Effective Rheology of Bubbles Moving in a Capillary Tube

We calculate the average volumetric flux versus pressure drop of bubbles moving in a single capillary tube with varying diameter, finding a square-root relation from mapping the flow equations onto that of a driven overdamped pendulum. The calculation is based on a derivation of the equation of motion of a bubble train from considering the capillary forces and the entropy production associated with the viscous flow. We also calculate the configurational probability of the positions of the bubbles.Comment: 4 pages, 1 figur

Outcomes after perioperative SARS-CoV-2 infection in patients with proximal femoral fractures: an international cohort study

Objectives Studies have demonstrated high rates of mortality in people with proximal femoral fracture and SARS-CoV-2, but there is limited published data on the factors that influence mortality for clinicians to make informed treatment decisions. This study aims to report the 30-day mortality associated with perioperative infection of patients undergoing surgery for proximal femoral fractures and to examine the factors that influence mortality in a multivariate analysis. Setting Prospective, international, multicentre, observational cohort study. Participants Patients undergoing any operation for a proximal femoral fracture from 1 February to 30 April 2020 and with perioperative SARS-CoV-2 infection (either 7 days prior or 30-day postoperative). Primary outcome 30-day mortality. Multivariate modelling was performed to identify factors associated with 30-day mortality. Results This study reports included 1063 patients from 174 hospitals in 19 countries. Overall 30-day mortality was 29.4% (313/1063). In an adjusted model, 30-day mortality was associated with male gender (OR 2.29, 95% CI 1.68 to 3.13, p80 years (OR 1.60, 95% CI 1.1 to 2.31, p=0.013), preoperative diagnosis of dementia (OR 1.57, 95% CI 1.15 to 2.16, p=0.005), kidney disease (OR 1.73, 95% CI 1.18 to 2.55, p=0.005) and congestive heart failure (OR 1.62, 95% CI 1.06 to 2.48, p=0.025). Mortality at 30 days was lower in patients with a preoperative diagnosis of SARS-CoV-2 (OR 0.6, 95% CI 0.6 (0.42 to 0.85), p=0.004). There was no difference in mortality in patients with an increase to delay in surgery (p=0.220) or type of anaesthetic given (p=0.787). Conclusions Patients undergoing surgery for a proximal femoral fracture with a perioperative infection of SARS-CoV-2 have a high rate of mortality. This study would support the need for providing these patients with individualised medical and anaesthetic care, including medical optimisation before theatre. Careful preoperative counselling is needed for those with a proximal femoral fracture and SARS-CoV-2, especially those in the highest risk groups. Trial registration number NCT0432364