The motion of active colloidal particles has been the subject of numerous experimental [1–3,6,7] and theoretical [8–12] studies. One realization is a particle with a catalytic surface promoting a chemical reaction in the surrounding solution [13]. For an axisymmetric particle lacking fore-and-aft symmetry, the distributions of reactant and product molecules may become nonuniform along its surface and the particle could move due to self-induced phoresis [14]. If the particle is spherically symmetric, it will remain immobile in bulk solution but can be set into motion by the vicinity of walls or other particles (not necessarily active) which break the spherical symmetry [10,13–16]. A relevant case corresponds to the movement of active particles bounded by a fluid-fluid interface. This situation raises new issues, in particular if the reactants or the products have a significant effect on the properties of the fluid interface implying tensioactivity. For example, it has been recently predicted that catalytically active, spherical particles which are trapped at the interface may be set into motion along the interface by Marangoni flows, selfinduced via the spatially nonuniform distribution of tensioactive molecules [17–19]. (A similar motility mechanism can originate from thermally induced Marangoni flows if, e.g., the particle contains a metal cap which is heated by a laser beam [20].) Furthermore, self-induced Marangoni flows, combined with a mechanism of triggering spontaneous symmetry breaking, have also been used to develop self-propelled droplets [21–23]. However, another category of experimental situations occurs if the particles are not trapped at the interface but may reside in the vicinity of the interface or get near it during their motion. In this study we provide theoretical evidence that such catalytically active or locally heated spherical particles, although immobile in bulk, experience a very strong, long-ranged effective force field due to the Marangoni stresses self-induced at the interface. This force of hydrodynamic origin manifests itself at spatial length scales much larger than those of typical wetting forces. It gives rise to a drift of the particle towards or away from the fluid interface, depending only on how the tensioactive agent, i.e., a gradient in chemical concentration or in temperature, affects the interface. This effect dominates any possible self-phoresis or dispersion interactions, and acts on time scales which can be orders of magnitude shorter than those associated with Brownian diffusion. This drift can facilitate particle adsorption towards the interface and therefore has important implications for the selfassembly of particles at fluid-fluid interfaces. We complement the theoretical calculations with a thorough analysis regarding the observability of these phenomena in future experiments. The model system consists of a spherical colloidal particle with radius Rin front of a flat interface at z¼0 between two immiscible fluids. Fluid 1 (2) occupies the half space z>0(z<0) (see Fig. 1). The spherical particle is located in fluid 1; its center is at x0¼ð0;0;LÞwith L>R (i.e., the particle does not penetrate through the interface). By virtue of a chemical reaction occurring uniformly over its surface [24], the particle acts as a spherically symmetric source (or sink) of a chemical species A. We assume that the time scale for diffusion of Ais much shorter than any relevant time scale associated with fluid flows [25]. Therefore, we consider only the stationary state neglecting advection by the ensuing Marangoni flow. Additionally, the number density cðx¼ rþzezÞof species A[with r¼ðx; y; 0Þin the following] is PRL 116, 078301 (2016) PHYSICAL REVIEW LETTERS week ending 19 FEBRUARY 2016 0031-9007=16=116(7)=078301(5) 078301-1 © 2016 American Physical Society assumed to be sufficiently small so that for Athe ideal-gas approximation holds, and thus cðxÞobeys Fick’s law for diffusion with constant diffusivity Dαin fluid α(¼1, 2): ∇2cðxÞ¼0;x∈fluid 1or 2;ð1aÞ subject to the boundary conditions [25] that (i) a single reservoir of species Afixes the number density far away from the particle to be c∞ αin fluid α(¼1, 2), (ii) the discontinuity of cðxÞat the interface, given by λ≔cðr;z¼0−Þ=cðr;z¼0þÞ¼c∞ 2=c∞ 1, is determined, as in equilibrium, by the distinct solvabilities of species Ain the two fluids, (iii) the current of species Aalong the direction of the interface normal is continuous at the interface ½D1ð∂c=∂zÞjz¼0þ¼D2ð∂c=∂zÞjz¼0−], and (iv) the current at the surface Spof the particle is n·½−D1∇cðxÞ ¼ Q 4πR2;x∈Sp;ð1bÞ where nis the unit vector normal to Sp(pointing into fluid 1); Q>0(Q<0) is the rate of production (annihilation) of species A. The surface tension γof the fluid interface is assumed to depend on the local number density of species Aand is modeled within the local equilibrium approximation as [25] γðrÞ¼γ0−b0½cðr;z¼0þÞ−c∞ 1:ð2Þ Here, γ0is the surface tension in equilibrium in which the density of Ain fluid 1 is c∞ 1; the effect of local deviations thereof are quantified by the coefficient b0, the sign of which depends on the chemical. This inhomogeneity of the surface tension induces Marangoni stresses which set the fluids into motion. The velocity field vðxÞcan be derived as a solution of the Stokes equations (i.e., in the limit of incompressible flow and negligible inertia): ∇·vðxÞ¼0;∇·σ ↔ðxÞ¼0;x∈fluid 1;2;ð3aÞ where σ ↔ðxÞ¼ηðxÞ½∇vþð∇vÞ†−pðxÞIis the stress tensor in the fluid, pðxÞthe pressure, ηðxÞ¼η1or η2the viscosity, and Idenotes the second-rank identity tensor. The Stokes equations are subject to the following boundary conditions: (i) vanishing velocity at infinity, (ii) no slip flow at the surface of the particle, (iii) at the interface, continuity of the tangential velocity and vanishing of the normal velocity, and (iv) balance between the tangential fluid stresses and the Marangoni stresses induced by the gradient of the surface tension along the interface: ðI−ezezÞ·½σ ↔jz¼0þ−σ ↔jz¼0−·ez¼−∇∥γ:ð3bÞ The tensor I−ezezprovides the projection onto the interfacial plane and ∇∥¼ð∂x;∂y;0Þis the nabla operator within the interfacial plane. (Actually, the interface must deform so that the normal component of the fluid stresses can be balanced by the Laplace pressure. A posteriori it turns out [25] that this deformation is typically so small that the flat interface approximation is reliable.) The translation velocity Vof the particle, or equivalently the force Fexerted by the particle on the fluid, can be inferred from the Lorentz reciprocal theorem [32].We consider the auxiliary flow field vauxðxÞ, for the same geometrical setup, corresponding to the translation of a rigid, spherical, chemically passive (i.e., without Marangoni stresses) particle in front of a flat fluid interface. This is the solution of Eq. (3a) subject to the same boundary conditions as above but with ∇∥γ¼0in Eq. (3b),a problem studied in Refs. [33–35]. We thus obtain [25] Faux ·V−Vaux ·F¼Zz¼0 d2r∇∥γðrÞ·vauxðrÞ ¼−ISp dS n·σ ↔ auxðxÞ·uðxÞ;ð4Þ with uðxÞ¼Zz¼0 d2r0∇∥γðr0Þ·Oðx−r0Þð5aÞ in terms of the Oseen tensor, OðxÞ¼ 1 8πηþxIþxx x2;ηþ≔ 1 2ðη1þη2Þ:ð5bÞ Here, uðxÞis the Marangoni flow, which would be induced solely by the Marangoni stresses ∇∥γðrÞ, i.e., as if the surface of the particle would not impose any boundary condition on the flow [25]. Note that Eq. (4) can be interpreted as a generalization of the Faxén laws [36] for the present problem. For a force-free [F¼0in Eq. (4)] spherical particle, the problem exhibits axial symmetry, R z fluid 1 (liquid) z = 0 fluid 2 (liquid or gas) L x y FIG. 1. Coordinates and configuration of the system. The interface between fluid 1 (liquid) and fluid 2 (liquid or gas) is located at z¼0. PRL 116, 078301 (2016) PHYSICAL REVIEW LETTERS week ending 19 FEBRUARY 2016 078301-2 which implies that Vis parallel to ez. Thus, it suffices to solve the auxiliary problem with Faux∥ez, which allows one to introduce the dimensionless stream function ψauxðr; zÞ, in terms of which Eq. (4) reduces to [25] V¼−ez2πR2b0ΓzZ∞ 0 dr ∂c ∂rz¼0þ ∂ψaux ∂zz¼0 ;ð6Þ where Γzis the L-dependent mobility of a (chemically passive) rigid spherical particle moving normal to the planar fluid interface [35]. The boundary-value problems given by Eqs. (1) and (3), subject to the coupling provided by Eq. (2), can be solved exactly as a series in terms of bipolar coordinates [25]. However, the relevant phenomenology can be highlighted and significant physical intuition can be gained from an approximate closed form valid asymptotically in the limit R=L →0. We therefore proceed with the latter; its range of validity will be assessed later by comparison with the exact solution (cf. Fig. 3). To the lowest order in R=L, the solution of Eq. (1) for the given boundary conditions can be obtained using the method of images in terms of monopoles located at x0¼ ð0;0;LÞand x 0¼ð0;0;−LÞ. In fluid 1 (z>0) one has cðxÞ¼c∞ 1þQ 4πD11 jx−x0jþD1−λD2 D1þλD2 1 jx−x 0j:ð7Þ Accordingly, the Marangoni flow (illustrated in Fig. 2)is given by Eqs. (2) and (5a) as uðxÞ¼ezuzðr; zÞþ erurðr; zÞwith [25] uzðr; zÞ¼−Qb0 16πDþηþ zðjzjþLÞ ½r2þðjzjþLÞ23=2;ð8aÞ urðr; zÞ¼ Qb0 16πDþηþr1−r2LþðjzjþLÞ3 ½r2þðjzjþLÞ23=2;ð8bÞ and Dþ≔ðD1þλD2Þ=2. The integral over Spin the second line of Eq. (4) can be evaluated by expanding the Marangoni flow in terms of a Taylor series about the particle center so that asymptotically uðxÞ≈uðx0Þfor R=L →0. Since HSpdS n·σ ↔ auxðxÞ¼−Faux, and Faux can be chosen arbitrarily, one concludes that a force-free (F¼0) active particle at a distance Lfrom the interface is carried by the flow with velocity VðLÞ≈uðx0Þ≈−ez Qb0 64πDþηþLð9Þ due to the self-induced Marangoni stresses. Since V∥ez, this implies a time dependence of L. Equation (9) captures the essence of all the relevant phenomenology. (i) For b0>0(i.e., the generic surfactant case) the particle drifts towards or away from the interface if it is a source (Q>0) or a sink ðQ<0Þof species A, respectively. For b0<0, the behavior is reversed. (ii) The slow 1=L decay of Vis tantamount to a long-ranged interaction with the fluid interface. The associated phenomenology can dominate the influence of dispersion forces between the particle and the interface, which decay ∼1=L4at best [37], and also the motion due to Brownian diffusion alone. The argument can be quantified by introducing the diffusion coefficient Dp≔kBT=ð6πηþRÞof the particle in a medium of viscosity ηþat temperature T. Equation (9) leads to the Peclet number of the particle PeðLÞ≔RjVðLÞj Dp ¼jqjR L;q≔ 3Qb0R 32DþkBT:ð10Þ FIG. 2. Vertical cut through the Marangoni flow uðxÞin the limit R=L →0[Eq. (8)]. The streamlines follow the direction of the vector field (assuming Qb0>0), while the color code corresponds to juðxÞj in units of jQb0j=ð16πDþηþLÞ. The center of the particle (white dot) is at y¼0,z=L ¼1. The threedimensional flow field is obtained by rotation around the zaxis and mirror reflection with respect to the interfacial plane z¼0. (This flow is driven by the stress located at the interface, not by the particle.) FIG. 3. The ratio V=uðx0Þ[Eqs. (6) and (9)] as a function of L=R for λD2=D1¼0.1, 1, 10 (circle, square, diamond) and η2=η1¼0.1, 10 (open, filled). The inset provides an enlarged view of the range L=R ≲2for λD2=D1¼10 and η2=η1¼0.02, 0.1, 1, 10, 50 (circle, square, diamond, triangle, times); at that scale, the data are indistinguishable. The dashed line indicates the approximation provided by Eq. (9). PRL 116, 078301 (2016) PHYSICAL REVIEW LETTERS week ending 19 FEBRUARY 2016 078301-3 The dominance of drift means PeðLÞ≳1. Thus, one estimates the distance Lmax from the interface, beyond which the motion of the particle is controlled by diffusion rather than by drift, as PeðLmaxÞ¼1so that Lmax ¼jqjR. Focusing on the case b0>0, one can determine the time tdrift it takes the particle to reach the interface starting (for Q>0) from a given distance L0(or, for Q<0, to reach a given distance L0starting from near the interface) via straightforward integration of the equation of motion dL=dt ¼ez·V(within the overdamped regime [25]). This renders the drift time tdrift ¼tdiff=ð2jqjÞ in terms of the time of diffusion tdiff ≔L2 0=Dpover the same distance L0. Therefore, for large values of jqjthe drift caused by the Marangoni flow, rather than diffusion, dominates the dynamics of the particle. In order to estimate the magnitude of q, we shall use the experimental result that typically b0can take values in the range from b0∼−10−3N=ðm×MÞ(M denotes mol/liter) for simple inorganic salts in water [38],uptob0∼ 102N=ðm×MÞfor dilute solutions of surfactants (i.e., far from their critical micelle concentrations) [39].We consider two distinct setups of potential experimental relevance. (i) The particle is a source. The chemical species Ais molecular oxygen liberated from peroxide in aqueous solution by a platinum-covered particle. For the experimental conditions described in Ref. [40], one has Q=ð4πR2Þ≈10−3mol=ðs×m 2Þ[compare Eq. (1b)]. At room temperature (300 K) and for R≃1μm, Eq. (10) leads to jqj∼3×10−4×½Dþ=ðm2×s −1Þ−1½jb0j= ðN×m −1×M −1Þ. For an air (fluid 2)-water (fluid 1) interface [41], diffusion in the gas phase dominates (typically D2≃10−5m2=s and D1≃10−9m2=s[42]), and Dþ≈λD2=2≃10−4m2=s (since λ∼10–100 for oxygen and air-water interface [43]), while b0is in the lower range of values [40]. Thus Lmax=R ¼jqj∼10−2, which explains the lack of reports of such effects for experimental setups as in Ref. [40]. However, for a liquid-liquid interface (e.g., water-decane), one has Dþ≃D1≃D2≃10−9m2=s (one expects λ≲1[42]) and thus jqj≳102across the range of values b0noted above. Therefore, for the same experimental setups of active colloids, but which involve liquidliquid interfaces instead of liquid-gas ones, we predict that the effective interactions discussed here dominate. The same conclusion holds for liquid-gas interfaces but with a reaction product with very low solubility in the gas phase (i.e., λ≪1). (ii) The particle is a sink; i.e., the tensioactive species Ais absorbed completely by the particle. One can infer Qfrom the diffusion-limited regime in which the surface of the particle acts as an absorbing boundary so that cðx∈SpÞ¼0, which with Eq. (7) provides the estimate Q≈−4πD1Rc∞ 1as R=L →0. With Eq. (10) one arrives at jqj∼3×108×ðD1=DþÞðR=μmÞ2ðc∞ 1=MÞ½jb0j= ðN×m−1×M−1Þ. Therefore, Lmax=R ¼jqjcan indeed be large for colloidal particles even if species Ais only weakly tensioactive (i.e., jb0jsmall) and even for liquid-gas interfaces (D1=Dþ≪1). The availability of an exact series representation for Vas given by Eq. (6) allows us to assess the range of validity of the asymptotic approximation [Eq. (9)] discussed above. For several values of the viscosity and diffusivity ratios [25], Fig. 3shows V=uðx0Þas a function of the separation L=R. It turns out that uðx0Þprovides a reliable approximation (less than 10% relative error) of the exact solution down to separations L=R ≃2, i.e., covering most of the range within which the model is relevant. Furthermore, the deviations from uðx0Þdepend very weakly on the ratios η2=η1and λD2=D1. These results, yet to be explored experimentally, have several implications, which we highlight in conclusion. First, as noted in the Introduction, if the particle maintains a temperature gradient, e.g., through local heating, the very same equations hold with the temperature playing the role of the number density cðxÞ. Therefore, all the phenomenology discussed above extends to this case, too. Second, sufficiently close to the interface the drift due to the induced Marangoni flows can dominate even self-phoretic motion. For instance, a Janus particle of size R¼1μm (with Dp∼ 10−13 m2=s in water) and self-propelling with a typical velocity of ∼1μm=s[1] has a Peclet number Pephor ≃10, which, e.g., at distances L=R < 10 is smaller than PeðLÞ¼ðR=LÞjqjif jqj≳102[see Eq. (10)]. Third, based on the single-particle phenomenology studied here one can infer potentially significant collective effects. Consider, for example, a dilute suspension of active particles which are driven towards the interface by the Marangoni stresses and in addition experience a short-ranged repulsion by the interface (e.g., due to electrostatic double layer interactions). Then the particles are expected to reside near the interface while experiencing a mutual long-ranged lateral repulsion as each particle is carried by the Marangoni flows induced by the others [see the flow lines in Fig. 2and Eq. (8b), which tells that ur exhibits also a slow in-plane decay ∼1=r]. Therefore, near the interface and in the presence of lateral boundaries self-organized crystal-like monolayers could be reversibly assembled and “dissolved”by simply turning on and off the activity of the particles. Finally, we note that this effective lateral pair interaction violates the actionreaction principle because nonidentical particles (e.g., due to size polydispersity, different production rates Q, or a heterogeneous coverage of the surface) create Marangoni flows of different strength. As for other systems in which such violations occur [44], this feature can be expected to give rise to a complex collective behavior and to a rich, barely explored phenomenology. The authors acknowledge the scientific benefits from the COST Action MP1106. A. D. acknowledges financial PRL 116, 078301 (2016) PHYSICAL REVIEW LETTERS week ending 19 FEBRUARY 2016 078301-4 support by the Spanish Ministerio de Economía y Competitividad through Grant No. FIS2014-53808-P (partially financed by FEDER funds). *[email protected] †[email protected] [1] S. J. Ebbens and J. R. Howse, Soft Matter 6, 726 (2010). [2] Y. Hong, D. Velegol, N. Chaturvedi, and A. Sen, Phys. Chem. Chem. Phys. 12, 1423 (2010). [3] S. Sánchez, L. Soler, and J. Katuri, Angew. Chem. Int. Ed. 54, 1414 (2015). [4] J. El-Ali, P. K. Sorger, and K. F. Jensen, Nature (London) 442, 403 (2006). [5] L. Soler, V. Magdanz, V. M. Fomin, S. Sánchez, and O. G. Schmidt, ACS Nano 7, 9611 (2013). [6] S. Ebbens, M.-H. Tu, J. R. Howse, and R. Golestanian, Phys. Rev. E 85, 020401 (2012). [7] T.-C. Lee, M. Alarcón-Correa, C. Miksch, K. Hahn, J. G. Gibbs, and P. Fischer, Nano Lett. 14, 2407 (2014). [8] R. Golestanian, T. B. Liverpool, and A. Ajdari, Phys. Rev. Lett. 94, 220801 (2005). [9] F. Jülicher and J. Prost, Eur. Phys. J. E 29, 27 (2009). [10] M. N. Popescu, M. Tasinkevych, and S. Dietrich, Europhys. Lett. 95, 28004 (2011). [11] R. Kapral, J. Chem. Phys. 138, 020901 (2013). [12] B. ten Hagen, S. van Teeffelen, and H. Löwen, J. Phys. Condens. Matter 23, 194119 (2011). [13] J. Palacci, S. Sacanna, A. S. Steinberg, D. J. Pine, and P. M. Chaikin, Science 339, 936 (2013). [14] S. Michelin and E. Lauga, Eur. Phys. J. E 38, 7 (2015). [15] G. R. Rückner and R. Kapral, Phys. Rev. Lett. 98, 150603 (2007). [16] L. Baraban, M. Tasinkevych, M. N. Popescu, S. Sánchez, S. Dietrich, and O. G. Schmidt, Soft Matter 8, 48 (2012). [17] E. Lauga and A. M. J. Davis, J. Fluid Mech. 705, 120 (2012). [18] H. Masoud and H. A. Stone, J. Fluid Mech. 741, R4 (2014). [19] H. Masoud and M. J. Shelley, Phys. Rev. Lett. 112, 128304 (2014). [20] A. Würger, J. Fluid Mech. 752, 589 (2014). [21] T. Toyota, H. Tsuha, K. Yamada, K. Takakura, T. Ikegami, and T. Sugawara, Chem. Lett. 35, 708 (2006). [22] M. M. Hanczyc, T. Toyota, T. Ikegami, N. Packard, and T. Sugawara, J. Am. Chem. Soc. 129, 9386 (2007). [23] S. Thutupalli, R. Seemann, and S. Herminghaus, New J. Phys. 13, 073021 (2011). [24] The straightforward extension to Janus particles does not change the main conclusions as contained in Eq. (9). [25] See Supplemental Material at http://link.aps.org/ supplemental/10.1103/PhysRevLett.116.078301, which includes Refs. [26–31], for a detailed explanation. [26] M. Teubner, J. Chem. Phys. 76, 5564 (1982). [27] A. Sellier and L. Pasol, Eur. J. Mech. B 30, 76 (2011). [28] R. B. Jones, B. U. Felderhof, and J. M. Deutch, Macromolecules 8, 680 (1975). [29] H. Brenner, Chem. Eng. Sci. 16, 242 (1961). [30] G. B. Jeffery, Proc. R. Soc. A 87, 109 (1912). [31] I. S. Gradshteyn and I. Ryzhik, Table of Integrals, Series, and Products, 7th ed. (Academic Press, Oxford, 2007). [32] S. Kim and S. J. Karrila, Microhydrodynamics: Principles and Selected Applications (Butterworth-Heinemann, Boston, 1991). [33] E. Bart, Chem. Eng. Sci. 23, 193 (1968). [34] S. H. Lee, R. S. Chadwick, and L. G. Leal, J. Fluid Mech. 93, 705 (1979). [35] S. H. Lee and L. G. Leal, J. Fluid Mech. 98, 193 (1980). [36] J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics (Noordhoff, Leyden, 1973). [37] V. A. Parsegian, Van der Waals Forces: A Handbook for Biologists, Chemists, Engineers, and Physicists (University Press, Cambridge, 2005). [38] G. Jones and W. A. Ray, J. Am. Chem. Soc. 63, 3262 (1941). [39] F. H.-B. de Castro, A. Gálvez-Borrego, and M. C. de Hoces, J. Chem. Eng. Data 43, 717 (1998). [40] W. F. Paxton, K. C. Kistler, C. C. Olmeda, A. Sen, S. K. S. Angelo, Y. Cao, T. E. Mallouk, P. E. Lammert, and V. H. Crespi, J. Am. Chem. Soc. 126, 13424 (2004). [41] It can be shown that the assumptions of incompressibility (low Mach number) and negligible inertia (low Reynolds number) hold also in the gas phase for the parameter values of interest. [42] L.-K. Ju and C. S. Ho, Biotechnol. Bioeng. 34, 1221 (1989). [43] R. Battino, T. R. Rettich, and T. Tominaga, J. Phys. Chem. Ref. Data 12, 163 (1983). [44] A. V. Ivlev, J. Bartnick, M. Heinen, C.-R. Du, V. Nosenko, and H. Löwen, Phys. Rev. X 5, 011035 (2015). PRL 116, 078301 (2016) PHYSICAL REVIEW LETTERS week ending 19 FEBRUARY 2016 078301-5