Richard Philip Llewellyn Sear

We study the trapping of charged particles and macromolecules (such as DNA) in salt gradients in aqueous solutions. The source for the salt gradient can be as simple as a dissolving ionic crystal, as shown by McDermott et al. [Langmuir 28, 15491 (2012)]. Trapping is due to a competition between localisation due to diffusiophoresis in the salt gradient, and spreading out by diffusion. The size of the trap is typically 1–100 µm. We further predict that at steady state, the particle (macromolecule) number density is a power law of the salt concentration, with an exponent that is the ratio of the diffusiophoretic mobility to the diffusion coefficient of the trapped species. This ratio increases with size and typically becomes ≫ 1 for particles or macromolecules with hydrodynamic radii of hundreds of nanometres and above. Thus large particles or macromolecules are easily caught and trapped at steady state by salt gradients.

A gradient of a single salt in a solution generates an electric field, but not a current. Recent theoretical work by one of us [Phys. Rev. Lett. 24, 248004 (2020)] showed that the Nernst-Planck equations imply that crossed gradients of two or more different salts generate ion currents. These currents in solution have associated non-local electric fields. Particle motion driven by these non-local fields has recently been observed in experiment by Williams et al. [Phys. Rev. Fluids 9, 014201 (2024)] ; a phenomenon which was dubbed action-at-a-distance diffusiophoresis. Here we use a magnetostatic analogy to show that in the far-field limit, these non-local currents and electric fields both have the functional form of the magnetic field of a magnetic dipole, decaying as 𝑟−𝑑 in 𝑑 = 2 and 𝑑 = 3 dimensions. These long-ranged electric fields are generated entirely within solutions and have potential practical applications since they can drive both electrophoretic motion of particles, and electro-osmotic flows. The magnetostatic analogy also allows us to import tools and ideas from classical electromagnetism, into the study of multicomponent salt solutions.

Statistical physicists have long studied systems where the variable of interest spans many orders of magnitude, the classic example is the relaxation times of glassy materials, which are often found to follow power laws. A power-law dependence has been found for the probability of transmission of COVID-19, as a function of length of time a susceptible person is in contact with an infected person. This is in data from the United Kingdom's COVID-19 app. The amount of virus in infected people spans many orders of magnitude. Inspired by this I assume that the power-law behaviour found in COVID-19 transmission, is due to the effective transmission rate varying over orders of magnitude from one contact to another. I then use a model from statistical physics to estimate that if a population all wear FFP2/N95 masks, this reduces the effective reproduction number for COVID-19 transmission by a factor of approximately nine.

In an externally imposed electrolyte (salt) concentration gradient, charged colloids drift at speeds of order one micrometre per second. This phenomenon is known as diffusiophoresis. In systems with multiple salts and 'crossed' salt gradients, a nonlocal component of the electric field associated with a circulating (solenoidal) ion current can arise. This is in addition to the conventional local component that depends only on the local salt gradients. Here we report experimental observations verifying the existence of this nonlocal contribution. To our knowledge this is the first observation of nonlocal diffusiophoresis. The current develops quasi-instantaneously on the time scale of salt diffusion. Therefore, in systems with multiple salts and crossed salt gradients, one can expect a nonlocal contribution to diffusiophoresis which is dependent on the geometry of the system as a whole and appears as a kind of instantaneous 'action-at-a-distance' effect. The interpretation is aided by a magnetostatic analogy. Our experiments are facilitated by a judicious particle-dependent choice of salt (potassium acetate) for which the two local contributions to diffusiophoresis almost cancel, effectively eliminating conventional diffusiophoresis. This enables us to clearly identify the novel, nonlocal effect and may be useful in other contexts, for example in sorting particle mixtures.

In an externally imposed electrolyte (salt) concentration gradient, charged
colloids drift at speeds of order one micrometre per second. This phenomenon is
known as diffusiophoresis. In systems with multiple salts and 'crossed' salt
gradients, a nonlocal component of the electric field associated with a
circulating (solenoidal) ion current can arise. This is in addition to the
conventional local component that depends only on the local salt gradients.
Here we report experimental observations verifying the existence of this
nonlocal contribution. To our knowledge this is the first observation of
nonlocal diffusiophoresis. The current develops quasi-instantaneously on the
time scale of salt diffusion. Therefore, in systems with multiple salts and
crossed salt gradients, one can expect a nonlocal contribution to
diffusiophoresis which is dependent on the geometry of the system as a whole
and appears as a kind of instantaneous 'action-at-a-distance' effect. The
interpretation is aided by a magnetostatic analogy. Our experiments are
facilitated by a judicious particle-dependent choice of salt (potassium
acetate) for which the two local contributions to diffusiophoresis almost
cancel, effectively eliminating conventional diffusiophoresis. This enables us
to clearly identify the novel, nonlocal effect and may be useful in other
contexts, for example in sorting particle mixtures.

We elucidate the origin of the critical Stokes number
$\mathrm{St}_\mathrm{c}$ for inertial particle capture by obstacles in flow
fields, and explain the empirical observation made by Araujo et al. [Phys. Rev.
Lett. 97, 138001 (2006)] that the capture efficiency grows as
$(\mathrm{St}-\mathrm{St}_\mathrm{c})^\beta$ with $\beta=1/2$ for some critical
Stokes number. This behaviour, which is inaccessible to classic perturbation
theory, derives from the global structure of the phase space of particle
trajectories from which viewpoint it is both generic and inevitable except in
the limit of highly singular stagnation point flows which we example. In the
context of airborne disease transmission, the phenomenon underlies the sharp
decline in filtration efficiency of face coverings for micron-sized aerosol
droplets.

The Earth's atmosphere is an aerosol; it contains suspended particles. When air flows over an obstacle such as an aircraft wing or tree branch, these particles may not follow the same paths as the air flowing around the obstacle. Instead, the particles in the air may deviate from the path of the air and so collide with the surface of the obstacle. It is known that particle inertia can drive this deposition and that there is a critical value of this inertia, below which no point particles deposit. Particle inertia is measured by the Stokes number St. We show that near the critical value of the Stokes number Stc, the amount of deposition has the unusual scaling law of exp[-1/(St - Stc)1/2]. The scaling is controlled by the stagnation point of the flow. This scaling is determined by the time it takes the particle to reach the surface of the cylinder, varying as 1/(St - Stc)1/2, together with the distance away from the stagnation point (perpendicular to the flow direction), increasing exponentially with time. The scaling law applies to inviscid flow, a model for flow at high Reynolds numbers. The unusual scaling means that the number of particles deposited increases only very slowly above the critical Stokes number. This has consequences for applications ranging from rime formation and fog harvesting to pollination.

Many common elastomeric products, including nitrile gloves, are manufactured by coagulant dipping. This process involves the destabilization and gelation of a latex dispersion by an ionic coagulant. Despite widespread application, the physical chemistry governing coagulant dipping is poorly understood. It is unclear which properties of an electrolyte determine its efficacy as a coagulant and which phenomena control the growth of the gel. Here, a novel experimental protocol is developed to directly observe coagulant gelation by light microscopy. Gel growth is imaged and quantified for a variety of coagulants and compared to macroscopic dipping experiments mimicking the industrial process. When the coagulant is abundant, gels grow with a t^1/2 time dependence, suggesting that this phenomenon is diffusion-dominated. When there is a finite amount of coagulant, gels grow to a limiting thickness. Both these situations are modeled as one-dimensional diffusion problems, reproducing the qualitative features of the experiments including which electrolytes cause rapid growth of thick gels. We propose that the gel thickness is limited by the amount of coagulant available, and the growth is, therefore, unbounded when the coagulant is abundant. The rate of the gel growth is controlled by a combination of a diffusion coefficient and the ratio of the critical coagulation concentration to the amount of coagulant present, which in many situations is set by the coagulant solubility. Other phenomena, including diffusiophoresis, may make a more minor contribution to the rate of gel growth.

The non-equilibrium assembly of bimodal colloids during evaporative processes is an attractive means to achieve gradient or stratified layers in thick films. Here, we show that the stratification of small colloids on top of large is prevented when the viscosity of the continuous aqueous phase is too high. We propose a model where a too narrow width of the gradient in concentration of small colloids suppresses the stratification.

During the COVID-19 pandemic, many millions have worn masks made of woven fabric, to reduce the risk of transmission of COVID-19. Masks are essentially air filters worn on the face, that should filter out as many of the dangerous particles as possible. Here the dangerous particles are the droplets containing virus that are exhaled by an infected person. Woven fabric is unlike the material used in standard air filters. Woven fabric consists of fibres twisted together into yarns that are then woven into fabric. There are therefore two lengthscales: the diameters of: (i) the fibre and (ii) the yarn. Standard air filters have only (i). To understand how woven fabrics filter, we have used confocal microscopy to take three dimensional images of woven fabric. We then used the image to perform Lattice Boltzmann simulations of the air flow through fabric. With this flow field we calculated the filtration efficiency for particles a micrometre and larger in diameter. In agreement with experimental measurements by others, we find that for particles in this size range, filtration efficiency is low. For particles with a diameter of 1.5 micrometres our estimated efficiency is in the range 2.5 to 10%. The low efficiency is due to most of the air flow being channelled through relatively large (tens of micrometres across) inter-yarn pores. So we conclude that fabric is expected to filter poorly due to the hierarchical structure of woven fabrics, they are expected to filter poorly.