Supplementary Materials for

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1 advances.sciencemag.org/cgi/content/full/4/8/eaat3276/dc1 Supplementary Materials for Free-standing liquid membranes as unusual particle separators Birgitt Boschitsch Stogin, Luke Gockowski, Hannah Feldstein, Houston Claure, Jing Wang, Tak-Sing Wong* The PDF file includes: *Corresponding author. Published 24 August 2018, Sci. Adv. 4, eaat3276 (2018) DOI: /sciadv.aat3276 Section S1. Descriptions of movies S1 to S10 Section S2. Sources of energy dissipation Legend for Movies S1 to S10 Fig. S1. A schematic diagram showing a bead passing through a liquid membrane. Fig. S2. Comparison of the relative magnitude of different energy terms. Fig. S3. Theoretical dependence of E* on relevant parameters. Fig. S4. Effect of mechanical perturbation frequency on the longevity of liquid membranes. Fig. S5. Residual liquid on both hydrophilic and hydrophobic particles. Table S1. Surface tension and density of different liquid membrane solutions. Table S2. Liquid membrane mass and thickness characterization. Table S3. Surface roughness measurements of various bead materials. Table S4. Advancing angles of liquid membrane solution droplets on a flat surface. Table S5. Reported inertial parameters for various organisms and particles. References (27 40) Other Supplementary Material for this manuscript includes the following: (available at advances.sciencemag.org/cgi/content/full/4/8/eaat3276/dc1) Movie S1 (.mov format). Large and small bead separation. Movie S2 (.mov format). Particle filtration. Movie S3 (.mov format). Insect retention. Movie S4 (.mov format). Live insect retention. Movie S5 (.mov format). In-film probe movement. Movie S6 (.mov format). Particle transport. Movie S7 (.mov format). Self-cleaning of liquid membranes. Movie S8 (.mov format). Simulated surgery. Movie S9 (.mov format). Liquid membranes as selective gas/solid barriers. Movie S10 (.mov format). Liquid membrane longevity.

2 Section S1. Descriptions of movies S1 to S10 Movie S1. Large and small bead separation. This video shows a liquid membrane retaining a small polytetrafluoroethylene (PTFE) bead while allowing a large one to pass through. Movie S2. Particle filtration. This video shows how a liquid membrane can be used to separate a mixture of glass particles according to their size. Here, the small glass particles are retained while the large one passes through the membrane. Movie S3. Insect retention. This video demonstrates that insects (i.e., fruit fly, house fly, and mosquito) can be retained within a liquid membrane at typical flight speeds. Here, dead insects were used in order to control the impact velocity of the insect. The dead insects impact the liquid membrane at speeds typical of their live counterparts. Movie S4. Live insect retention. This video demonstrates that live insects (i.e., fruit flies) can be retained within a liquid membrane. Movie S5. In-film probe movement. This video shows a PTFE rod freely moving while embedded in the liquid membrane. Movie S6. Particle transport. This video demonstrates that small glass particles retained in the liquid membrane can be transported within the membrane due to gravity. Movie S7. Self-cleaning of liquid membranes. Our experimental setup involves a tilted liquid membrane where contaminates (here, small sand particles) are passively removed from the separation region by gravity, allowing the large particle to be collected. The small particles are collected in the accumulation region and removed from the membrane when the weight of the aggregate exceeds the capillary force exerted by the liquid membrane ( aggregate removal ). Particles used here were sand (small particles) and glass (large particles). Movie S8. Simulated surgery. This video shows a simulated surgery. Here, the membrane allows medical tools (i.e., scalpel and tweezers) and bovine flesh to pass through it while blocking dust particles (oil based pink UV fluorescent powder, Slice of The Moon). Movie S9. Liquid membranes as selective gas/solid barriers. This video shows that a liquid membrane can be used to contain/divert fog (to simulate and visualize gas sequestration) while allowing solid particles to pass through. This property may be useful in solid waste/odor management.

3 Movie S10. Liquid membrane longevity. Here we demonstrate that a liquid membrane can last for over three hours when replenished, even when perturbed with a glass probe. Here, the period of probe oscillation is 3.55 s; images were acquired at a rate of 1 frame/sec. A subset of these images were used to generate this video (an effective acquisition rate of 1 frame per 63 s with a playback frame rate of 5 frames/s). In total, 3042 probing cycles were completed to make this video. The video duration was limited by camera memory rather than membrane lifetime.

4 Section S2. Sources of energy dissipation After a bead impacts a liquid membrane, bead-membrane interactions lead to energy exchange and dissipation. As the bead travels through the membrane, it stretches the membrane, converting some of the bead kinetic energy into film surface energy. Furthermore, the liquid-solid interface may slide along the bead surface, leading to energy dissipation due to membrane pinning. We investigate the significance of these energy terms here (see fig. S1 for definition of variables). Fig. S1. A schematic diagram showing a bead passing through a liquid membrane. Several variables used throughout our discussion are shown. Surface energy change due to film stretching As the bead passes through the membrane, the membrane stretches, increasing the surface energy. As this occurs, the bead-film contact line may slide along the bead surface, thus changing the boundary conditions of the membrane over time. We anticipate that this contact line motion is a function of the dynamics and geometry of the system, as well as the advancing contact angle of the membrane on the bead surface. In an effort to make a rough estimate of the maximum membrane stretching and thus the maximum change in surface area of the membrane, we simplify our system by assuming that the membranebead contact line remains fixed to the equator of the bead. Since the bead is traveling at relatively low speeds and existing work (13) has shown that beads impacting films at low Weber number (We) generate catenoid surfaces (i.e., minimal surfaces), we assume that in all of our experiments the membrane is approximately a minimal surface at each moment in time as it stretches. Since a minimal surface has a mean curvature κ of zero everywhere on the surface, the pressure difference Δp across the membrane interfaces should be approximately zero (based on the Young-Laplace equation, Δp = 2γκ) so we ignore energy losses due to drag arising from film movement. The minimal surface formed by two concentric circular boundaries is a catenoid, a surface that can be represented as the surface of rotation (about the y-axis) of the following equation

5 x = a cosh ( y a ) (S1) where a is a constant. Since we assume (1) that the film remains attached to the bead at the equator and (2) the membrane is a catenoid (with boundaries at the ring and at the bead equator), we approximate the maximum film stretch area to be the area of the catenoid formed when the liquid membrane is tangent to the equator of the bead at the bead-film contact line. Any further stretching would mathematically allow membrane-bead intersection, which is non-physical. The boundary conditions associated with these assumptions are x(y max ) = R f x(y = 0) = R b dx dy y=0 = 0 where R f is the film radius, R b is the bead radius, and y max is the vertical distance between the film and the bead center associated with the maximum membrane stretch area. Solving equation S1 using the above boundary conditions, the catenary associated with our maximal stretching conditions is x = R b cosh ( y R b ) (S2) and the maximum stretch distance is y max = R b cosh 1 ( R f R b ) (S3) The surface of revolution about the y-axis of this shape (i.e., a catenoid) has an area A cat (which accounts for the two sides of the film) given by A cat = πr b 2 (sinh φ + φ) (S4) where φ = 2 cosh 1 ( R f R b ) We consider the maximum change in surface energy to be the difference between the surface energy of a film with area A cat and that of the flat annular film (inner radius R b, outer radius R f ) at bead impact. The maximum surface energy change is thus given by

6 E s = πγr b 2 [sinh φ + φ] 2πγ(R f 2 R b 2 ) (S5) where γ is the surface tension of the liquid membrane. Friction (pinning) when film slides along bead As the liquid membrane contact line slides along the surface of the bead, energy may be lost due to friction. This energy can be captured by the pinning energy. The pinning force is given by Furmidge (27) F P = 2γπR(α)(cosθ R cosθ A ) where R(α) = R b sinα and 2πR(α) is the perimeter of the film-bead contact line when the contact line is at an angle α from vertical (fig. S1). Since work is force multiplied by distance, we can calculate the energy dissipated as the film moves from different values of α as follows α 2 2 E P = 2γπR b α 1 sinα (cos θ R cos θ A )dα While the initial liquid membrane motion may be more of a wrapping than sliding motion, we assume a sliding motion from α 1 = 0 to α 2 = π (possibly leading to an overestimate of E P ), leading to E P = 2πγR b 2 (cosθ R cosθ A ) (S6) Relative magnitude of different energy terms The kinetic energy of a bead at impact is approximately E ub = ρ b gh ( 4 3 πr b 3 ) (S7) where ρ b is the bead density, g is the magnitude of the acceleration due to gravity, and H is the height above the membrane from which the bead was dropped, assuming all potential energy is converted to kinetic energy. According to Equations S5, S6, and S7 and our experimental conditions, E P /E ub << 1 but E s is comparable to E ub (fig. S2). We thus conclude that, for our experiments, E P is negligible and define E as E = E s E ub (S8)

7 Fig. S2. Comparison of the relative magnitude of different energy terms. The relative magnitude of different energy terms (E S and E P ) compared to the kinetic energy (E ub ) at bead impact with the liquid membrane for (A) glass, (B) polytetrafluoroethylene (PTFE), and (C) polystyrene (PS) beads.

8 Fig. S3. Theoretical dependence of E* on relevant parameters. Here we plot lne analytically, assuming we are dropping a glass bead (ρ b = 2500 kg/m 3 ) into the membrane from height H. The plots on the right panels show a zoomed-in region of the plots on the left panels for 0.01< R b /R f < 0.1. (A, B) Influence of R f on E : lne as a function of R b /R f at a fixed drop height H and surface tension γ. The inset in (A) shows a dimensional x-axis for clarity. Here we see that increasing R f should lead to an increase in R b,cr (the maximum value of R b where bead retention will occur) when all other parameters are held constant. (C, D) Influence of γ on E : lne as a function of R b /R f at fixed R f and H for different γ. Here we see that increasing γ leads to an increase in R b,cr when all other parameters are held constant. (E, F) Influence of H on E : lne as a

9 function of R b /R f with a fixed R f and γ for different H. Here we see that an increase in H leads to a decrease in R b,cr when all other parameters are held constant. These relationships only hold if the weight of the bead does not exceed the capillary force acting on the bead. Fig. S4. Effect of mechanical perturbation frequency on the longevity of liquid membranes. (A) A plot showing the longevity of the liquid membrane with respect to the perturbation frequency. Each data point represents the measured longevity of a single liquid membrane. The longevity L of the liquid membrane is normalized with respect to the maximum longevity of the membrane at 0 Hz, L 0,max. In this experiment, external perturbations took place using a Pasco Mechanical Wave Driver oscillating vertically at an amplitude of ~3 mm. The driver was connected to a metal plate with an array of circular cutouts 2 cm in diameter. Liquid membranes were applied to the holes. (B, C) Response of the liquid membrane to different forcing frequencies. Liquid membranes lasted ~1 second at 55 Hz, but lasted significantly longer at 85 Hz, suggesting that membrane lifetime depends on the perturbation frequency. The liquid membranes used here were comprised of 7:3 ratio by volume of deionized water and glycerol and a 8.5 mm concentration of sodium dodecyl sulfate. The scale bars each represent 1 cm.

10 Fig. S5. Residual liquid on both hydrophilic and hydrophobic particles. Residual liquid on both hydrophilic and hydrophobic particles after liquid membrane detachment and self-healing. The liquid membrane is composed of 7:3 volume ratio of water and glycerol, and 8.5 mm of sodium dodecyl sulfate.

11 Table S1. Surface tension and density of different liquid membrane solutions. The average surface tension and density (with standard deviations) were calculated from 5 independent measurements. [SDS] (M) Surface Tension (mn/m) Density (kg/m 3 ) ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 1.9 Table S2. Liquid membrane mass and thickness characterization. Ring Radius (cm) [SDS] (M) Film Mass (mg) Thickness (μm) ± 5.5 ~ ± 6.5 ~40

12 Table S3. Surface roughness measurements of various bead materials. Surface roughness measurements of various bead materials used in our experiments. Note that the scan area denotes the projected area of the scan region. Material ξ (μm) Scan Area (μm μm) Manufacturer Glass (sphere; soda lime) ± Cospheric Glass slide (flat; borosilicate) ± VWR PTFE (sphere) ± McMaster-Carr PTFE (flat) ± McMaster-Carr PS (sphere) ± Cospheric PS (flat) ± McMaster-Carr Table S4. Advancing angles of liquid membrane solution droplets on a flat surface. All advancing angle measurements for polytetrafluoroethylene (PTFE) and polystyrene (PS) were taken using a drop volume addition and subtraction method. The advancing angles of water and 10.6 mm SDS solution on glass were measured to be < 10. θ A ( o ) [SDS] (M) PTFE PS ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 2.1

13 Table S5. Reported inertial parameters for various organisms and particles. Reported inertial parameters for various organisms and particles, as well as their E value assuming R f = 1.5 cm and γ = 35.6 mn/m. If mass data was unknown, E ub was calculated using the organism/particle volume, assuming a spherical geometry with radius equal to half the characteristic size. House fly measurements were conducted inhouse using 10 dead house flies purchased from Dead Insects (deadinsects.net). The average measured size (distance from top of head to bottom of abdomen) and mass of these house flies are m (standard deviation of m) and kg (standard deviation of kg), respectively. Organism/ Particle Characteristic Size (m) Speed (m/s) Mass (kg) Density (kg/m 3 ) ln ( E s E ub ) pollen (28) (29) (28) 11 dust (29) (30) (31) 9 fruit fly (32) (33) (34) - 6 mosquito (35) 1.18 (36) (35) - 1 gnat (37) 3 (38) (38) - 1 house fly (39) honey bee (40) 7 (38) (38) - -4