The Kapitza pendulum is the paradigm for the phenomenon of dynamical stabilization, whereby an otherwise unstable system achieves a stability that is induced by fast modulation of a control parameter. In the classic, macroscopic Kapitza pendulum, a rigid pendulum is stabilized in the upright, inverted pendulum using a particle confined in a ring-shaped optical trap, subject to a drag force via fluid flow and driven via oscillating the potential in a direction parallel to the fluid flow. In the regime of vanishing Reynold's number with high-frequency driving the inverted pendulum is no longer stable, but new equilibrium positions appear that depend on the amplitude of driving. As the driving frequency is decreased a yet different behavior emerges where stability of the pendulum depends also on the details of the pendulum hydrodynamics. We present a theory for the observed induced stability of the overdamped pendulum based on the separation of timescales in the pendulum motion as formulated by Kapitza, but with the addition of a viscous drag. Excellent agreement is found between the predicted behavior from the analytical theory and the experimental results across the range of pendulum driving frequencies. We complement these results with Brownian motion simulations, and we characterize the stabilized pendulum by both time- and frequency-domain analyses of the pendulum Brownian motion.
Diabetic retinopathy (DR) is a microvascular complication of diabetes mellitus (DM) in which high blood sugar levels cause swelling, leaking and occlusions in the blood vessels of the retina, often resulting in a loss of sight. The microvascular system requires red blood cells (RBCs) to undergo significant cellular deformation in order to pass through vessels whose diameters are significantly smaller than their own. There is evidence to suggest that DM impairs the deformability of RBCs, and this loss of deformability has been associated with diabetic kidney disease (or nephropathy) - another microvascular complication of DM. However, it remains unclear whether reduced deformability of RBCs correlates with the presence of DR. Here we present an investigation into the deformability of RBCs in patients with diabetic retinopathy using optical tweezers. To extract a value for the deformability of RBCs we use a dual-trap optical tweezers set-up to stretch individual RBCs. RBCs are trapped directly (i.e. without micro-bead handles), so rotate to assume a ‘side-on’ orientation. Video microscopy is used to record the deformation events, and shape analysis software is used to determine parameters such as initial and maximum RBC length, allowing us to calculate the deformability for each RBC. A small decrease in deformability of diabetes cells subject to this stretching protocol is observed when compared to control cells. We also report on initial results on three dimensional imaging of individual RBCs using defocussing microscopy.
KEYWORDS: Particles, Modulation, Optical tweezers, Digital video recorders, Video microscopy, Video, Frequency modulation, CMOS cameras, Objectives, Motion analysis
It is well known that a rigid pendulum with minimal friction will occupy a stable equilibrium position vertically upwards when its suspension point is oscillated at high frequency. The phenomenon of the inverted pendulum was explained by Kapitza by invoking a separation of timescales between the high frequency modulation and the much lower frequency pendulum motion, resulting in an effective potential with a minimum in the inverted position. We present here a study of a microscopic optical analogue of Kapitza's pendulum that operates in different regimes of both friction and driving frequency. The pendulum is realized using a microscopic particle held in a scanning optical tweezers and subject to a viscous drag force. The motion of the optical pendulum is recorded and analyzed by digital video microscopy and particle tracking to extract the trajectory and stable orientation of the particle. In these experiments we enter the regime of low driving frequency, where the period of driving is comparable to the characteristic relaxation time of the radial motion of the pendulum with finite stiffness. In this regime we find stabilization of the pendulum at angles other than the vertical (downwards) is possible for modulation amplitudes exceeding a threshold value where, unlike the truly high frequency case studied previously, both the threshold amplitude and equilibrium position are found to be functions of friction. Experimental results are complemented by an analytical theory for induced stability in the low frequency driving regime with friction.
We present a study of correlated Brownian fluctuations between optically confined particles in a number of different configurations. First we study colloidal particles held in separate optical tweezers. In this configuration the particles are known to interact through their hydrodynamic coupling, leading to a pronounced anti-correlation in their position fluctuations at short times. We study this system and the behavior of the correlated motion when the trapped particles are subject to an external force such as viscous drag. The second system considered is a chain of optically bound particles in an evanescent wave surface trap. In this configuration the particles interact both through hydrodynamic and optical coupling. Using digital video microscopy and subsequent particle tracking analysis we study the thermal motion of the chain and map the covariance of position fluctuations between pairs of particles in the chain. The experiments are complemented by Brownian motion simulations.
We present a study of dynamical stabilisation of an overdamped, microscopic pendulum realised using optical tweezers. We first derive an analytical expression for the equilibrium dynamically stabilised pendulum position in a regime of high damping and high modulation frequency of the pendulum pivot. This model implies a threshold behavior for stabilisation to occur, and a continuous evolution of the angular position which, unlike the underdamped case, does not reach the fully inverted position. We then test the theoretical predictions using an optically trapped microparticle subject to fluid drag force, finding reasonable agreement with the threshold and equilibrium behavior at high modulation amplitude. Analytical theory and experiments are complemented by Brownian motion simulations.
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