Method and system for forming a liquid mixture

A system for forming a liquid mixture comprising:

• a first mixing tank having a continuously curved upper wall and a lower wall having a central axis and a perimeter that joins a lower end of the upper wall to define a tank interior, the lower wall comprising a continuously curved surface tapering inward from the upper wall along the perimeter;
• a pump having a pump intake and pump discharge for pumping liquids of the system at selected flow rates;
• a tank inlet in fluid communication with the pump discharge for introducing a liquid stream comprising at least a first liquid from the pump discharge into the tank interior, the tank inlet configured to cause the liquid stream from the pump discharge to be directed at a first selected flow rate towards the upper wall of the first mixing tank to create a swirling liquid flow within the tank interior so that the swirling liquid forms a liquid vortex having a vortex core that is substantially free of liquid for at least a portion of the height of the mixing tank;
• at least one tank outlet opening formed in the lower wall, at least a portion of the opening being an offset portion that is positioned to one side of the central axis of the lower wall, the tank outlet opening having an upstream edge and a downstream edge relative to the swirling liquid flow that is circumferentially spaced from the upstream edge, the downstream edge extending along a line that is oriented at an angle from −45° to 45° relative to a line that extends along the upstream edge, the geometric center of the offset portion of the opening being spaced a distance L1 from the perimeter that is from >0 to 0.99 times the length of a radial line L2 extending from the perimeter across the geometric center of the offset portion to the central axis of the lower wall, and wherein a radial outermost point of the offset portion of the opening is spaced a distance L3 from the perimeter of the lower tank wall, as measured along a radial line having a length L4 that extends from the perimeter through the outermost point of the offset portion to the central axis, the distance L3 being from 0 to 0.9 times L4, for withdrawing a portion of the swirling liquid within the tank interior, the tank outlet opening being in fluid communication with the pump intake of the pump for circulating the withdrawn portion as all or a part of the liquid stream introduced into the tank inlet;
• and
• a second material inlet in communication with at least one of the tank interior, the pump intake, and the pump discharge so that a second material can be introduced and mixed with the first liquid in the swirling liquid flow within the tank interior to form a liquid mixture comprising the first liquid and second material.