Dynamics of Fattening and Thinning 2D Sessile Droplets

We investigate the dynamics of a droplet on a planar substrate as the droplet volume changes dynamically due to liquid being pumped in or out through a pore. We adopt a diffuse-interface formulation which is appropriately modified to account for a localized inflow-outflow boundary condition (the pore) at the bottom of the droplet, hence allowing to dynamically control its volume, as the droplet moves on a flat substrate with a periodic chemical pattern. We find that the droplet undergoes a stick-slip motion as the volume is increased (fattening droplet) which can be monitored by tracking the droplet contact points. If we then switch over to outflow conditions (thinning droplet), the droplet follows a different path (i.e., the distance of the droplet midpoint from the pore location evolves differently), giving rise to a hysteretic behavior. By means of geometrical arguments, we are able to theoretically construct the full bifurcation diagram of the droplet equilibria (positions and droplet shapes) as the droplet volume is changed, finding excellent agreement with time-dependent computations of our diffuse-interface model.

Density functional study of condensation in capped capillaries

We study liquid adsorption in narrow rectangular capped capillaries formed by capping two parallel planar walls (a slit pore) with a third wall orthogonal to the two planar walls. The most important transition in confined fluids is arguably condensation, where the pore becomes filled with the liquid phase which is metastable in the bulk. Depending on the temperature T, the condensation in capped capillaries can be first-order (at T≤Tcw) or continuous (at T>Tcw), where Tcw is the capillary wetting temperature. At T>Tcw, the capping wall can adsorb mesoscopic amounts of metastable under-condensed liquid. The onset of condensation is then manifested by the continuous unbinding of the interface between the liquid adsorbed on the capping wall and the gas filling the rest of the capillary volume. In wide capped capillaries there may be a remnant of wedge filling transition, which is manifested by the adsorption of liquid drops in the corners. Our classical statistical mechanical treatment predicts a possibility of three-phase coexistence between gas, corner drops and liquid slabs adsorbed on the capping wall. In sufficiently wide capillaries we find that thick prewetting films of finite length may be nucleated at the capping wall below the boundary of the prewetting transition. Prewetting then proceeds in a continuous manner manifested by the unbinding interface between the thick and thin films adsorbed on the side walls. Our analysis is based on a detailed numerical investigation of the density functional theory for the fluid equilibria for a number of illustrative case studies.

Unification of dynamic density functional theory for colloidal fluids to include inertia and hydrodynamic interactions: derivation and numerical experiments

Starting from the Kramers equation for the phase-space dynamics of the N-body probability distribution, we derive a dynamical density functional theory (DDFT) for colloidal fluids including the effects of inertia and hydrodynamic interactions (HI). We compare the resulting theory to extensive Langevin dynamics simulations for both hard rod systems and three-dimensional hard sphere systems with radially symmetric external potentials. As well as demonstrating the accuracy of the new DDFT, by comparing with previous DDFTs which neglect inertia, HI, or both, we also scrutinize the significance of including these effects. Close to local equilibrium we derive a continuum equation from the microscopic dynamics which is a generalized Navier-Stokes-like equation with additional non-local terms governing the effects of HI. For the overdamped limit we recover analogues of existing configuration-space DDFTs but with a novel diffusion tensor.

In situ arthrodesis with lateral-wall ostectomy for the sequelae of fracture of the os calcis

Distraction bone-block arthrodesis has been advocated for the treatment of the late sequelae of fracture of the os calcis. Between 1997 and 2003 we studied a consecutive series of 17 patients who had in situ arthrodesis for subtalar arthritis after fracture of the os calcis with marked loss of talocalcaneal height. None had undergone any previous attempts at reconstruction. We assessed the range of dorsiflexion and plantar flexion and measured the talocalcaneal height, talocalcaneal angle and talar declination angle on standing lateral radiographs, comparing them with the normal foot. The mean follow-up was for 78.7 months (48 to 94). The mean American Orthopaedic Foot and Ankle Society hindfoot score improved from 29.8 (13 to 48) to 77.8 (48 to 94) (Student's t-test, p < 0.001). The mean loss of talocalcaneal height was 10.3 mm (2 to 17) and the mean talar declination angle was 6.7 degrees (0 degrees to 16 degrees) which was 36% of the normal side. One patient suffered anterior ankle pain but none had anterior impingement. Two patients complained of difficulty in ascending slopes and stairs and four in descending. The mean ankle dorsiflexion on the arthrodesed side was 11.6 degrees (0 degrees to 24 degrees) compared with 14.7 degrees (0 degrees to 24 degrees) on the normal side, representing a reduction of 21.1%. The mean plantar flexion on the arthrodesed side was 35.5 degrees (24 degrees to 60 degrees) compared with 44.6 degrees (30 degrees to 60 degrees ) on the normal side, a reduction of 20.4%. These results suggest that anterior impingement need not to be a significant problem after subtalar arthrodesis for fracture of the os calcis, even when the loss of talocalcaneal height is marked. We recommend in situ arthrodesis combined with lateral-wall ostectomy for all cases of subtalar arthritis following a fracture of the os calcis, without marked coronal deformity, regardless of the degree of talocalcaneal height loss.

Spontaneous resolution of solitary osteochondroma in the young adult

Spontaneous resolution of a solitary osteochondroma is rare. Such a case is presented in a patient nearing skeletal maturity. Based on a search of the English literature this is the first such report in a patient of this age.

The relationship between the strength of supination of the forearm and rotation of the shoulder

In children with obstetric brachial plexus palsy (OBPP) who develop an internal rotation deformity of the shoulder, release of subscapularis improves the range of external rotation of the shoulder and the strength of supination of the forearm. We studied the strength of supination in 35 healthy adult volunteers at 45 degrees of both internal and external rotation. The mean and maximum torques were greater in external than internal rotation by 8.7% and 7.5%, respectively. This was highly significant (p < 0.0001). The increased strength of supination in external rotation is probably because the maximum power of biceps, particularly the long head, may be exerted in this position. In children the difference may be even greater due to anatomical differences causing the dramatic increases in the strength of supination after surgery for OBPP. In adults our findings suggest that the supination exercises which are undertaken after injury or surgery to the forearm or wrist should be performed in external rotation.

The relationship between the strength of supination of the forearm and rotation of the shoulder

In children with obstetric brachial plexus palsy (OBPP) who develop an internal rotation deformity of the shoulder, release of subscapularis improves the range of external rotation of the shoulder and the strength of supination of the forearm. We studied the strength of supination in 35 healthy adult volunteers at 45° of both internal and external rotation.

The mean and maximum torques were greater in external than internal rotation by 8.7% and 7.5%, respectively. This was highly significant (p < 0.0001).

The increased strength of supination in external rotation is probably because the maximum power of biceps, particularly the long head, may be exerted in this position. In children the difference may be even greater due to anatomical differences causing the dramatic increases in the strength of supination after surgery for OBPP.

In adults our findings suggest that the supination exercises which are undertaken after injury or surgery to the forearm or wrist should be performed in external rotation.