Mass Advection-Diffusion in Creeping Flow Through an Orifice Plate: A Model for Nanoporous Atomically Thin Membranes

Continuum transport equations are commonly applied to nanopores in atomically thin membranes for simple modeling. Although these equations do not apply for nanopores approaching the fluid or solute molecule size, they can be reasonably accurate for larger nanopores. Relatively large graphene nanopores have applications in small particle filtration and appear as unwanted defects in large-area membranes. Solute transport rates through these nanopores determine the rejection performance of the membrane. Atomically thin membranes commonly operate in a regime where advection and diffusion both contribute appreciably to transport. Solute mass transfer rates through larger nanopores have previously been modeled by adding continuum estimates for pure diffusion and pure advection through an infinitesimally thick orifice plate, as if the separate contributions were independent. We show here that estimating the transport rate in this way is accurate to within 30%. We further derive an expression for the net mass transfer rate in advection-diffusion through an infinitesimal thickness orifice plate at low Reynolds numbers that is accurate to within 1% for positive Peclet numbers (where diffusion is in the same direction as advection) and applies for negative Peclet numbers as well. Based on our expression, we devise an equation for the net mass transfer rate in creeping flow through orifice plates of arbitrary thickness that matches finite volume calculations to within 3% for positive Peclet numbers. These simple but accurate analytical equations for mass transfer rates in creeping flow through an orifice plate are useful tools in constructing approximate transport models.

Optimal portfolio and consumption for a Markovian regime-switching jump-diffusion process

We consider the optimal portfolio and consumption problem for a jump-diffusion process with regime switching. Under the criterion of maximizing the expected discounted total utility of consumption, two methods, namely, the dynamic programming principle and the stochastic maximum principle, are used to obtain the optimal result for the general objective function, which is the solution to a system of partial differential equations. Furthermore, we investigate the power utility as a specific example and analyse the existence and uniqueness of the optimal solution. Under the constraints of no-short-selling and nonnegative consumption, closed-form expressions for the optimal strategy and the value function are derived. Besides, some comparisons between the optimal results for the jump-diffusion model and the pure diffusion model are carried out. Finally, we discuss our optimal results in some special cases. doi:10.1017/S1446181121000122

Digital holographic study of vapor transport of heavy hydrocarbon from heated well cavity

Thin film evaporative cooling is one of the liquid cooling technologies, capable of removing high heat flux with lower junction temperature due to the utilization of latent heat of vaporization. To understand the various transport processes involved in vapour phase during thin film evaporation, evaporation from a heated well cavity of diameter 3 mm and height 2 mm is studied using Digital holographic interferometry technique. A flat disk-shaped vapour cloud is appeared for heated as well as not- heated well surface case. This signifies radial outward natural convection instead of pure diffusion. A higher vapour concentration is obtained at each time instants for heated surface case due to the higher evaporation rate as compared to non-heated, ambient case.

Comparative study of multicomponent Lattice Boltzmann models for binary mixture flows

Two lattice Boltzmann method (LBM) models for binary mixture flows are numerically compared. The first model solves the Navier–Stokes equations within the incompressible limit and considers the mixture as one single fluid. A multi relaxation time (MRT) collision operator tunes the fluid diffusivity independently of the fluid viscosity. The second model emerges from a different theoretical derivation of the kinetic theory, where the governing equations are recovered for each species of the mixture. A source term in the LBM defines the interspecies friction force and couples the species of the mixture. A pure diffusion flow and a 2D plane Poiseuille binary mixture flow verify both models in the incompressible limit where diffusive and viscous transport occurs. The influence of molecular mass ratio, dynamic viscosity ratio, and Schmidt number on species and mixture flow behavior is investigated. The numerical results show good agreement against their respective analytical solutions and capture the deviation between the velocity profiles according to the flow regime. The present numerical study underlines the difference between the models as a function of the flow regimes which was observed from the macroscopic governing equations.

OPTIMAL PORTFOLIO AND CONSUMPTION FOR A MARKOVIAN REGIME-SWITCHING JUMP-DIFFUSION PROCESS

We consider the optimal portfolio and consumption problem for a jump-diffusion process with regime switching. Under the criterion of maximizing the expected discounted total utility of consumption, two methods, namely, the dynamic programming principle and the stochastic maximum principle, are used to obtain the optimal result for the general objective function, which is the solution to a system of partial differential equations. Furthermore, we investigate the power utility as a specific example and analyse the existence and uniqueness of the optimal solution. Under the constraints of no-short-selling and nonnegative consumption, closed-form expressions for the optimal strategy and the value function are derived. Besides, some comparisons between the optimal results for the jump-diffusion model and the pure diffusion model are carried out. Finally, we discuss our optimal results in some special cases.

Renal Diffusion-Weighted Imaging in Healthy Dogs: Reproducibility, Test-Retest Repeatability, and Selection of the Optimal b-value Combination

Diffusion-weighted imaging (DWI) magnetic resonance imaging can evaluate alterations in the microstructure of the kidney. The purpose of this study was to assess the apparent diffusion coefficient (ADC) and the intravoxel incoherent motion model (IVIM) parameters of a normal kidney in healthy dogs, to evaluate the effect of b-value combinations on the ADC value, and the reproducibility and test-retest repeatability in monoexponential and IVIM analysis. In this experimental study, the ADC, pure diffusion coefficient (D), pseudodiffusion coefficient (D*), and perfusion fraction (fp) were measured from both kidneys in nine healthy beagles using nine b-values (b = 0, 50, 70, 100, 150, 200, 500, 800, and 1,000 s/mm2) twice with a 1-week interval between measurements. Interobserver and intraobserver reproducibility, and test-retest repeatability of the measurements were calculated. ADC values were measured using 10 different b-value combinations consisting of three b-values each, and were compared to the ADC obtained from nine b-values. All the ADC, D, D*, and fp values measured from the renal cortex, medulla, and the entire kidney had excellent interobserver and intraobserver reproducibility, and test-retest repeatability. The ADC obtained from a b-value combination of 0, 100, and 800 s/mm2 had the highest intraclass correlation coefficient with the ADC from nine b-values. The results of this study indicated that DWI MRI using multiple b-values is feasible for the measurement of ADC and IVIM parameters with high reproducibility and repeatability in the kidneys of healthy dogs. A combination of b = 0, 100, and 800 s/mm2 can be used for ADC measurements when multiple b-values are not available in dogs.

Noninvasive assessment of endometrial fibrosis in patients with intravoxel incoherent motion MR imaging

Recently, few noninvasive methods have been reported to evaluate endometrial fibrosis. Our study was to investigate the feasibility of intravoxel incoherent motion (IVIM) MR imaging in the detection of endometrial fibrosis in patients with intrauterine injury. 30 patients with hysteroscopy-confirmed endometrial fibrosis and 28 healthy women were enrolled to undergo MR examination including the IVIM sequence. Endometrial thickness (ET); apparent diffusion coefficient (ADC); and IVIM parameters, including pure diffusion coefficient (D), pseudodiffusion coefficient (D*) and vascular fraction (f) were evaluated. A multivariable model combing ADC, D, and f values using binary logistic regression analysis was built to diagnose endometrial fibrosis. Endometrial fibrosis patients demonstrated lower endometrial ADC, D, f values and ET (all p < 0.05). The multivariable model, ADC, D, f values and ET performed well in diagnosing endometrial fibrosis with AUC of 0.979, 0.965, 0.920, 0.901 and 0.833, respectively. The multivariable model revealed a better diagnostic accuracy than D, f and ET (all p < 0.05). Although ADC achieved a better diagnostic value than ET (z = 2.082, p < 0.05), no difference in AUC was shown among ADC, D, and f (all p > 0.05); between ET and D (p > 0.05); and between ET and f (p > 0.05). The reproducibility of ADC, D, f and D* values in patients with endometrial fibrosis and healthy women were good to excellent (ICC: 0.614–0.951). IVIM parameters exhibit promising potential to serve as imaging biomarkers in the noninvasive assessment of endometrial fibrosis.

Swimming, fast and slow: strategy and survival of bacterial predators in response to chemical cues

ABSTRACTBdellovibrio bacteriovorus is a predatory bacterium that preys upon gram-negative bacteria. As such, B. bacteriovorus has the potential to control antibiotic-resistant pathogens and biofilm populations. To survive and reproduce, B. bacteriovorus must locate and infect a host cell. However, in the temporary absence of prey, it is largely unknown how B. bacteriovorus modulate their motility patterns in response to physical or chemical environmental cues to optimize their energy expenditure. To investigate B. bacteriovorus’ predation strategy, we track and quantify their motion by measuring speed distributions and velocity autocorrelations as a function of starvation time. An initial unimodal speed distribution, relaxing to that expected for pure diffusion at long times, may be expected. Instead, we observe a complex, non-Brownian, search strategy as evidenced by distinctly bimodal speed distributions. That is, for an increasing amount of time over which B. bacteriovorus is starved, we observe a progressive re-weighting from a fast mode to a slow mode in the speed distribution obtained over consecutive frames. By contrast to its predator, B. bacteriovorus’ prey, Escherichia coli exhibits almost immediate decrease to a speed expected from passive diffusion following resuspension from rich to poor media. Distributions of trajectory-averaged speeds for B. bacteriovorus are largely unimodal, indicating nontrivial switching between fast and slow swimming modes within individual observed trajectories rather than there being distinct fast and slow populations. We also find that B. bacteriovorus’ slow speed mode is not merely caused by the diffusion of inviable bacteria as subsequent spiking experiments show that bacteria can be resuscitated and bimodality restored. Indeed, starved B. bacteriovorus may modulate the frequency and duration of active swimming as a means of balancing energy consumption and procurement. Our results are evidence of a nontrivial predation strategy, which contrasts with the comparatively simple search pattern of its prey, in response to environmental cues.SIGNIFICANCEBdellovibrio bacteriovorus is a predatory bacterium that is poised to help control gram-negative bacterial populations in environmental and clinical settings. In order to locate its prey in solution, B. bacteriovorus must expend energy in order to fight hydrodynamic drag. This raises the question as to how B. bacteriovorus should expend its energy reserves in the absence of chemical cues from its prey. Here, we show that B. bacteriovorus adapts its motility to minimize energy expenditure (due to fighting drag in swimming) upon prolonged starvation by exploiting two modes of motility. This is in sharp contrast to its prey, E. coli, which shows little active motility under starvation conditions.

Determining the inherent reaction-diffusion properties of actin-binding proteins in cells by incorporating genetic engineering to FRAP-based framework

Proteins in cells undergo repeated association to other molecules, thereby reducing the apparent extent of their intracellular diffusion. While much effort has been made to analytically decouple these combined effects of pure diffusion and chemical reaction, it is difficult to attribute the measured quantities to the nature of specific domains of the probed proteins particularly if, as is often the case, the protein has multiple domains to independently interact with the same types but different molecules. Motivated by the common goal in cell signaling research aimed at identifying the protein domains responsible for particular intermolecular interactions, here we describe a new approach to determining the domain-level reaction and pure diffusion properties. To validate this methodology, we apply it to transgelin-2, an actin-binding protein whose intracellular dynamics remains elusive. We develop a fluorescence recovery after photobleaching (FRAP)-based framework, in which comprehensive combinations of domain-deletion mutants are created with genetic engineering, and the difference among the mutants in FRAP response is analyzed. We demonstrate that transgelin-2 in cells interacts with F-actin via two separate domains, and the chemical equilibrium constant of the interaction is determined at the individual domain levels. Its pure diffusion properties independent of the association to F-actin is also obtained. This approach requires some effort to construct the mutants, but instead enables in situ domain-level determination of the physicochemical properties, which will be useful, as specifically shown here for transgelin-2, in addressing the signaling mechanism of cellular proteins.

Numerical Evaluation of Liquid Mixing in a Serpentine Square Convergent-divergent Passive Micromixer

Micromixers are crucial components to carry out chemical, biomedical and bio-chemical analyses on µTAS (micro total analysis system) or Lab-on-chips. Simple planar type passive mixers are always most desirable over three dimensional or complex geometries of passive mixers or active mixers as they are less expensive, easy to fabricate, and easy to integrate into complex miniaturized systems. However, at very low Reynolds numbers (0 to 100), due to the inherent laminar nature of the microfluidic flows, mixing remains challenging in passive mixers. Previous studies reported that serpentine square-wave micromixer is one of the simple and effective passive device for micromixing. In the present study, to further enhance the mixing efficiency of the device, horizontal straight portions of serpentine square wave mixer are replaced with convergent-divergent passages and the mixing performance of both mixers are evaluated in the Re range of 0 to 100. It is observed in the low Re (0 to 10), mixing in the square wave mixer with convergent-divergent portions (SQW-CD mixer) is governed completely by pure diffusion as in the case of square wave mixer with straight horizontal portions (SQW mixer). However, at high Re (Re > 10), the presence of convergent-divergent portions in the SQW-CD mixer considerably intensify the stretching and folding of samples in the mixing channel. Additionally, the extra recess available at the bends of SQW-CD mixer creates recirculation zones in the mixer. Therefore, a significant improvement in the mixing performance is achieved at high Re (Re > 10) for SQW-CD mixer as compared to conventional SQW mixer. This would allow shorter mixing lengths for SQW-CD mixer as compared to Sq wave mixer. However, with increase in Re, the rise in pressure drop is considerably high for SQW-CD mixer as compared to SQW mixer.