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Register a new userTrajectories of a droplet driven by an internal active device
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We consider a liquid droplet which is propelled solely by internal flow. In a simple model, this flow is generated by an autonomous actuator, which moves on a prescribed trajectory inside the droplet. In a biological system, the device could represent a motor, carrying cargo and moving on a filamentary track. We work out the general framework to compute the self-propulsion of the droplet as a function of the actuating forces and the trajectory. The simplest autonomous device is composed of three point forces. Such a device gives rise to linear, circular or spiraling motion of the droplet, depending on whether the device is stationary or moving along a radial track. As an example of a more complex track we study in detail a spherical looped helix, inspired by recent studies on the propulsion of Synechococcus1 and Myxobacteria2. The droplet trajectories are found to depend strongly on the orientation of the device and the direction of the forces relative to the track with the posibility of unbounded motion even for time independent forcing.
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A liquid droplet, immersed into a Newtonian fluid, can be propelled solely by internal flow. In a simple model, this flow is generated by a collection of point forces, which represent externally actuated devices or model autonomous swimmers. We work out the general framework to compute the self-propulsion of the droplet as a function of the actuating forces and their positions within the droplet. A single point force, F with general orientation and position, r_0, gives rise to both, translational and rotational motion of the droplet. We show that the translational mobility is anisotropic and the rotational mobility can be nonmonotonic as a function of | r_0|, depending on the viscosity contrast. Due to the linearity of the Stokes equation, superposition can be used to discuss more complex arrays of point forces. We analyse force dipoles, such as a stresslet, a simple model of a biflagellate swimmer and a rotlet, representing a helical swimmer, driven by an external magnetic field. For a general force distribution with arbitrary high multipole moments the propulsion properties of the droplet depend only on a few low order multipoles: up to the quadrupole for translational and up to a special octopole for rotational motion. The coupled motion of droplet and device is discussed for a few exemplary cases. We show in particular that a biflagellate swimmer, modeled as a stresslet, achieves a steady comoving state, where the position of the device relative to the droplet remains fixed. In fact there are two fixpoints, symmetric with respect to the center of the droplet. A tiny external force selects one of them and allows to switch between forward and backward motion.
We discuss the flow field and propulsion velocity of active droplets, which are driven by body forces residing on a rigid gel. The latter is modelled as a porous medium which gives rise to permeation forces. In the simplest model, the Brinkman equation, the porous medium is characterised by a single length scale $ell$ --the square root of the permeability. We compute the flow fields inside and outside of the droplet as well as the energy dissipation as a function of $ell$. We furthermore show that there are optimal gel fractions, giving rise to maximal linear and rotational velocities. In the limit $elltoinfty$, corresponding to a very dilute gel, we recover Stokes flow. The opposite limit, $ellto 0$, corresponding to a space filling gel, is singular and not equivalent to Darcys equation, which cannot account for self-propulsion.
Droplet-based microfluidics turned out to be an efficient and adjustable platform for digital analysis, encapsulation of cells, drug formulation, and polymerase chain reaction. Typically, for most biomedical applications, the handling of complex, non-Newtonian fluids is involved, e.g. synovial and salivary fluids, collagen, and gel scaffolds. In this study we investigate the problem of droplet formation occurring in a microfluidic T-shaped junction, when the continuous phase is made of shear thinning liquids. At first, we review in detail the breakup process providing extensive, side-by-side comparisons between Newtonian and non-Newtonian liquids over unexplored ranges of flow conditions and viscous responses. The non-Newtonian liquid carrying the droplets is made of Xanthan solutions, a stiff rod-like polysaccharide displaying a marked shear thinning rheology. By defining an effective Capillary number, a simple yet effective methodology is used to account for the shear-dependent viscous response occurring at the breakup. The droplet size can be predicted over a wide range of flow conditions simply by knowing the rheology of the bulk continuous phase. Experimental results are complemented with numerical simulations of purely shear thinning fluids using Lattice Boltzmann models. The good agreement between the experimental and numerical data confirm the validity of the proposed rescaling with the effective Capillary number.
The design of artificial microswimmers is often inspired by the strategies of natural microorganisms. Many of these creatures exploit the fact that elasticity breaks the time-reversal symmetry of motion at low Reynolds numbers, but this principle has been notably absent from model systems of active, self-propelled microswimmers. Here we introduce a class of microswimmer that spontaneously self-assembles and swims without using external forces, driven instead by surface phase transitions induced by temperature variations. The swimmers are made from alkane droplets dispersed in aqueous surfactant solution, which start to self-propel upon cooling, pushed by rapidly growing thin elastic tails. When heated, the same droplets recharge by retracting their tails, swimming for up to tens of minutes in each cycle. Thermal oscillations of approximately 5 degrees Celsius induce the swimmers to harness heat from the environment and recharge multiple times. We develop a detailed elastohydrodynamic model of these processes and highlight the molecular mechanisms involved. The system offers a convenient platform for examining symmetry breaking in the motion of swimmers exploiting flagellar elasticity. The mild conditions and biocompatible media render these microswimmers potential probes for studying biological propulsion and interactions between artificial and biological swimmers.
The fundamental insight into Brownian motion by Einstein is that all substances exhibit continual fluctuations due to thermal agitation balancing with the frictional resistance. However, even at thermal equilibrium, biological activity can give rise to non-equilibrium fluctuations that cause ``active diffusion in living cells. Because of the non-stationary and non-equilibrium nature of such fluctuations, mean square displacement analysis, relevant only to a steady state ensemble, may not be the most suitable choice as it depends on the choice of the ensemble; hence, a new analytical method for describing active diffusion is desired. Here we discuss the stochastic energetics of a thermally fluctuating single active diffusion trajectory driven by non-thermal random forces. Heat dissipation, usually difficult to measure, can be estimated from the active diffusion trajectory; guidelines on the analysis such as criteria for the time resolution and driving force intensity are shown by a statistical test. This leads to the concept of an ``instantaneous diffusion coefficient connected to heat dissipation that may be used to analyse the activity and molecular transport mechanisms of living systems.
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